spacecraft navigation and timing using x-ray pulsars_ion_navigation… · 2004-06-23 · wide...

Spacecraft Navigation and TimingUsing X-ray Pulsars

SUNEEL I. SHEIKHASTER Labs, Inc.

JOHN E. HANSONCrossTrac Engineering Inc.

PAUL H. GRAVENMicrocosm, Inc.

DARRYLL J. PINESThe University of Maryland

Received October 2010; Revised April 2011

ABSTRACT: Pulsars are unique celestial sources that produce distinctive, periodic signals. Since their discov-ery, they have been considered as potential navigation aids and timing beacons to form a reference coordinatesystem and universal time scale. Further study of these astronomical objects has shown that their pulse timingcan achieve sub-microsecond level performance, and interest and research into these sources has grown to con-ceive a fully autonomous navigation and timing system for deep space vehicles. Sources that radiate within theX-ray band of the electromagnetic spectrum have high potential for creating a practical spacecraft navigationsolution, which includes accurate time and position determination onboard a space vehicle using the preciselyperiodic sources, and precise attitude determination using both pulsating and steady sources. This paper pro-vides an overview of spacecraft navigation methods and various research and results that have evolved sincethe concept of X-ray pulsar-based navigation was first proposed.

INTRODUCTION

Recent analysis, scientific discoveries, and tech-nological developments have moved the concept ofusing variable, celestial X-ray sources as naviga-tion aids for spacecraft from an idea to a futurereality. After being theorized for many decades,spinning neutron stars were discovered in the ra-dio band in 1967 [1]. Due to their unique periodicpulses, these neutron stars are referred to as pul-sars. Subsequent observations have discovered pul-sars emitting radiation throughout the electromag-netic spectrum [2, 3]. However the X-radiationemitting sources are the most promising attitude,time, and position beacons for spacecraft opera-tions, since smaller detectors can be employedwhen compared to optical or radio-band instru-ments. Over the past 40 years, the astronomy com-munity has logged accurate time histories of theseperiodic signals, which have been crucial to thecharacterization of these sources. A particularly

intriguing aspect of a subset of these cataloguedsources is the measured inherent stability of theperiodicity of their emissions, which has beenshown to match the quality of today’s atomic clocks[4–6]. As such, pulse-timing models have beendeveloped for the stable, periodic signals fromthese sources, which can be employed as naviga-tion aids.

The baseline X-ray pulsar-based navigation, orXNAV, approach uses observations of the X-rayemissions of millisecond period pulsars. With theirwide geometric distribution in the sky and periodicradiation, pulsars appear to act as a kind of natu-ral celestial beacon, or celestial lighthouse. How-ever, as a group they conceivably act as a naturalGlobal Positioning System (GPS), or, UniversalPositioning System (UPS) on an intergalactic scale.Accurate pulse time-of-arrival estimates from mul-tiple non-coplanar sources allow simultaneousdetermination of both position and velocity autono-mously anywhere in the solar system. Accuratetime can be maintained on a spacecraft by couplingonboard high-quality clocks with the long-term sta-bility of several well-characterized pulsars, as an

NAVIGATION: Journal of The Institute of NavigationVol. 58, No. 2, Summer 2011Printed in the U.S.A.

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X-ray timing, or XTIM system. The generation of areference timescale from an ensemble of pulsars asthe pulsar timescale, or PT, is also conceivable dueto their stability and regularity [7, 8]. In addition,brighter, but less stable X-ray sources may haveutility as well, particularly in applications thatrequire only relative navigation or to determine ve-hicle attitude.

This paper provides an overview of this novelnavigation and timing technology. It provides abackground on the types of sources and their char-acteristics that make them usable for navigationpurposes, as well as the types of detectors that canbe employed to observe them. It also provides abrief history of the research pursued to define anavigation system based upon these sources. Adetailed review of proposed attitude, time, position,and velocity determination is provided, as well asa discussion on potential performance. Future mis-sion applications are presented along with theknown challenges for deploying this navigationsystem. This paper will concentrate on summariz-ing the work completed in the United States ofAmerica, although discussion of work completed inEurope and Asia is also provided.

VARIABLE CELESTIAL SOURCES

Celestial sources have proven to be significantaids for navigation throughout human history. An-cient mariners traveled vast distances across theglobe with only the stars in the sky to guide them.A majority of these sources are fixed in their emis-sions and are considered optical point sources fornavigation references. Instruments such as modernstar trackers make use of the fact that in the visi-ble band of the electromagnetic spectrum the starsin the sky are essentially constant in number andsteady in brightness. As such, optical sources havecontributed greatly to exploration. A fraction of ce-lestial sources are objects that emit radiation withvarying levels of intensity. Additionally, within theX-ray band (photon energies roughly within the0.1–100 keV band), there are effectively no steadypoint sources.

Subsets of these variable celestial sources arespinning neutron stars [2, 3]. A neutron star (NS)is the result of a massive star that has exhaustedits nuclear fuel and undergone a core-collapseresulting in a supernova explosion [9–11]. Duringtheir collapse, conservation of angular momentumspins these stars up to very high rotation rates.Newly born neutron stars typically rotate withperiods on the order of tens of milliseconds, whileolder neutron stars through energy dissipationeventually slow down to periods on the order ofseveral seconds. A unique aspect of this rotation is

that it can be extremely stable and predictable[4–6].

Neutron stars harbor immense magnetic fields.Under the influence of these strong fields, chargedparticles are accelerated along the field lines tovery high energies. Powerful beams of electromag-netic waves including X-rays are radiated out fromthe magnetic poles. If the neutron star’s spin axisis not aligned with its magnetic field axis, then anobserver will sense a pulse of electromagnetic radi-ation as the magnetic pole sweeps across theobserver’s line of sight to the star, hence thesesources are referred to as pulsars. Since their dis-covery in 1967 [1], pulsars have been found to emitthroughout the radio, infrared, visible (optical),ultraviolet, X-ray, and gamma-ray energies of theelectromagnetic spectrum. Due to their specificevolution, variability mechanisms, and geometricorientation relative to Earth, each pulse frequencyand shape provides a unique identifying signaturefor each star. A simple diagram of a pulsar show-ing its unique features is presented in Figure 1[12].

Since radio band emissions from these pulsarsare receivable on Earth’s surface, much of the as-tronomical observation of these sources has beendone in radio. X-ray emissions from these sources,however, are absorbed by Earth’s atmosphere, anduse of this wavelength is limited to space or plane-tary body applications. X-radiation observationrequires much smaller detector sizes (order of asquare meter) versus radio pulsars (requiring tensof square meters of detector area). Along with pul-sars, the X-ray sky contains several other types ofvariable objects that can be used for differentaspects of spacecraft navigation. Variable X-rayobjects employ an array of energy sources for theirX-ray emissions, and their variability is producedby either intrinsic or extrinsic mechanisms.

Many X-ray pulsars are rotation-powered pul-sars (RPSRs). The energy source of this class ofneutron stars is the stored rotational kineticenergy of the star itself. The X-ray pulsationsoccur due to two types of mechanisms, either mag-netospheric or thermal emissions [13]. The bettertiming sources are the rotation-powered millisec-ond period pulsars (MSPs), and by far the bright-est of these sources is the Crab Pulsar (PSRB0531þ21) [14]. Unfortunately, young bright sour-ces like the Crab tend to have relatively poor tim-ing stability, whereas the best timing sources tendto be orders of magnitude dimmer. A subset ofthese rotation-powered pulsars is known asrecycled MSPs, which are highly stable rotors withmuch lower dissipation rates than normal MSPs.

Accretion-powered pulsars (APSRs) are neutronstars in binary systems, where stellar material isbeing transferred from a companion star onto the

166 Navigation Summer 2011

neutron star. This flow of material is channeled bythe magnetic field of the neutron star towards itspoles, which creates hot spots on the star’s surface.The pulsations are a result of the changing view-ing angle of these hot spots as the neutron starrotates. Accretion powered pulsars generate X-raysdue to the gravitational acceleration of the mate-rial from an accretion disk, which can reach rela-tivistic velocities as the material approaches thesurface of the star. They tend to be brighter butless stable due to the unsteadiness of the accretionprocess, sometimes fading in and out due to the ec-centricity of the companion’s orbit [15, 16]. Twotypes of APSRs are frequently catalogued basedupon the mass of the orbiting companion of the

neutron star, either a high-mass X-ray binary sys-tem (HMXB), where the companion object is typi-cally 10–30 solar masses in size, or a low-mass X-ray binary system (LMXB), where the companionstar is perhaps the size of less than one solar mass[13, 15]. Although they possess complicated pulsetiming models due to their binary system dynam-ics, and many are transient sources with unpre-dictable durations of low signal intensity, thesetypes of pulsars also have characteristics conduciveto navigation.

Figure 2 provides an image of X-ray stars on theGalactic sphere in Galactic Longitude and Latitudecoordinates [12, 17]. Many X-ray sources are foundin binary systems and a majority of the detectedsources are located in our Milky Way galaxy. Thisimage shows the concentration of sources locatedalong the Galactic plane and near the Galactic cen-ter, however, a sufficient number of sources fornavigation are distributed off plane. The diffuseX-ray background is an appreciably strong signalthat is observed when viewing the X-ray sky, andmeasures of this background radiation must beconsidered when observing a source [13].

Although pulsars have good visibility and detect-ability near Earth and throughout the solar sys-tem, they are extremely distant objects. Thus,unlike Earth satellite ranging systems, the abso-lute distances of these sources cannot be directlymeasured. Instead, once the initial location of thespacecraft is established, phase tracking of the pul-sar signal must be used continuously to updateestimated position. This is analogous to carrierphase tracking techniques that have become wellestablished with Global Navigation Satellite Sys-tem (GNSS) applications.

Fig. 1–Neutron star with rotation and magnetic axes [12]

Fig. 2–Catalogued X-ray sources in Galactic longitude and latitude. The size of the marker indi-cates the relative magnitude of the source’s flux in a logarithmic scale. [12]

Vol. 58, No. 2 Sheikh et al.: Spacecraft Navigation and Timing Using X-ray Pulsars 167

Aperiodic Sources

In addition to the stable periodic sources, theuse of unstable, but bright and highly variableX-ray sources can be utilized for cooperative obser-vations between multiple spacecraft. The keysource types are active galactic nuclei (AGN), cata-clysmic variables (CV), supernova remnants, X-raybinaries, X-ray galaxy clusters, and stellar coronal.Nearly all of the bright X-ray point sources in thesky are X-ray binaries containing a compact object(neutron star or black hole) accreting materialfrom a stellar companion. The accretion process ishighly unstable and many of these sources exhibitpronounced variability over a broad range of fre-quency scales up to about 1000 Hz. This variabilitycan take the form of red noise, broadband noise,shot noise, periodicities, and quasi-periodic oscilla-tions (QPOs). A catalogue of bright X-ray sourcesis based on the continuous monitoring of the X-raysky with the All-Sky Monitor (ASM) instrumentaboard the Rossi Timing Explorer (RXTE) [18].

In addition to the short timescale variability,many of these sources exhibit transient behavior,when a source that normally is extremely faintbrightens by a factor of 1000 or more [19]. Thetransient outbursts in these sources can last fromhours to years, with most outbursts lasting one toseveral months. The recurrence times of these out-bursts vary from a year to decades, or longer [19].

The Pulse Profile

At X-ray energy wavelengths, the primary meas-urable values of the received signal from a sourceare the individual high-energy photons emitted bythe source. The rate of arrival of these photons canbe measured in terms of flux of radiation, or num-ber of photons per unit area per unit time. Toobserve a source, an X-ray detector is initiallyaligned along the line of sight to the chosen source.Once photon events from this source are positivelyidentified, components within the detector systemrecord the time of arrival of each individual X-rayphoton to high precision with respect to the sys-tem’s clock. During the total observation time of aspecific source, a large number of photons willhave each of their arrival times recorded. Themeasured individual photon arrival times mustthen be converted from the detector’s system clockto their coordinate time in an inertial frame. Thisconversion provides an alignment of the photon’sarrival time into a frame that is not moving withrespect to the observed source [20, 21].

The profile of each pulse from an X-ray source is arepresentation of the characteristics of the pulse.Pulse profiles vary in terms of shape, size, cyclelength, and intensities. Some sources produce sharp,

impulsive, high intensity profiles, while others pro-duce sinusoidal, elongated profiles. Although manysources produce a single, identifiable pulse, otherpulse profiles contain sub-pulses, that are evidentwithin the signal [2, 3].

This process of assembling all the measured pho-ton events into a pulse profile is referred to asepoch folding, or averaging synchronously all thephoton events with the expected pulse period ofthe source. An ensemble of these folded photonscreates well-defined pulse shapes. For X-ray obser-vations that record individual photon events, Pois-son counting statistics typically dominate the ran-dom noise in pulse time-of-arrival (TOA) compu-tation. Thus there will be a large amount ofvariability in the observed light curve simply dueto counting statistics. The time shift necessary toalign the peaks within the observed profile and astandard pulse template is added to the start timeof the observation to produce the absolute TOA ofthe pulse for a particular observation. An estimateof the accuracy of the TOA measurement can becomputed as an outcome of this comparison pro-cess. This estimate provides an assessment on thequality of the TOA measurement, and can be use-ful in the navigation algorithms [20]. Figure 3shows a standard pulse template for the Crab pul-sar in the X-ray band (1–15 keV) created usingmultiple observations with the Naval ResearchLaboratory’s Unconventional Stellar Aspect (USA)experiment onboard the ARGOS vehicle [22].

Four of the fundamental classes of pulse TOAmeasurement processing techniques are summar-ized in Table 1. These approaches outline the vari-ous methods that can be used to process the indi-vidual pulsar photon data, either in a batch (large

Fig. 3–Crab pulsar standard pulse template. The period is about33.5 milliseconds. Two pulse cycles are shown for clarity, witheach cycle containing one sharp main pulse and a smaller sec-ondary inter-pulse with lower intensity amplitude


single set) process, or a continuous mode wheredata is processed as soon as it is made available. Afurther distinction can be made between algorithmsthat use binned photon data, where the data arerepresented by the number of photons arriving infixed duration time bins, versus single event proc-essing algorithms that use a series of time-taggedphoton events to provide pulse TOA updates,thereby using all available data to create the TOAestimate. This can be compared to the aforemen-tioned binned approaches, which essentially trun-cate all photons’ times-of-arrival in the binning pro-cess, thereby ignoring useful information.

Pulse timing is required to adequately character-ize each source’s unique characteristics such as spinperiod, companion orbit elements, and a star’s evo-lutionary stage [2, 3]. A timing model is constructedby fitting data obtained over the entire observatio-nal history of a particular source, accounting for ev-ery pulse of the source. These models predict whenspecific pulses from the sources will arrive withinthe solar system. It is precisely this predictablebehavior that allows pulsars to be considered asnavigation beacons. Previous pulse timing methodshave created binned pulse profiles through extendedobservations of a specific source and folding the fullobserved signal with the expected pulse period ofthe source [20]. These methods compute theobserved pulse TOA by correlating an observedpulse profile with a high signal-to-noise ratio (SNR)profile template.

Pulse timing models are often represented as thetotal accumulated phase of the source’s signal as afunction of time. A starting cycle number, F0 ¼F(t0), can be arbitrarily assigned to the pulse thatarrives at a fiducial time, t0, and a reference loca-tion, often selected as the solar system barycenter(SSB); all subsequent pulses can be numberedincrementally from this first pulse. The totalphase, F, can be modeled as the sum of the frac-tional portion of the pulse period, /, and the totalnumber of integer cycles, N. Thus, total phase isexpressed as a function of time as,

U tð Þ ¼ / tð Þ þN tð Þ (1)

This model may also be expressed as a functionof angular phase, Y ¼ 2pF. Using the determinedpulse frequency, f, and its derivatives, the totalphase can be specified using a pulsar phase modelof,

U tð Þ ¼ U t0ð Þ þ f t� t0½ � þ_f

2t� t0½ �2þ

€f

6t� t0½ �3 (2)

Eq. (2) is known as the pulsar spin equation, orpulsar spin down law [2, 3]. In this equation, theobservation time, t, is the coordinate time of ar-rival of the signal phase and t0 is the chosen refer-ence epoch for the model parameters [3, 21].

The model in Eq. (2) utilizes frequency and twoof its derivatives; however, any number of deriva-

Table 1—Pulse TOA Measurement Techniques

Batch Processing Continuous Processing

Binned Photons � Traditional astronomy approach � Similar to communications approach� Photons collected into finite size bins � Photons collected into finite size bins� Many pulses folded together and known

profile fit to data to estimate TOA� Pulsar signal extracted from noisy

background with phase-locked loops (PLL)or digital PLL� 104 sec or more between measurements

� Good single TOA solution � Continuous measurements� Information lost in binning photons � PLL loop filter limits bandwidth of

measurements to 10 mHz or less� No information available to updateposition between measurements � Information lost in binning photons� Reference: [23] � Reference: [24]

Time-TaggedPhotons

� E.g. Maximum Likelihood Estimation � Single photon processing� Individual photons time-tagged � Individual photons time-tagged� TOA estimated from entire photon

history� Position/time estimate updated at each

photon or small batch of photons based onindividual photon times� 104 sec or more between measurements

� Best possible single TOA solution� No information lost in time tagging

photons

� Continuous measurements

� No information available to updateposition between measurements

� Good single TOA solution

� Large processing burden

� Maximum use of photon time information

� Reference: [25]

� Reference: [26]


tives may be required to accurately model a partic-ular pulsar’s timing behavior. Additional requiredparameters include the angular coordinates of thesource (e.g., right ascension and declination andsometimes proper motion and parallax), orbitalparameters for pulsars in binary systems, and dis-persion measure (the column density of free elec-trons) for sources with timing measurements madein the radio band. Precise external informationis also required to complete an accurate timingmeasurement, such as Earth and celestial refer-ence frames, planetary ephemerides, and coordi-nate time scales. Each observation must accuratelytime the pulse signal with respect to an inertialcoordinate system and time, effectively removingthe dynamic motion of the observation station andthe higher-order relativistic effects on the electro-magnetic signal within the solar system [2, 3, 20,27–29]. If the removal of motion and higher ordercontributions were done improperly, a smearingeffect would be present within the observed pulseprofile, and the uncertainty of the measured pulseTOA would increase. While the location and orien-tation of the coordinate system is not critical, it isimportant that the pulse timing models of all pul-sars used as navigation beacons use the same ref-erence frame.

To investigate pulsar source characteristics,accuracies on the order of 1 ls or better are oftendesired, and a number of sources are timed at thislevel or better [30, 31]. For spacecraft navigation,a desired accuracy of pulse arrival time on theorder of 1 ns (�0.3 m) would allow significantlyincreased position and velocity solution accuracy.Thus, any errors within the analytical timingexpressions or pulse timing models must be on theorder of these uncertainties [21]. The data of thecharacteristics of several well-studied pulsars hasbeen presented in past publications [12, 23, 32].Nearly all of the useful X-ray pulsars are alsobright radio pulsars and are routinely timed aspart of long-term pulsar timing studies with largeground-based radio telescopes, which will contrib-ute significantly to XNAV’s future success.

As select sources have had extended observa-tions over many years, long-term data analysis hasverified that the spin rates are extremely stable forsome of these sources and compare well to the sta-bility of current day atomic clocks [5, 6]. Unfortu-nately, many of the pulsars that provide the moststable long-term timing models tend to be lessbright, and conversely, the brightest sources tendto be less stable. Less stable sources can also beutilized, but they will require more frequentephemeris and pulse model updates and couldresult in a lower performance system.

The key parameter for determining stability isthe timing residuals, differences between the

measured TOA and the best pulsar-timing model.These residuals can be used to create the squareroot of a third-order Allan variance, rz(t), which isa measure of pulsar and atomic clock stability [6].It has been shown that the stability of two pulsars,B1855þ09 and B1937þ21, detected in the radioband and measured over a range of data lengthsup to decades is comparable to that of terrestrialatomic time standards [5]. In this work, thesesources have been shown to reach values of rz(t) ¼10213.2 and 10214.1, respectively, for a data setlength of one year. Figure 4 shows a comparison ofPSRs B1937þ21, B1855þ09, and J0437-4715 withseveral atomic clocks.

X-ray Navigation and Timing Instruments

The instrument for X-ray navigation and timingwill consist of three primary components: a colli-mator or imaging system to select the pulsar to beobserved; a detector and time tagging system tomeasure the arrival times of the photons; and,processing electronics and algorithms to turn thephoton time histories into position and/or timemeasurements. The design of the instrument willdepend on the mission of the spacecraft. Some mayrequire the instrument to be on a gimbal to allowthe instrument to track pulsars serially, whileother missions may require multiple detectors totrack them simultaneously. Other missions mayuse a single fixed instrument and slew the space-craft to track the pulsar during an observation.The instrument system design to optimize thedetectability of these sources depends on theenergy spectrum of the emitted X-rays. The mag-netospheric emitting sources have very narrowpulse profiles and much harder X-ray emission andare best detected in the 2–10 keV medium-energyX-ray band, while the thermal emission sourcestend to be intrinsically fainter and have broaderpulse widths and are best detected in the 0.5–2 keV soft X-ray band.

Various types of detectors have been used inX-ray astronomy missions depending on the type ofapplication of timing or imaging, such as gas pro-portional counters with collimators, microchannelplates, charge-coupled device semiconductors, scin-tillators, or focusing optics with small solid statedetectors [34]. The instruments used on the previ-ous 40 years of X-ray astronomy science missions,while extremely capable, were optimized for theneeds of science and not for those of an operationalXNAV system. In particular, gas proportional coun-ters with their pressure regulation systems andlifetime limiting expendable gas are not suitablefor a long-term XNAV system. The use of collima-tors to limit the instrument field-of-view has beendemonstrated on several missions (HEAO-1, USA),


as have coded aperture masks (HETE-II) and graz-ing incidence mirrors (Chandra, RXTE). Selectionof the detector, optimized for the energy profilesof select pulsars, will be a key determinant inthe overall performance of the system. Solid-statedetectors with their sensitivity maximized inthe medium (2-10 keV) energy band are likely can-didates.

BRIEF HISTORY OF PAST RESEARCH

The principal scientific and technical advancesthat make the X-ray-based approach feasible havecome about fairly recently. These include the char-acterization of sufficient numbers of highly stableX-ray pulsar sources using several recent scientificspacecraft (RXTE, USA, ASCA, Chandra, ROSAT,XMM, and others) to provide the basis for a timingsystem and the development of new X-ray detectortechnology with high time resolution of recordedevents.

Technologies for exploiting celestial observationshave improved tremendously over millennia, but itwas not until the 1970s that terrestrial observa-tions of radio pulsars suggested a fundamentallynew type of measurement might be possible basedon stable celestial timing signals from pulsars.A broad scope of navigation methods has been pro-posed to make use of variable sources that emit atradio or X-ray band wavelengths [12, 17, 22, 24,32, 35, 36]. Much of this past navigation researchhas concentrated on using rotation-powered pul-sars. Provided in Table 2 are some of the keyevents regarding navigational use of these sources.In addition to those listed, numerous conferenceand journal articles published by researchers inthe United States, Europe, Russia, and China haveelaborated further on various aspects on the con-

cepts. Many of these engineering researchers,along with all the astronomical observations andastrophysical discoveries, have contributed greatlyto the overall understanding of methods and tech-niques, and with these continued worldwideresearch efforts it is likely that this technology willyield useful capabilities.

X-RAY SOURCE NAVIGATION CONCEPTS

The navigation solutions proposed here arederived from X-radiation photon detection. An en-semble of many detected photons, formed eitherinto images or average pulse profiles, can be usedto compute directional (in the case of imaging) ortiming (in the case of pulse profiles) information.Full three-dimensional (3-D) solutions are achieva-ble from variable celestial sources, including vehi-cle attitude determination, position, and velocitydetermination, and clock corrections for maintain-ing accurate time. It is this potential of the fullsuite of onboard navigation solutions from theseperiodic sources that is currently driving the inter-est and research into their capabilities.

By measuring the pulse TOA from each source,this data can be related to a range measurementin order to update or compute 3-D position and ve-locity solutions. As most current X-ray telescopeand detector designs can observe only a singlesource along one point on the celestial sphere, nav-igation concepts that utilize single axis ranging in-formation have shown that accurate orbit solutionscan be achieved [12, 32]. Extensions to this singlemeasurement have also been pursued, includingapproaches similar to GNSS, where multiple vari-able sources are used to compute full 3-D positionsolutions [23, 42, 46]. These methods use laterationconcepts to estimate the range from an inertial ori-

Fig. 4–Comparison of selected pulsars and atomic clocks [5, 6, 33]


gin along multiple axes. As eventual detector sys-tems may be produced that will monitor the wholesky, simultaneous observations of multiple sourcesignals from different directions allow this conceptto produce full 3-D solutions. Spacecraft that haveaccurate clocks onboard can track these signalsover time to maintain full dynamic trajectory solu-tions. It has been considered to extend this conceptand use the stable, periodic signals from thesesources to produce accurate time as well as vehicleposition, allowing complete navigation solutionswith reduced needs for an on-board, ultra-stableclock.

It is important to time pulsar observations withinan inertial reference frame that is stationary (atrest) with respect to the pulsar’s frame. This isdone in part so that all subsequent observationscan be directly compared to the model, and anyeffects of an observer in a rotating frame areremoved. Since an observer’s frame will most likelybe in motion with respect to the inertial frame, asan observer on Earth or on a spacecraft in orbit,and the observer will experience a different gravita-tional potential than a reference clock, the observerclock’s measured proper-time must be converted tocoordinate time in order to compare the result toother clocks. Standard methods provide conversionsfrom the observer’s proper time to coordinate timebased upon the observer’s clock motion and experi-enced gravitation potential [47–51].

For many pulsar observations, the commonframe utilized as the SSB coordinate frame is theInternational Celestial Reference Frame (ICRF)whose axes are aligned with the equator and theequinox of epoch J2000 [52]. The reference timescale for these observations for variable t in Eqs.(1) and (2) is the Temps Coordonnee Barycentrique(TCB, Barycentric Coordinate Time), although theslightly different time scale of the Temps Dynami-que Barycentrique (TDB, Barycentric DynamicTime) has also been utilized [52]. These pulse-tim-ing models are often described to be valid at theorigin of the SSB frame. In order to compare ameasured pulse arrival time at a remote observa-tion station with the predicted time at the SSB ori-gin, the station must project arrival times of pho-tons by its detector onto the SSB origin. This com-parison requires that time be transferred from theobservation station, or spacecraft, to the SSB. Theequations from this theory relate the emissiontime of photons that emanate from a source totheir arrival time at a station, and define the pathof the photons traveling through curved spacetime[27–29, 37–40].

Along with a well-defined pulsar pulse-timingmodel, providing pulse period and higher orderderivatives, additional characteristics are requiredfor use by the navigation algorithms. These includepulsar unit line of sight direction or apparent posi-tion, often represented as Right Ascension and

Table 2—Key Events Contributing Towards X-ray Navigation Advancement

� 1967: Bell J., Hewish A. et al., Successful discovery of radio pulsar [1]� 1974: Downs, G.S. of NASA JPL, Outlines concepts of interplanetary navigation using pulsating radio sources [35]� 1977: Manchester, & Taylor J., Initial detailed text describing pulsars [2]� 1981: Chester & Butman of NASA JPL, Introduces navigation using X-ray pulsars [36]� 1981–1983: Richter, G.W. & Matzner, R.A., Relativistic corrections for photon time of arrival [37–40]� 1988: Wallace K., Presents use of radio stars for navigational systems [41]� 1988: The NRL USA experiment proposed [22]

- Operated onboard ARGOS from May 1999–Nov 2000- Investigated attitude, position, timekeeping� 1996: Hanson, J.E., Stanford University Ph.D. dissertation ‘‘Principles of X-ray Navigation’’ [24]� 1997: Matsakis, D., et al., Develops new statistic for pulsar and clock statistics [6]� 2004: ESA Advanced Concepts Team ARIADNA, Pulsar navigation study [42]� 2005: Sheikh, S.I., University of Maryland Ph.D. dissertation ‘‘The Use of Variable X-ray Sources for Spacecraft

Navigation’’ [12]� 2005: Woodfork, D. W., Air Force Institute of Technology Master’s thesis ‘‘The Use of X-ray Pulsars for Aiding GPS

Satellite Orbit Determination’’ [43]� 2005–2006: Defense Advanced Research Projects Agency (DARPA) XNAV Phase I Program

- Source characterizations, detector development, navigation algorithms- Demonstration system architecture (planned for ISS flight)- Did not proceed to Phase II flight demonstration development� 2006–2011: Multiple NASA SBIR contracts on topic, including augmentation with Deep Space Network

- Studying potential NASA applications of X-ray navigation� 2006–2008: Rodin A., Concepts on developing ensemble of pulsars signals for new timescale [44]� 2009: Emadzadeh, A.A., University of California Ph.D. dissertation ‘‘Relative Navigation Between Two Spacecraft

Using X-ray Pulsars’’ [45]� 2009–2010: DARPA XTIM Seedling program

- Study use of pulsars for time transfer and investigate future demo scenarios


Declination of the source, distance, and proper-motion; X-ray photon flux rate from the source, of-ten measured in photon counts per unit area perunit time; pulsed fraction, the ratio of pulsed pho-tons to total source photons received; pulse profile,or flux variation as a function of time or phasecycle; and, any known transient, flaring, or burst-ing aspects of the source. Many techniques use thesource direction information within their equa-tions, thus any unknown errors in this term reducethe performance of the overall solutions. In orderto have a negligible effect within the solar system,coordinate position accuracies on the order of0.0005 lrad are required to approximately provideone km of spacecraft range accuracy. Fortunately,well-timed pulsars have sufficiently accurate posi-tion knowledge as part of their timing analysis.However, since their position accuracy is connectedto their timing accuracy, or timing noise, otherinteresting potential pulsars do not have this qual-ity of position accuracy. Other techniques, such astheir closeness to optical partners, must beemployed to help improve the positional accuraciesof these lesser-studied sources.

Just as it is important to monitor and cataloguethe defining characteristics of optical stars for on-Earth navigation and spacecraft attitude determi-nation, in order for an eventual XNAV system tooperate with high efficiency and accuracy, it will benecessary to continuously monitor, catalogue, anddisseminate the information of existing and per-haps newly detected sources at regular intervals tospacecraft that rely on this information. In addi-tion to ground-based radio source timing and char-acterization, it is envisioned that an orbiting X-rayobservatory, serving as both an astrophysics sci-ence research instrument and a navigation basestation would be required for long term X-ray navi-gation operations. Existing X-ray astrophysics mis-sions can tentatively serve this function, such asRXTE [53] and XMM-Newton. However, a dedi-cated X-ray observatory that can communicate thiscritical pulsar almanac information would functionmore optimally for operational applications.

The XNAV navigation processing can be sepa-rated into the three general areas: attitude deter-mination, time correction, and position and velocitydetermination. The following sections describe thefurther details of the techniques for solutions usingX-ray celestial sources. Methods of evaluating theperformance of these navigation solutions are pre-sented as well as a review and summary of poten-tial applications for this new technology.

Attitude Determination

X-ray emitting sources can be used as an atti-tude reference for resolving spacecraft orientation

as well as navigation and timing beacons [22, 24].Thus, the XNAV concept offers the potential for asingle instrument to provide attitude, time, posi-tion, and velocity information to its host space-craft. The operation and algorithms of an X-raysource-based attitude sensor is similar to that of atraditional optical star camera [54]. A camera com-prised of a pixel array of detectors, when combinedwith a coded aperture mask or set of grazing inci-dence mirrors, that images sets of X-ray sourcescould determine the camera’s orientation bymatching multiple source patterns in the field ofview or identifying a unique source. Alternatively,large single pixel cameras or trackers could usethe source flux to determine spacecraft spin or ori-entation based upon a pattern of detected X-raysources. However, an X-ray star camera offersseveral other advantages over traditional opticalcameras:

• The diffraction limited angular resolution ofan X-ray star camera is much finer than a tra-ditional star camera of similar size due to theextremely short wavelengths of X-rays whencompared to visible or UV wavelengths. Thiscan lead to either a much higher performancestar camera (sub-arcsecond accuracies), or amuch smaller camera in a similar form-factor.

• The sensors used in an X-ray star camera areinherently radiation hardened due to their rel-atively large feature sizes, making them usefulon missions in high radiation environments,including national security missions and mis-sions to the outer planets.

• X-ray star cameras are robust against opticalblinding by Sun, Moon and Earth crossings,eliminating the need for keep out zones andsimplifying mission planning.

Three different classes of X-ray attitude sensorhave been considered:

• The imaging star camera uses grazing inci-dence mirrors or a coded aperture mask anda pixilated detector to create an image of theX-ray sky. The stars in the image are identi-fied and their positions are compared to aguide star catalogue using the same techni-ques used in traditional optical star cameras.

• The collimated star camera uses a collimatorand a large, single pixel detector to measurethe X-ray flux in a given direction. A mechani-cal gimbal is used to scan the instrument overa certain area of sky containing one or moreguide stars. A map of guide stars is created bycorrelating the X-ray flux with gimbal angle.The known and measured locations of theguide stars determine the orientation of thespacecraft.


• The X-ray star scanner uses a fixed collimatoron a spinning spacecraft to create a pattern ofX-ray flux peaks. By having a narrow field-of-view in the direction of spin and a wide field-of-view normal to the spin direction, this pat-tern of guide stars can be matched against acatalogue to determine the orientation of thevehicle. Using flight data from the HEAO-1spacecraft, it has been shown that sub-arcmi-nute level attitude determination is feasibleusing an instrument of this class [24].

The imaging X-ray star camera can be operatedin a very similar manner to conventional opticalstar cameras, the primary advantage being the op-portunity to achieve much more accurate solutionsin a small form factor due to the short wavelengthof X-ray light when compared with visible or ultra-violet light. While the majority of X-ray stars avail-able to be used as guide stars are relatively contin-uous in their emission, the variability of somestars can be used to hasten the initial attitude ac-quisition – the lost-in-space scenario. While a tra-ditional star camera has to sort through a largecatalogue of guide stars to determine the initialattitude solution, an X-ray star camera can quicklyidentify the pulsars in its field of view and matchtheir distinct pulse periods to the catalogue, rap-idly arriving at an initial solution.

The key to the success of any X-ray star camera isthe availability of a catalogue of X-ray guide stars,with the positions of the guide stars accuratelydefined. Several all-sky surveys have been made inX-rays over the past 40 years, including Uhuru(1973), OSO-7 (1973), HEAO-1 (1979), ARIEL(1980) and ROSAT (1991) that are useful in generat-ing a guide star catalogue. The ROSAT Bright StarSurvey is extensive, including a total of 18,806 starscovering three orders of magnitude in brightness[55]. The observations were made in the soft X-ray(0.1–2.4 keV) and extreme ultra-violet (0.025–0.2keV) energy bands using imaging telescopes withproportional counters. While the response of theproportional counters is optimized for sensing softerX-rays than most likely will be detected by the solid-state detectors to be used in an X-ray star camera itstill presents a complete catalogue that allows forreasonable proof of the concept. The spatial distribu-tion of the brightest 200 stars in the ROSAT BSS isshown in Figure 5 indicating that the sources aresufficiently distributed in the sky to provide guidestars for missions in any orbit (about Earth oranother planet) and in any orientation. A majorityof the sources in the ROSAT BSS are not pulsars, sosome of the brightest X-ray sources can be used asguide stars, making the X-ray star camera solutionless susceptible to photon noise compared to a tim-ing or position solution.

Time Determination

A unique capability that X-ray source detectioncan support to improve spacecraft mission opera-tions is the ability to provide atomic clock qualitytime by monitoring these ultra-stable pulsars. Thishas been demonstrated with several highly stablesources [4–6]. Detection of these sources over longdurations could reduce onboard clock errors, or atleast stabilize any long-term clock drifts. Althoughabsolute time cannot be recovered since no identi-fying code is attached to any pulsar signal, inter-estingly, once the position is determined, time rela-tive to arriving pulsar wavefronts can be recovereduniquely from the time difference of arrival(TDOA) among the sources.

The frequency stability of the signals from X-rayand radio pulsars can be used to create a universaltimescale, as Pulsar Time (PT) [7, 8]. The X-rayTiming system, or XTIM, is envisioned to createPT by combining long-term pulsar observationswith an ultra-stable local clock for short-term sta-bility. The concept of PT is not limited to X-raypulsars, as work on creating a stable time refer-ence based on pulsar observations has been doneusing radio pulsars [4–6] and comparisons of PTbased on an ensemble of radio pulsar observationsto UTC have been performed [8]. This new PT-based system has several unique and potentiallymission-enabling characteristics:

• Stability – XTIM is based on observations ofhighly stable pulsars. While the accuracy ofthe pulsar observations are shot noise limitedover short periods (seconds to hours), they areextremely stable over long periods (weeks tomonths) [4–6]. By slaving a local atomic clockto an ensemble of pulsars, a new clock with

Fig. 5–Distribution of brightest 200 guide stars in the ROSATcatalogue. The top ten stars are shown with a diamond marker[55]


unprecedented stability over short to long timescales would be created.

• Autonomy – XTIM would provide users with anindependent and precise measure of time. Thismeasurement is not dependent on an externalsystem, or on regular communication with otherusers. By tracking the same pulsars, multipleusers can be guaranteed access to the sameclock without communication between them.

• Universality – The pulsars used by XTIM arecelestial sources, making them available toany user, anywhere in the solar system. Fur-thermore, any two users, no matter howwidely separated, or without line-of-sight com-munications, can use XTIM to correlate eventsthat occur on two or more spacecraft, enablingnew missions for near-Earth observing space-craft to spacecraft in the distant solar system.This also provides an opportunity to correlatemeasurements between platforms not origi-nally designed for this task. If each spacecraftis using PT, comparison of observations afterthe fact becomes possible.

The XTIM concept diagram of Figure 6 uses afine collimator or imaging system (grazing inci-dence mirrors or coded aperture mask) to selectthe pulsar signal and reject the signals from back-ground radiation and other pulsars. The photonsare detected, time-tagged, and passed to the proc-essing algorithms. Knowledge of the spacecraftposition and velocity over the observation isrequired to create PT. Position can be provided bya separate system, or more likely, by an XNAV sys-tem through the simultaneous observations of mul-tiple pulsars. Concepts for XTIM algorithms aresimilar to those being developed for position andvelocity determination, and include batch pro-cessing maximum likelihood estimators (MLEs)as well as new single photon processing concepts[23, 26].

While existing systems can provide accuratetime through the broadcast of a common referencesuch as GNSS, or the transfer of precision timefrom one user to the next, such as two-way satel-lite time and frequency transfer (TWSTFT) [56],these systems will likely not offer the simultaneous

Fig. 6–Functional concept of an X-ray timing (XTIM) system


stability, autonomy, and universality of XTIM. Fur-thermore, XTIM with XNAV is the only systemthat offers simultaneous attitude, time, and posi-tion determination from a single instrument any-where in the solar system.

Position and Velocity Determination

Several methods and techniques of position andvelocity determination using X-ray sources havebeen studied [12, 17, 22, 24, 32, 35, 36, 42, 43, 46].These approaches can be categorized in an abso-lute sense, where methods are created to deter-mine the absolute 3-D position and velocity in aninertial reference frame, and a correction, or delta-correction, sense, where updates to estimate rangeand range-rate values are generated from the pul-sar measurements. Either of these methods con-tributes to maintaining a continuous, accuratenavigation solution.

For deep space missions, where contact withEarth may be limited and where there may be noplanetary bodies in the near vicinity, methods touniquely determine the full 3-D absolute positionsolution are sought. Spacecraft that can generateautonomous absolute position solutions haveincreased functionality over vehicles that mustrely upon transmitted solutions. Accurate positionknowledge ensures the vehicle is following itsintended path, allows the vehicle to safely controlitself around potential obstacles, and most im-portantly assists the vehicle in pursuing itsintended goals. Alternatively, techniques that pro-duce spacecraft position solutions relative to othervehicles or planetary bodies that are typically inmotion themselves allow the spacecraft to safelyand reliably operate within the close proximity tothese objects.

Methods to solve for the absolute position of aspacecraft include: orbit determination based uponmeasurements from Earth-based observation sta-tions in either the optical or radio band; vehicletracking using the NASA Deep Space Network(DSN) [57]; and, occultation of celestial objects [58,59]. Increased use of GNSS has demonstrated sig-nificant utility for spacecraft navigation in orbitabout Earth [50, 60]. However, limitations exist forGNSS systems used in orbit, including reduced sig-nal visibility, availability, and low signal strength.GNSS systems are designed to operate only near-Earth, thus for applications far from Earth alter-nate methods must be utilized. The primarymethod of navigation for deep space missions is ra-diometric tracking using the DSN [57, 61]. TheDSN provides range and range-rate measurementsalong the line-of-sight (LOS) from Earth via time-of-flight and Doppler measurements. The use ofvery long baseline interferometry (VLBI) with two

of the three primary DSN tracking stations alongwith temporally close observations of nearby qua-sars to reduce some error contributions, called dif-ferential one-way ranging (Delta-DOR), angularmeasurements with accuracies near 1 nrad can beachieved [62]. Current and projected navigationperformance for the DSN at long ranges have beenestablished [63]. However, emerging accuracy andautonomy requirements for new missions cannotbe satisfied by GNSS, DSN, or their current alter-natives alone.

An XNAV position determination concept thatborrows from optical source methods is the conceptof occultation, where an X-ray source is viewed tobe occulted by a planetary body passing in front ofthe source and becoming blocked from the field ofview for some duration of the spacecraft’s detector[22]. As with optical sources, given the knowndimensions of the planetary body, the durationthat the distant pulsar is occulted by the body pro-vides an angular measure that helps determinehow close the spacecraft is with respect to the body[12, 17]. Using accurate ephemeris information forthe body and the unit direction to the source, esti-mated range to the body can be determined for thespacecraft. This method would require a body to bewithin the field of view and would be affected byany atmosphere of the body that may absorb theX-ray photons [64].

In order to utilize the variable celestial sourcesfor absolute position determination, the specificpulse cycle received from a source must be identi-fied. Analysis has demonstrated how the unknown,or ambiguous, number of pulse cycles can beresolved, such that the absolute position of a space-craft can be produced with respect to a chosen ref-erence frame origin [46]. An important attribute ofthese methods is they are applicable to all regionsof space, throughout the solar system, as well asfurther into the Milky Way galaxy, and perhapsbeyond. The determination of unknown cycles forvariable celestial sources, or the pulse phase cycleambiguity resolution process, is in some mannersimilar to the methods used in GNSS navigationsystems. However, the ambiguity resolution pro-cess for variable celestial sources is also uniquein many ways from its GNSS counterparts [46].Instantaneous, full 3-D position solutions wouldrequire multiple X-ray detectors pointed towardsall these individual sources, or a single X-raydetector system that has all-sky monitoring capa-bilities.

The primary analysis approach for determina-tion of pulsar characteristics, or spacecraft naviga-tion solutions, is to compare the pulse TOA mea-sured at an observation site on Earth, or onboardan orbiting spacecraft, to the predicted arrivaltime based upon the model represented in Eq. (2).


The TOA timing residual is the calculated differ-ence multiplied by the pulse period, P, as in [65],

dtTOA ¼ U tTOAð Þ � nint U tTOAð Þ½ �f gP (3)

In Eq. (3), the function nint rounds the value tothe nearest integer. In order to determine the tim-ing residual with high performance, it is critical tocompute tTOA as accurately as possible, as well asto maintain well-defined pulse-timing models. Anyerrors in the pulsar-timing model will directlytranslate to errors in the navigation solution deter-mined from them.

A common implemented approach is a single de-tector technique that provides corrections to esti-mated range using the TOA-difference describedwithin Eq. (3). When viewing a single pulsar, withits known pulse-timing model as in Eq. (2), thecomputed TOA residual can be used to estimatethe error in range along the line of sight to thesource. Blending this information with estimatedposition from an orbit propagator produces correc-tions to the position and velocity solution whichmaintains accurate solutions over time.

Figure 7 shows the relationship of pulses from apulsar as they arrive into the solar system relativeto the SSB inertial frame and a spacecraft orbitingEarth. The positions of the spacecraft, r, and thecenter of Earth, rE, with respect to the SSB areshown, as well as the unit direction to the pulsar,n. To produce accurate TOA measurements, longobservation durations (many thousands of seconds)are required from sources based upon the errorbudget analysis or the Cramer-Rao lower boundachievable performance [23, 26].

An alternative delta-correction technique thatcan potentially provide continuous update informa-tion versus the infrequent TOA-difference tech-nique is the method of continuous phase trackingof a source while it is being observed [26]. Thismethod can estimate and lock onto the phase andfrequency of a source based upon the known modelof Eq. (2). By tracking these expected parametersof the source signal an estimate of the spacecraftvehicle motion within its orbit in an inertial frameis produced. Thus, over short time intervals (tensof seconds), continuous updates of vehicle motionare estimated and many measurements are possi-ble [26]. Digital phase-locked loops (DPLL) can beimplemented to insure proper tracking of these sig-nals [12, 24]. An example of this tracking of pulsarfrequency is shown in Figure 8 using an RXTE ob-servation of the Crab pulsar while in orbit [26].The measured DPLL frequency of the observationwith short time blocks of several seconds showsgood tracking of the true frequency variations dueto spacecraft motion.

Fig. 7–Position of spacecraft as pulses arrive into solar system from distant pulsar [12]

Fig. 8–Doppler frequency tracking of crab pulsar in RXTE orbit[26]


One method to determine a spacecraft’s velocityis to compute the difference of successive positionestimates divided by the time interval betweenestimates. However, this differentiation processwill amplify noise in the system, which reduces theaccuracy of the velocity calculation. Alternatively,for systems that evaluate pulse cycle ambiguities,the triple difference calculation can be utilized toproduce an estimate of spacecraft velocity [46].Although this method may also amplify measure-ment noise, once accurate pulse cycles are known,only the less noisy cycle phase measurements areprocessed.

A more straightforward method to determine ve-hicle speed is through the use of a pulsar’s signalDoppler shift. Because pulsars transmit periodicsignals, Doppler effects will be present in meas-ured pulsar signals as a spacecraft moves towardor away from the source. Measuring the pulsar’spulse frequency and comparing this to its expectedmodel can determine the Doppler shift. Second-order and higher order relativistic Doppler effectsmay be significant depending on the specific pulsarsignal and vehicle motion and should be includedto increase measurement accuracy [66]. Assem-bling measurements from several pulsars allowsfull three-dimensional velocity to be determined.Whereas some navigation processes attempt tominimize the Doppler effect by selecting sourcesthat are perpendicular to the vehicle’s plane ofmotion, this velocity determination method wouldpursue sources that produce the maximum Dopplereffect.

Once measurements are produced from pulsarobservations, effective techniques to incorporatethis information must be designed within thespacecraft navigation system. The use of extendedKalman filters, which use the numerically inte-grated orbital dynamics of the spacecraft blendedwith pulsar observation measurements, has beenproven very effective for this task [12, 32]. Errorswithin the position and velocity solutions havebeen correctly removed with these implementa-tions, and filters such as these can be operated inreal time onboard spacecraft for improved autono-mous operations.

In addition to filter processing techniques, theaugmentation of auxiliary navigation sensor meas-urements can lead to further improved solutions.Incorporating inertial sensors like gyros and accel-erometers allows for attitude, position, and velocityprocessing [67]. Incorporating attitude sensorssuch as optical star trackers, sun sensors, horizonsensors, etc. improve not only the overall space-craft navigation solution, but can aid in X-ray de-tector inertial pointing as well. To facilitate com-puting XNAV measurements, raw time-tagged pho-ton events or pre-processed pulse TOAs or phases

could be included as part of the downlink messagefrom the spacecraft to the DSN tracking stationantenna. The goal of this augmented navigation so-lution would be to improve the navigation solutionof either DSN or XNAV alone. For those spacecraftalready using DSN tracking, the additional range,range-rate, and angular position measurementsfrom this Earth-based service would combine wellwith XNAV solutions to improve the overall naviga-tion accuracy [63, 68, 69]. In addition, the three sol-utions of DSN-only, XNAV-only, and DSNþXNAVwould provide a level of verification for each ofthese systems.

Relative Navigation

Various applications, such as coordinated com-munication or scientific observation, only requirerelative distance and speed information sharedbetween similar instruments operating on cooper-ating multiple vehicles, rather than requiring anindependent, complete 3-D absolute position andvelocity solution for each vehicle. Absolute solu-tions may be difficult to obtain in some circumstan-ces, particularly on missions where GNSS signalsare not available, DSN tracking cannot be com-pleted, or solutions may not have the accuracydesired for specific applications [50, 57]. In thesecases, a method that directly determines relativeposition vectors between spacecraft may be benefi-cial. These vehicles may be following their ownfree paths, or be following prescribed trajectoriessuch that multiple vehicles remain in a defined for-mation [70]. Thus, relative navigation betweenvehicles has been explored using variable X-raysources [67, 71]. In these techniques, bright sour-ces are desired so that high photon flux rates areprovided, which help reduce the observation dura-tions. Additionally, any type of signal variability isusable, thus many other sources other than thehighly stable periodic sources can be utilized [71].

Given sufficient observation time, significantlygreater than the light travel time between the twovehicles, the observed pattern of variability at onedetector will appear as a delayed version of thatseen by the other detector. The measurement ofthis delay provides a distance measurementbetween the two detectors, projected along the lineof sight to the source, which is assumed to be ateffectively infinite distance. There is no require-ment that the variability pattern be predictable. Infact, a large number of bright X-ray sources exhibitsome level of variability in their emitted radiation,which differentiates this from the MSP-based navi-gation techniques discussed above. Additionally,when utilizing aperiodic sources in this manner,one does not encounter the integer phase ambigu-


ity problems that can occur with the periodic pul-sar-based methods [46].

Figure 9 presents this concept, where two space-craft are shown in orbit about Earth simultane-ously measuring the arriving X-radiation from avariable source. This would be applicable to otherapplications, including those in orbit about anyplanetary body or operating in conjunction on deepspace trajectories. This method requires that bothspacecraft observe the celestial source simultane-ously, but does not require an unobstructed line ofsight between the two vehicles, as long as the datacan be communicated between each other at somelater time, or through some intermediary method.If there is significant delay between an observationand its data transmission between vehicles, it willbe necessary to store vehicle navigation data overthis interval to correctly compute a relative navi-gation solution.

To first order, by assuming that the difference inthe relativistic effects is negligible, the range dif-ference, Dq, along the direction to the source, n, isrelated to the measured time difference, Dt, and c,the speed of light, by

Dq ¼ n � rB � rAð Þ ¼ n � Dx ¼ cDt (4)

In Eq. (4), Dx is the relative position vectorbetween the two spacecraft. Relativistic effects arepresent in principle [28, 29], and should beincluded for greater precision.

The source photons detected by each spacecraftare distinct and independent, thus a measurementis not made through direct comparison of individ-ual photon arrival times. Rather, a comparison ofthe time variability of the rate of detection ofX-ray photons at each detector is computed. Therewill be a large amount of variability in theobserved light curve simply due to counting statis-tics, and only the correlated portion of each signalcontains useful information content for a relativerange measurement.

The accuracy of a relative navigation offset mea-surement from a particular source will depend onthe total photon count rate from the source, thetotal fractional variability, and the frequency dis-tribution of the variability power. From Eq. (4),this accuracy is determined by the precision of thedetermination of Dt. Relative timing accuracies towithin 1 ms produce range accuracies on the orderof 300 km, whereas accuracies on the order of 1 lsyield 0.3 km range accuracies. The desired accu-racy would depend on the specific application.With multiple sequential measurements, evaluat-ing the rate of change of range provides an esti-mate of relative range-rate in the direction of thesource. Also with multiple measurements, particu-larly from multiple sources, an estimate of a full3-D relative navigation solution can be created.

The relative navigation scheme could be imple-mented in a variety of methods. For example, onespacecraft may have a large area detector arrayused for measuring the X-ray photon arrival, andall remaining spacecraft could have smaller sizeddetectors. This concept of a single base-stationspacecraft and other remote spacecraft (or parent-child concept) may have all measured data trans-mitted to the base station. After processing onboardthe base station, the relative navigation informa-tion between the base station and each remote vehi-cle would be transmitted to those vehicles thatrequire this information. An alternative techniquewould be to utilize identical detectors on all space-craft and maintain data communication between allvehicles such that each spacecraft can compute arelative navigation solution to other vehicles asneeded. This symmetric scheme is useful when allspacecraft require constant communication betweenone another, and does not identify a hierarchybetween vehicles. Depending on the type of commu-nication, especially one that can encode time infor-mation with the data transmission for a prelimi-nary range estimate, the methods discussed herecan supplement this estimate as needed.

Noise Analysis and System Performance

The performance of any particular XNAV orXTIM implementation is a function of the charac-teristics of the X-ray pulsar and nature of its faintemission, the characteristics of the X-ray instru-ment, as well as the mission itself. A number ofthese potential noise sources have been addressedin the form of a noise table, as shown in Table 3.In general, a navigation measurement is made byfirst measuring the TOA of a pulse train from agiven pulsar over some length of time. A prioriknowledge of the pulse shape, pulse period, andpulse period derivatives is key to this fitting pro-cess and errors in the knowledge of these parame-

Fig. 9–Relative navigation between two spacecraft observing thesame variable celestial source [46, 71]


ters, clock errors, and instrument noise will intro-duce errors into the TOA measurement. Further-more, the signal being measured (the pulsar emis-sion), being a weak signal, is dominated by photonnoise. The measured TOA must be corrected forchanges in spacecraft velocity and position duringthe observation as well as the impact of relativisticeffects on the X-ray photons. Errors in the esti-mated spacecraft velocity and position introduceerrors of their own. Finally, the knowledge of theposition of the pulsar in the sky is used to deter-mine the position of the spacecraft in the X-raynavigation frame-of-reference. Uncertainty in theposition of the pulsar will introduce a final errorwhether a system using observations of a singlepulsar and a gravitational model are used, orwhether four or more pulsars are used to create aninstantaneous position measurement.

For most missions, the primary source of errorin the navigation solution is the ability to measurethe TOA of the pulse train from each source while

contending with the shot noise that is inherent inthe faint signal, the diffuse X-ray background, cos-mic ray events, and detector background. The SNRof the measurement (and hence the accuracy of theTOA estimate) can always be improved by using alarger detector, or increasing the observation time.However, physical limits of the spacecraft andmass considerations will limit the maximum possi-ble collection area of the detector. The particularmission being considered will place limits on theduration of any observation through changes inthe spacecraft velocity or orbit parameters, orthrough occultation of sources being observed byplanetary bodies or asteroids. Thus, the problembecomes one of extracting the most informationfrom an observation in order to minimize therequired detector area and observation time.

This is complicated by the fact that the inten-sities of the pulsars are a function of photonenergy (as a general rule, the flux decreases as apower law with energy), making the detector sensi-tivity as a function of energy an important param-eter in predicting the performance of an XNAVsystem.

Several methods have been used to estimate theimpact of these noise sources on XNAV perform-ance. In general, three analytical approaches havebeen used, each of which has been verified withsome form of Monte-Carlo simulation:

• A simple relationship between the SNR andthe width of the pulse [12, 17];

• A least-squares (LS) fit of the pulse shape tothe X-ray data assuming the photons are col-lected into finite duration time bins over thelength of the observation and folded perfectlyat the pulse period [23]; and,

• A Cramer-Rao lower bound to the performanceof an MLE, assuming that the photons aretime-tagged, but not binned [26].

The total number of photons in an observationbin can be characterized by the mean number ofphotons expected, yi, as

yi ¼ bþ s � h ti; t0ð Þ½ �A �N � g � tbin (5)

where b is the background rate (including detectornoise, the diffuse X-ray background, uncancelledcosmic ray events, and steady emission from thepulsar), s is the source flux, h(ti,t0) describes theshape of the pulse, ti is the time at the center ofbin i, t0 is the time of arrival of the pulse, A is thecollection area, tbin is the size of the bins used tocount photons, N is the number of waveformsfolded, and g is the detector efficiency. A usefuland very simple relationship for the expected pulseTOA accuracy (rTOA) as a function of the instru-

Table 3—Key X-ray Navigation Error Sources [23]

Source Parameters

Source Shot Noise(Periodic)

s: Source strengthA: Detector areaDt: Observation timeg: Detector efficiency

Source Shot Noise(Steady)

bs: Source background

Diffuse X-rayBackground Noise

bd: Diffuse X-raybackground

Cosmic BackgroundNoise

bc: Cosmic X-raybackground (afterrejection)

Detector Noise bdet: Detector noise

Local Clock Noise n(f): Noise power spectraldensity as a function offrequency

Clock Quantization qclk: Clock quantization bit

Photon Binning tbin: Bin size

Source ShapeUncertainty

Db: Source parameter error

Pulse Period Uncertainty DP: Source period error

Source Phase Jitter D/(t): Source phase error

Source PositionUncertainty

n


ment SNR and the full-width-half-maximum of thepulse shape is presented as [12, 17, 46],

rTOA ¼12FWHM

SNR(6)

In Eq. (6), FWHM is the full-width at half-maxi-mum of the main peak in the pulse profile. Thisapproach can be used to approximate TOA per-formance in observing a particular pulsar, but itneglects the full contribution of pulse shape to per-formance. For example, two pulses might have thesame FWHM value, but if one pulse is sharperthan the other, one would expect a more accurateTOA measurement.

This simple TOA accuracy concept was furtherextended to include the pulse shape for the LSestimator case [23]. In this case, the followingassumptions are made:

• The pulse shape and pulse period are known;

• The photons are time-tagged and collected intobins of fixed time width (e.g., 0.1 msec);

• The photon arrival times are corrected for rel-ativistic effects;

• The series of N pulses, measured over the totaltime Dt, are folded together to form a light-curve profile that is the sum of the individualpulsations; and,

• After folding, the number of photons in anybin are sufficiently large such that the Poissondistribution of the number of photons in a bincan be approximated by a Gaussian distribu-tion (i.e. nphotons . 20).

The error in the time-of-arrival estimate of apulse train from a pulsar has two components, onedescribing the shot noise inherent in the signalitself and one describing the added shot noise dueto all background photons, including the steadyemission from the source, the diffuse X-ray back-ground, cosmic rays, and detector noise:

E t20

� �¼ C2

s

P

ADtsþ C2

b

P

ADts

b

s(7)

where the two parameters Gs and Gb (the pulseshape factors) describe the impact of the pulseshape on the estimate error for source shot noiseand background shot noise, respectively, as,

C2s ¼

Rh t; t0ð Þ @h t;t0ð Þ

@t0

� �2dt

R @h t;t0ð Þ@t0

� �2dt

� �2(8)

C2b ¼

1R @h t;t0ð Þ@t0

� �2dt

(9)

The error in the TOA estimate of a pulse train isinversely proportional to the square root of theproduct of the detector area and the observationtime. In addition, The pulse shape factors for sev-eral promising X-ray pulsars have been computedand used to predict performance [23, 69].

While the previous analyses provide performancepredictions for XNAV systems using binned photondata with LS estimators, a different approach isnecessary if the performance of single photon proc-essing systems is to be evaluated. In this case, theCramer-Rao Lower Bound (CRLB) provides a lowerbound to the performance of an XNAV systemusing an MLE [26]:

Var t½ � � f 2Dt

Z 1

0

spf@h /ð Þ=@/� �h i2

spf h /ð Þ þ sð1� pf Þ þ b� �d/

8><>:

9>=>;

�1

(10)

where the profile shape function, h, is written interms of cycle phase, /, and pulsed fraction, pf.This theoretical technique provides a lower bound(i.e., optimistic) estimate to the error in an MLE.Several sources have been analyzed and it wasdetermined that the CRLB is very sensitive tosource flux and profile and these must be modeledappropriately to obtain the best analytical esti-mates. This also suggests that the performance ofXNAV is highly dependent on accurate, high SNRmodels of the pulse profiles and source strengthsand that current XNAV models may underestimatethe accuracy achieved when using sources withshorter historical observations. The CRLB analysiscan be employed to verify the potential perform-ance of several processing techniques, such asMLE, LS, and non-linear LS.

The results of Monte-Carlo simulations and LSanalytical data are shown in Figure 10, and the LStechnique compares well after the initial breakportion of the plots. This break in the plot of theMonte Carlo simulated accuracy indicates that theactual system accuracy is poorer than the modelpredicted accuracy when considering area-timeproducts less than 5�104 m2�s for PSR B1821þ24.This may be due to a low signal-to-noise ratioresulting in poor performance of the gradientsearch algorithm used in the Monte Carlo simula-tion. This behavior was also seen in the MonteCarlo simulations of [26] and is a subject of on-going research in the field. The CRLB method alsodemonstrates good comparisons to the LS analyti-cal solution, typically showing only a 10–20 per-cent improvement over LS in accuracy at low flux,and a 20–40 percent improvement in observationtime. There is a possible improvement in the loca-tion of the threshold point of the break, where the


LS method approaches the theoretical CR limit.A similar comparison shows an asymptotic conver-gence at high area-time products [25]. Theseresults indicate that the single photon algorithmsmay reduce the time-area product required for agiven accuracy.

As presented in the accuracy equations above,the overall performance of an XNAV system ishighly dependent on the detector area, the obser-vation time, and the pulsar being observed. In gen-eral, the TOA measurement error is inversely pro-portional to the square root of the product of thedetector area, observation time, and source inten-sity. Hence, a four-fold increase in detector area orobservation time will result in a halving of the

TOA measurement error. A 1000 cm2 detectormaking a 1000 second observation of the Crab pul-sar would have a TOA measurement error ofapproximately 1.5 lsec.

Mission Applications

Among the most promising applications for thisX-ray navigation technique are science and explo-ration missions far from Earth. These types of mis-sions can combine relatively small detectors(�1000 cm2) and relatively long observation times(103–105 seconds), along with a benign disturbanceenvironment to achieve useful navigation esti-mates. Additionally, for missions that pass close to

Fig. 10–Comparison of monte-carlo simulation and least-squares photon processing approaches,with parameters in Panel A for the Crab pulsar (PSR B0531þ21) and Panel B for PSRB1821þ24 [23]


the Sun, spacecraft emergencies, and landing on ororbiting asteroids or comets, it is desirable, and incertain cases essential, to provide an autonomouscapability for the position and velocity determina-tion in real time onboard. In such circumstances,for the execution of orbit correction maneuvers ina timely manner, the ability to estimate anonboard position, as well as maintain a very accu-rate clock, is essential and mission enabling.

Augmentation with existing systems, such asDSN, further enables missions to succeed or oper-ate at lower cost. For example, orbits in the vicin-ity of the Earth-Sun L2 point are considered fairlystable; however, they will diverge after approxi-mately 23 days without periodic maintenanceburns. Thus, for these L2 orbit applications, XNAVcould provide increased autonomy and potentialreductions in DSN operation costs. Another mis-sion is one to investigate the Pioneer anomaly – anapparent deviation of Pioneer’s anticipated trajec-tory from model predictions [72]. Navigationwith XNAV would provide both significantly im-proved navigation accuracy over DSN alone, andan independent measurement from radiometrictechniques.

Formation flying and relative navigation withXNAV shows promise in a few different ways, pri-marily by opening up the realm of potential sour-ces to include bright, aperiodic sources, which can-not be easily modeled for independent use, but canprovide excellent relative results by correlatingobservations between multiple spacecraft [25, 71].With the inclusion of an accurately navigated X-ray observatory platform and the ability to commu-nicate observations, this approach could be used tosupport navigation of individual spacecraft.

Along with these documented benefits for space-craft navigation, accurate pulse timing from pul-sars is beneficial for future science observationsthat utilize these signals, such as gravitationalwave detection [73–75] and planetary mass andephemeris calculations [76].

Operational Benefits and Challenges

There are numerous potential benefits from thistechnology. A navigation and/or timing system uti-lizing X-ray pulsars would be available anywherecosmic X-ray sources can be observed, from lowEarth orbits to interplanetary trajectories andplanetary orbits. The system is passive, requiringonly infrequent pulsar ephemeris updates, and canoperate in an autonomous mode, independent ofGNSS and NASA DSN systems. In addition, it canbe used in modes where it supplements or enhan-ces DSN capabilities by stabilizing onboard timereferences for accurate range computations. It canprovide measurements that are in a direction per-

pendicular to the line of sight from Earth to thespacecraft. The detectors are highly resistant toblinding or contaminating events. Detectors usedwithin the XNAV system are intrinsically radiationhardened due to their design for recording X-rayphoton events. Previous research on this technol-ogy has shown that the achievable navigation per-formance using these sources can be on the orderof existing navigation technologies. Even withthese numerous benefits, significant challenges re-main that must be addressed before an operationalsystem can be deployed.

Through five decades of X-ray astronomy bothsource characteristic knowledge and sensor detec-tor system concepts continue to mature. New radioMSPs are continually being discovered but few ofthese have been adequately investigated for meredetection of X-ray millisecond pulsations. Withnewly proposed X-ray astronomy missions, detectorconcepts are undergoing major revisions to achieveperformance beyond current day capabilities. Manyfuture designs center on solid-state detectors com-bined variously with collimators, coded apertures,or concentrators. X-ray detectors with high quan-tum efficiency, low-power, low-noise, accurate timeresolution, and minimum size and mass will beneeded to make broad adoption practical.

A navigation system that utilizes pulsed emis-sions from pulsars will have to address the faint-ness, transient, flaring, bursting, and glitchingaspects of these sources, in addition to the numberof signal phase cycles received and the presence ofthe noise from the X-ray background, cosmic rayevents, and detector noise [15]. An operational sys-tem would require a pulsar almanac database withcurrent source characteristics and profile informa-tion. Faint, noisy sources drive solutions towardlarge detectors and long integration times to pre-cisely resolve TOAs, but this comes as a tradeoffbetween available payload mass and power usageversus the overall mission spacecraft size andobjective. Bright sources such as the Crab pulsarhave relatively poor timing stability and are achallenge to be modeled accurately for long-termpredictions. Motion of sources relative to the ECIframe requires accurate measurement and model-ing of source position, proper motion, and binaryorbit parameters. Source frequency drifts due to apulsar’s slow energy loss and must be modeled.Maintaining accurate timing models will requireeither a dedicated observatory spacecraft or devel-opment of a capability to predict X-ray behaviorbased on ground-based radio band observations.General and special relativity effects must beaccounted for because the vehicle is moving and isinfluenced by gravity.

A stable onboard clock would be an essentialpart of a complete XNAV system, which increases


mass and cost to any vehicle. Although data fromactual X-ray astronomy missions have been usedto demonstrate the capability, a dedicated flightexperiment is yet to be built and flown.

CONCLUSIONS

The novel concepts of XNAV and XTIM holdgreat promise for future deep space explorationand for the developing user community becausethey are enabling technologies for fully autono-mous planetary orbiting and interplanetary navi-gation. These new systems will provide significantfuture mission operating enhancements as anadjunct to the DSN and ground-based navigationmethods. Even with the noted challenges that thissystem faces, the conceived benefits of this newX-ray navigation and timing technology warrantsits continued investigation.

ACKNOWLEDGMENTS

Over the past few decades the authors have hadthe opportunity and privilege of working withmany outstanding individuals and groups on thisinteresting topic, and appreciate all of their contri-butions and discussions. This includes Kent Wood,Paul Ray, Michael Lovellette, and Michael Wolff ofthe Naval Research Laboratory; Daniel Jablonskiand John Goldsten of Johns Hopkins UniversityApplied Physics Laboratory (JHU/APL); RobertGolshan formerly of JHU/APL now with The Aero-space Corporation; Derek Tournear formerly of LosAlamos National Laboratory now with DARPA;Keith Gendreau, Keith Jahoda, Zaven Arzouma-nian, Russell Carpenter, James Simpson, NicholasWhite, and Dennis Woodfork of NASA GoddardSpaceflight Center; Chuck Naudet, Walid Majid,and Al Cangauahula of NASA Jet Propulsion Labo-ratory; David Howe and Neil Ashby of NIST; Rich-ard Matzner of University of Texas, Austin; RonaldHellings of Montana State University; David Niceformerly at Princeton University now at LafayetteCollege; Donald Backer of UC Berkeley; DavidBeckett of Ball Aerospace; Demetrios Matsakis ofUS Naval Observatory; John Collins and KseniaKolcio of Microcosm, Inc.; Robert Nelson of Satel-lite Engineering Research Corp.; Coleman Miller,Charles Misner, and Chris Reynolds of the Univer-sity of Maryland; Eliot Bloom and the Astrogravityresearch group at Stanford Linear AcceleratorCenter; and, Daniel DeBra of Stanford University.

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