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Autonomous Spacecraft Navigation With Pulsars

Werner Becker1,2∗, Mike G. Bernhardt1, Axel Jessner2

1Max-Planck-Institut fur extraterrestrische Physik, Gießenbachstraße, 85748 Garching, Germany2Max-Planck-Institut fur Radioastronomie, Auf dem Hugel69, 53121 Bonn, Germany

March 13, 2013

Abstract

An external reference system suitable for deepspace navigation can be defined by fast spinningand strongly magnetized neutron stars, called pul-sars. Their beamed periodic signals have timingstabilities comparable to atomic clocks and providecharacteristic temporal signatures that can be usedas natural navigation beacons, quite similar to theuse of GPS satellites for navigation on Earth. Bycomparing pulse arrival times measured on-boarda spacecraft with predicted pulse arrivals at a refer-ence location, the spacecraft position can be deter-mined autonomously and with high accuracy ev-erywhere in the solar system and beyond. Theunique properties of pulsars make clear already to-day that such a navigation system will have its ap-plication in future astronautics. In this paper wedescribe the basic principle of spacecraft naviga-tion using pulsars and report on the current devel-opment status of this novel technology.

1 Introduction

Today, the standard method of navigation for in-terplanetary spacecraft is a combined use of radiodata, obtained by tracking stations on Earth, andoptical data from an on-board camera during en-counters with solar system bodies. Radio mea-

∗wbecker@mpe.mpg.de

surements taken by ground stations provide veryaccurate information on the distance and the ra-dial velocity of the spacecraft with typical ran-dom errors of about 1 m and 0.1 mm/s, respectively(Madde et al., 2006). The components of positionand velocity perpendicular to the Earth-spacecraftline, however, are subject to much larger errors dueto the limited angular resolution of the radio an-tennas. Interferometric methods can improve theangular resolution to about 25 nrad, correspond-ing to an uncertainty in the spacecraft position ofabout 4 km per astronomical unit (AU) of distancebetween Earth and spacecraft (James et al., 2009).With increasing distance from Earth, the positionerror increases as well, e.g., reaching a level of un-certainty of the order of±200 km at the orbit ofPluto and±500 km at the distance of Voyager 1.Nevertheless, this technique has been used suc-cessfully to send space probes to all planets in thesolar system and to study asteroids and comets atclose range. However, it might be necessary for fu-ture missions to overcome the disadvantages of thismethod, namely the dependency on ground-basedcontrol and maintenance, the increasing positionand velocity uncertainty with increasing distancefrom Earth as well as the large propagation delayand weakening of the signals at large distances. Itis therefore desirable to automate the proceduresof orbit determination and orbit control in order tosupport autonomous space missions.

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Possible implementations of autonomous navi-gation systems were already discussed in the earlydays of space flight (Battin, 1964). In principle,the orbit of a spacecraft can be determined by mea-suring angles between solar system bodies and as-tronomical objects; e.g., the angles between theSun and two distant stars and a third angle be-tween the Sun and a planet. However, becauseof the limited angular resolution of on-board startrackers and sun sensors, this method yields space-craft positions with uncertainties that accumulatetypically to several thousand kilometers. Alterna-tively, the navigation fix can be established by ob-serving multiple solar system bodies: It is possi-ble to triangulate the spacecraft position from im-ages of asteroids taken against a background fieldof distant stars. This method was realized andflight-tested on NASA’s Deep-Space-1 mission be-tween October 1998 and December 2001. The Au-tonomous Optical Navigation (AutoNav) systemon-board Deep Space 1 provided the spacecraftorbit with 1σ errors of±250 km and±0.2 m/s,respectively (Riedel et al., 2000). Although Au-toNav was operating within its validation require-ments, the resulting errors were relatively largecompared to ground-based navigation.

In the 1980s, scientists at NRL (United StatesNaval Research Laboratory) proposed to fly ademonstration experiment called the Unconven-tional Stellar Aspect (USA) experiment (Wood,1993). Launched in 1999 on the Advanced Re-search and Global Observation Satellite (ARGOS),this experiment demonstrated a method of positiondetermination based on stellar occultation by theEarth’s limb as measured in X-rays. This tech-nique, though, is limited to satellites in low Earthorbit.

An alternative and very appealing approach toautonomous spacecraft navigation is based on pul-sar timing. The idea of using these celestialsources as a natural aid to navigation goes backto the 1970s when Downs (1974) investigated theidea of using pulsating radio sources for interplan-etary navigation. Downs (1974) analyzed a method

of position determination by comparing pulse ar-rival times at the spacecraft with those at a refer-ence location. Within the limitations of technol-ogy and pulsar data available at that time (a setof only 27 radio pulsars were considered), Downsshowed that spacecraft position errors on the or-der of 1500 km could be obtained after 24 hoursof signal integration. A possible improvement inprecision by a factor of 10 was estimated if better(high-gain) radio antennas were available for theobservations.

Chester & Butman (1981) adopted this idea andproposed to use X-ray pulsars, of which aboutone dozen were known at the time, instead of ra-dio pulsars. They estimated that 24 hours of datacollection from a small on-board X-ray detectorwith 0.1 m2 collecting area would yield a three-dimensional position accurate to about 150 km.Their analysis, though, was not based on simula-tions or actual pulsar timing analyses; neither didit take into account the technological requirementsor weight and power constraints for implementingsuch a navigation system.

These early studies on pulsar-based navigationestimated relatively large position and velocity er-rors so that this method was not considered to bean applicable alternative to the standard naviga-tion schemes. However, pulsar astronomy has im-proved considerably over the last 30 years sincethese early proposals. Meanwhile, pulsars havebeen detected across the electromagnetic spectrumand their emission properties have been studied ingreat detail (cf. Becker, 2009a, for a collection ofcomprehensive reviews on pulsar research). Alongwith the recent advances in detector and telescopetechnology this motivates a general reconsidera-tion of the feasibility and performance of pulsar-based navigation systems. The present paper re-ports on our latest results and ongoing projects inthis field of research. Its structure is as follows:After summarizing the most relevant facts on pul-sars and discussing which pulsars are best suitedfor navigation purposes in§2, we briefly describethe principles of pulsar-based navigation in§3.

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Pulsars emit broadband electromagnetic radiationwhich allows an optimization for the best suitedwaveband according to the highest number of bitsper telescope collecting area, power consumption,navigator weight and compactness. A possible an-tenna type and size of a navigator which detectspulsar signals at 21 cm is described in§4. In §5we discuss the possibility of using X-ray signalsfrom pulsars for navigation. The recent develop-ments of low-mass X-ray mirrors and active-pixeldetectors, briefly summarized in§ 6, makes it veryappealing to use this energy band for pulsar-basednavigation.

2 The Various Types of Pulsarsand their Relevance for Naviga-tion

Stars are stable as long as the outward-directedthermal pressure, caused by nuclear fusion pro-cesses in the central region of the star, and theinward-directed gravitational pressure are in equi-librium. The outcome of stellar evolution, though,depends solely on the mass of the progenitor star.A star like our sun develops into a white dwarf.Stars above≈ 8 M⊙ undergo a gravitational col-lapse once their nuclear fuel is depleted. Verymassive stars of more than about 30 M⊙ end upas black holes and stars in the intermediate massrange of about 8 to 30 M⊙ form neutron stars.It is assumed that a neutron star is the result ofa supernova explosion, during which the bulk ofits progenitor star is expelled into the interstellarmedium. The remaining stellar core collapses un-der its own weight to become a very compact ob-ject, primarily composed of neutrons – a neutronstar. With a mass of typically 1.4 M⊙, compressedinto a sphere of only 10 km in radius, they are quasigigantic atomic nuclei in the universe. Because oftheir unique properties they are studied intensivelyby physicists of various disciplines since their dis-covery in 1967 (Hewish et al., 1968).

Fast spinning and strongly magnetized neutron

stars are observable as pulsars if their spin axisand magnetic field axis are not aligned. Havingco-rotating magnetic fields ofB⊥ ≈ 109–1013 Gand spin periods down to milliseconds they ra-diate broadband electromagnetic radiation alongnarrow emission cones. If this radiation conecrosses the observer’s line of sight a pulse of in-tensity is recorded in the observing device (cf. Fig-ure 1). The namePulsar refers to this prop-erty. They have been discovered by their radiosignals (Hewish et al., 1968). In source catalogstheir common abbreviation is thereforePSR whichstands for Pulsating Source of Radio, althoughthey have also been detected in other bands of theelectromagnetic spectrum meanwhile. Three dif-ferent classes of pulsars can be distinguished ac-

Figure 1: Artist’s impression of a rotation-poweredpulsar. The neutron star appears as a pulsating source ofradiation if the rotating emission beam crosses the ob-server’s line of sight. Averaging these periodic pulsesof intensity over many rotation cycles results in a stablepulse profile. Because of the timing stability of mostpulsars, the arrival time of pulses can be predicted withvery high precision, which is an essential requirementfor a navigation system based on pulsar observations.

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cording to the energy source of their electromag-netic radiation. As we will see, only one class issuitable for spacecraft navigation:

• Accretion-powered pulsars are close binarysystems in which a neutron star is accretingmatter from a companion star, thereby gain-ing energy and angular momentum. Thereare no radio waves emitted from the accre-tion process, but these systems are bright inX-rays. The observed X-ray pulses are dueto the changing viewing angle of a milliondegree hot spot on the surface of the neu-tron star. These hot spots are heated byin-spiraling matter from an accretion disk.The accretion disk and the accretion col-umn itself can also be sources of X-rays.The spin behavior of accretion-powered pul-sars can be very complicated and complex.They often show an unpredictable evolutionof rotation period, with erratic changes be-tween spin-up and spin-down as well as X-ray burst activities (Ghosh, 2007). Althoughaccretion-powered pulsars are usually brightX-ray sources, and thus would give only mildconstraints on the sensitivity requirements ofa pulsar-based navigation system, their un-steady and non-coherent timing behavior dis-qualifies them as reference sources for navi-gation.

• Magnetars are isolated neutron stars with ex-ceptionally high magnetic dipole fields of upto 1015 G. All magnetars are found to have ro-tation periods in the range of about 5 to 10seconds. RXTE and other X-ray observato-ries have detected super-strong X-ray burstswith underlying pulsed emission from theseobjects. According to the magnetar modelof Duncan & Thompson (1992), their steadyX-ray emission is powered by the decay ofthe ultra-strong magnetic field. This modelalso explains the X-ray burst activity observedfrom these objects, but there are also alterna-tive theories, which relate these bursts to a

residual fall-back disk (Trumper et al., 2010,2013). However, their long-term timing be-havior is virtually unknown, which invali-dates these sources for the use in a pulsar-based spacecraft navigation system.

Concerning their application for navigation, theonly pulsar class that really qualifies is that ofrotation-powered ones.

• Rotation-powered pulsars radiate broad-band electromagnetic radiation (from radioto optical, X- and gamma-rays) at the ex-pense of their rotational energy, i.e., the pul-sar spins down as rotational energy is radiatedaway by its co-rotating magnetic field. Theamount of energy that is stored in the rota-tion of the star can be estimated as follows: Aneutron star with a radius ofR = 10 km anda mass ofM = 1.4 M⊙ has a moment of in-ertia I ≈ (2/5)M R2 ≈ 1045g cm2. The rota-tional energy of such a star isErot = 2π2 I P−2.Taking the pulsar in the Crab nebula withP ≈ 33 ms as an example, its rotational En-ergy isErot ≈ 2×1049erg, which is compara-ble with the energy released by thermonuclearburning of our sun in hundred million years.The spin period of a rotation-powered pulsarincreases with time due to a braking torqueexerted on the pulsar by its magneto-dipoleradiation. For the Crab pulsar, the observedperiod derivative isP = 4.2× 10−13 s s−1,which implies a decrease in rotational energyof Erot =−4π2I PP−3 ≈ 4.5×1038erg s−1. Ithas been found, though, that the spin-downenergy is not distributed homogeneously overthe electromagnetic spectrum. In fact, onlya fraction of about(10−7 − 10−5) Erot is ob-served in the radio band whereas it is roughly(10−4 − 10−3) Erot in the X-ray band and(10−2 − 10−1) Erot in the gamma-ray band(Becker, 2009b).

There are two types of rotation-powered pul-sars: (1) Field pulsars have periods between

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tens of milliseconds to several seconds andconstitute more than 90% of the total pulsarpopulation. (2) About 10% of the known pul-sars are so-called millisecond pulsars, whichare defined to have periods below 20 mil-liseconds. They are much older than nor-mal pulsars, posses weaker magnetic fieldsand, therefore, relatively low spin-down rates.Accordingly, they exhibit very high timingstabilities, which are comparable to atomicclocks (Taylor, 1991; Matsakis et al., 1997).This property of millisecond pulsars is ofmajor importance for their use in a pulsar-based navigation system. Figure 2 clearlyshows that these two types of pulsars be-long to distinct populations. Most likely,

Figure 2: The P-P diagram; distribution of rotation-powered pulsars according to their spin parameters.X-ray detected pulsars are indicated by colored sym-bols. The straight lines correspond to constant agesτ = P/(2P) and magnetic field strengthsB⊥ = 3.2×1019(PP)1/2 as deduced within the framework of themagnetic braking model.

they are connected by an evolutionary pro-cess: It is assumed that millisecond pulsarsare born as normal pulsars in a close binarysystem, but their rotation accelerates as theypass through a phase of accretion in whichmass and angular momentum are transferredfrom the evolving companion star to thepulsar (e.g., Bhattacharya & van den Heuvel,1991). However, the fact that millisecondpulsars are often found in binary systemsdoes not affect their suitability for space-craft navigation as the binary motion caneasily be accounted for in pulsar timing(Blandford & Teukolsky, 1976). Millisecondpulsars – also referred to as recycled pul-sars – were discovered by Backer et al. (1982)and studied extensively in the radio bandby, e.g., Kramer et al. (1998). Pulsed X-rayemission from millisecond pulsars was dis-covered by Becker & Trumper (1993) usingROSAT. However, only XMM-Newton andChandra had the sensitivity to study their X-ray emission properties in the 0.5− 10 keVband in greater detail. The quality of datafrom millisecond pulsars available in the X-ray data archives, though, is still very inho-mogeneous. While from several of them highquality spectral, temporal and spatial infor-mation is available, many others, especiallythose located in globular clusters, are detectedwith just a handful of events, not allowing,e.g., to constrain their timing and spectralproperties in greater detail. From those mil-lisecond pulsars detected with a high signal-to-noise ratio strong evidence is found fora dichotomy of their X-ray emission prop-erties. Millisecond pulsars having a spin-down energy ofE ≥ 1035 erg/s (e.g., PSRJ0218+4232, B1821−24 and B1937+21)show X-ray emission dominated by non-thermal radiation processes. Their pulse pro-files show narrow peaks and pulsed fractionsclose to 100% (cf. Figure 3). Common forthese pulsars is that they show relatively hard

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Figure 3: X-ray and radio pulse profiles for the sixbrightest millisecond pulsars. Two full pulse cycles areshown for clarity. From Becker (2009b).

X-ray emission, making it possible to studysome of them even with RXTE. For exam-ple, emission from B1821−24 in the globu-lar cluster M28 is detected by RXTE up to≈ 20 keV, albeit with limited photon statistics.For the remaining millisecond pulsars the X-ray emission is found to be much softer, andpulse profiles are more sinusoidal. Their typ-ical fraction of pulsed X-ray photons is be-tween 30 and 60%.

Some rotation-powered pulsars have shown

glitches in their spin-down behavior, i.e., abruptincreases of rotation frequency, often followed byan exponential relaxation toward the pre-glitchfrequency (Espinoza et al., 2011; Yu et al., 2013).This is often observed in young pulsars but veryrarely in old and millisecond pulsars. Neverthe-less, the glitch behavior of pulsars should be takeninto account by a pulsar-based navigation system.

Today, about 2200 rotation-powered pulsars areknown (Manchester et al., 2005). About 150 havebeen detected in the X-ray band (Becker, 2009b),and approximately 1/3 of them are millisecond pul-sars. In the past 30− 40 years many of themhave been regularly timed with high precision es-pecially in radio observations. Consequently, theirephemerides (RA, DEC,P, P, binary orbit param-eters, pulse arrival time and absolute pulse phasefor a given epoch, pulsar proper motion etc.) areknown with very high accuracy. Indeed, pul-sar timing has reached the 10−15 fractional level,which is comparable with the accuracy of atomicclocks. This is an essential requirement for usingthese celestial objects as navigation beacons, as itenables one to predict the pulse arrival time of apulsar for any location in the solar system and be-yond.

3 Principles of Pulsar-Based Navi-gation

The concept of using pulsars as navigational aids isbased on measurements of pulse arrival times andcomparison with predicted arrival times at a givenepoch and reference location. A typical chainfor detecting, e.g., radio signals from a rotation-powered pulsar is shown in Figure 4. An impor-tant step in this measurement is the barycenter cor-rection of the observed photon arrival times. Thepulsar ephemerides along with the position and ve-locity of the observer are parameters of this correc-tion. Using a spacecraft position that deviates fromthe true position during the observation results in aphase shift of the pulse peak (or equivalently in a

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de-dispersionbarycenter correctioncoherent folding

TIMETOA

Reference clock

Telescope

Receiver

Pulsar

Figure 4: Typical pulsar detection chain. The pulsarbeams sweep across the radio antenna. Radio signalsare recorded and analyzed in order to produce a meanpulse profile. The data processing comprises a removalof dispersion effects caused by the interstellar medium(“de-dispersion”), correction for the position and propermotion of the observatory (“barycenter correction”) andcoherent folding of many pulses. The time of arrival(TOA) of the pulse peak is measured against a referenceclock.

difference in the pulse arrival time). Therefore, theposition and velocity of the spacecraft can be ad-justed in an iterative process until the pulse arrivaltime matches with the expected one. The corre-sponding iteration chain is shown in Figure 5.

An initial assumption of position and velocityis given by the planned orbit parameters of thespacecraft (1). The iteration starts with a pulsarobservation, during which the arrival times of in-dividual photons are recorded (2). The photonarrival times have to be corrected for the propermotion of the spacecraft by transforming the ar-rival times (3) to an inertial reference location; e.g.,the solar system barycenter (SSB). This correctionrequires knowledge of the (assumed or deduced)spacecraft position and velocity as input parame-ters. The barycenter corrected photon arrival timesallow then the construction of a pulse profile or

Figure 5: Iterative determination of position and ve-locity by a pulsar-based navigation system.

pulse phase histogram (4) representing the tempo-ral emission characteristics and timing signature ofthe pulsar. This pulse profile, which is continu-ously improving in significance during an observa-tion, is permanently correlated with a pulse profiletemplate in order to increase the accuracy of theabsolute pulse-phase measurement (5), or equiva-lently, pulse arrival time (TOA). From the pulsarephemeris that includes the information of the ab-solute pulse phase for a given epoch, the phase dif-ference∆φ between the measured and predictedpulse phase can be determined (cf. Figure 6). Inthis scheme, a phase shift (6) with respect to theabsolute pulse phase corresponds to a range differ-ence∆x = cP(∆φ + n) along the line of sight to-ward the observed pulsar. Here,c is the speed oflight, P the pulse period,∆φ the phase shift andn = 0,±1,±2, . . . an integer that takes into accountthe periodicity of the observed pulses. If the phaseshift is non-zero, the position and velocity of thespacecraft needs to be corrected accordingly andthe next iteration step is taken (7). If the phaseshift is zero, or falls below a certain threshold, theposition and velocity used during the barycentercorrection was correct (8) and corresponds to theactual orbit of the spacecraft.

A three-dimensional position fix can be derivedfrom observations of at least three different pul-

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Ampl

itude

(arb

itrar

y un

its)

Ampl

itude

(arb

itrar

y un

its)

SSB

Spacecraft(barycentred)

Figure 6:Measuring the phase difference between theexpected and measured pulse peak at an inertial refer-ence location; e.g., the solar system barycenter (SSB).The top profile shows the main pulse peak locationas expected at the SSB. The bottom profile is the onewhich has been measured at the spacecraft and trans-formed to the SSB by assuming the spacecraft positionand velocity during the observation. If the position andvelocity assumption was wrong, a phase shift∆φ is ob-served.

sars (cf. Figure 7). If on-board clock calibrationis necessary, the observation of a fourth pulsar isrequired.

Since the position of the spacecraft is deducedfrom the phase (or pulse arrival time) of a peri-odic signal, ambiguous solutions may occur. Thisproblem can be solved by constraining the domainof possible solutions to a finite volume aroundan initial assumed position (Bernhardt et al., 2010,2011), or by observing additional pulsars as illus-trated in Figure 7.

Pulsar 3

Pulsa

r 4

Pulsar 2

Pulsar 1 Pulsar 1

Figure 7:Solving the ambiguity problem by observingfour pulsars (drawn in two dimensions). The arrowspoint along the pulsar’s lines-of-sight. Straight linesrepresent planes of constant pulse phase; black dots in-dicate intersections of planes.

4 Radio Antenna for Pulsar-BasedNavigation

Pulsars emit broadband electromagnetic radiation.Therefore, the observing device of a pulsar-basednavigator can be optimized for the waveband ac-cording to the highest number of bits per tele-scope collecting area, power consumption, naviga-tor weight, cost and compactness. Especially forthe question of navigator compactness it is impor-tant to estimate what size a radio antenna wouldhave to have in order to detect the emission frompulsars in a reasonable integration time. In order toestimate this we assume pulsar parameters that aretypical for millisecond pulsars. As the radio fluxfrom pulsars shows aν−1.5 dependence, observa-tions at lower frequencies seem to be preferred, butscintillation and scattering effects are stronger at

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lower frequency. For a navigation system operat-ing in the radio band of the electromagnetic spec-trum, the L-band at 21 cm might therefore be bestsuited.

For a pulsar detection we require a signal-to-noise ratio ofS/N = 10, a minimum integrationtime of tint = 3600 s and assume a frequency band-width of ∆ν = 100 MHz. For the receiver noisetemperature we takeTrec= 100 K. A lower temper-ature would require active, e.g., cryogenic cooling,which would increase cost, weight, and power con-sumption of a navigator. Furthermore, active cool-ing would severely limit the lifetime of the navi-gator due to consumables like helium. For the skytemperature we takeTsky = 5 K and for the tele-scope efficiencyε = 0.5. If Aant is the geometri-cal antenna area, the effective antenna area com-putes asAeff = ε Aant. For the period of the pul-sar we assumeP = 10 ms and for the pulse widthW = 2 ms. For the average flux density we adopt∆S = 10 mJy. Using the canonical sensitivity equa-tion (Lorimer & Kramer, 2005) which correspondsto the radiometer equation applied to pulsar obser-vations

∆Smin =2k

εAant

(Trec+Tsky)√

np tint ∆ν

√

WP−W

and converting it to the geometrical antenna area,including theS/N requirement, we get:

Aant=SN

2kε∆S

(Trec+Tsky)√2tint ∆ν

√

WP−W

Here we have also assumed that both polarizationsare averaged (np = 2). From this we compute anantenna area ofAant ≈ 342 m2 for the parametersspecified above. For a parabolic antenna it wouldmean a radius of about

√

Aant/π ≈ 10.5 m. In-creasing the integration time to 4 hours, we findan area of≈ 171 m2, which corresponds to a ra-dius of ≈ 7.3 m. For comparison, the radius ofthe communication antenna used on Cassini andVoyager is 2 m. It may depend on the satelliteplatform what size and antenna weight is accept-able, but a parabolic antenna does not seem to be

very practical for navigation purposes. A naviga-tor would have to observe several pulsars, either atthe same time or in series. The pulsars must belocated in different sky regions in order to get anaccurate navigation result in thex, y and z direc-tion. This, however, means that one either rotatesthe parabolic antenna or, alternatively, the wholesatellite to get the pulsar signals into the antennafocus. Rotating the satellite, though, would meanthat the communication antenna will not point toearth any more, which is undesirable. On earthsatellites and space missions to the inner solar sys-tem, power is usually generated by solar panels.Rotating the satellite would then also mean to bringthe solar panels out of optimal alignment with thesun, which is another counter argument for usinga parabolic antenna, not to mention the effects ofshadowing of the solar panels.

It thus seems more reasonable to use dipole-array antennas for the pulsar observations. Singledipole antennas organized, e.g., as antenna patchescould be used to build a larger phased array an-tenna. Such a phased array would still be large andheavy, though. Depending on the frequency, 104–105 single patches are required. There have beenno phased-array antennas of that size been buildfor use in space so far, although smaller prototypesexist (Datashvili et al., 2011). From them one mayestimate the weight of such antenna arrays. As-suming an antenna thickness of 1 cm and an aver-aged density of the antenna material of 0.1 g/cm3

still yields an antenna weight of 170 kg for the170 m2 patched antenna array. The signals fromthe single dipole antennas have to be correlated inphase to each other, which means that all patcheshave to be connected to each other by a wiredmesh and phase correlators. If this phase corre-lation and the real-time coherent correction for thepulse broadening by interstellar dispersion is doneby software, it requires a computer with a Terra-flop GPU of about 500 W power consumption. Aclear advantage of a phased antenna array would bethat it allows to observe different pulsars located indifferent sky regions at the same time. That means

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of course that such an antenna can be smaller ifthe sameS/N ratio is to be achieved for a num-ber Nsourcesof sources within a given time. Witha single-dish antenna one would have to increaseits diameter byN1/4

sourcesif these had to be observedwithin the same given time interval.

5 Using X-ray Signals from Pul-sars for Spacecraft Navigation

The increasing sensitivity of the X-ray observa-tories ROSAT, RXTE, XMM-Newton and Chan-dra allowed for the first time to explore in de-tail the X-ray emission properties of a largersample of rotation-powered pulsars. The dis-covery of pulsed X-ray emission from millisec-ond pulsars (Becker & Trumper, 1993), the de-termination of the X-ray efficiency of rotation-powered pulsars (Becker & Trumper, 1997) aswell as discoveries of X-ray emission fromvarious pulsars (e.g., Becker & Trumper, 1999;Becker et al., 2005, 2006) and their detailed spa-tial, spectral and timing studies are just a fewof many accomplishments worth mentioning inthis context (e.g., Pavlov et al., 2001; Kuiper et al.,2002; Weisskopf et al., 2004; De Luca et al., 2005;Becker, 2009a; Hermsen et al., 2013). With thesenew results at hand it was only natural to start look-ing at their applicability to, e.g., spacecraft nav-igation based on X-ray data from pulsars. Theprospects of this application are of even furtherinterest considering that low-mass X-ray mirrors,which are an important requirement for a realisticimplementation of such a navigation system, havebeen developed for future X-ray observatories.

Given the observational and systematical limita-tions mentioned above it was a question of generalinterest, which we found not considered with suffi-cient gravity in the literature, whether it would befeasible to navigate a spaceship on arbitrary orbitsby observing X-ray pulsars.

In order to address the feasibility question wefirst determined the accuracy that can be achieved

by a pulsar-based navigation system in view of thestill limited information we have today on pulseprofiles and absolute pulse phases in the X-rayband. To overcome the limitations introduced byimproper fitting functions, undefined pivot pointsof pulse peaks and phase shifts by an unmodeledenergy dependence in the pulsed signal, we con-structed pulse profile templates for all pulsars forwhich pulsed X-ray emission is detected. Wheresupported by photon statistics, templates were con-structed for various energy ranges. These energyranges were chosen in order to optimize theS/Nratio of the pulsed signal while sampling as muchas possible of the energy dependence of the X-raypulses.

In the literature various authors applied differ-ent analysis methods and often used different def-initions for pulsed fraction and pulse peak pivotpoints. Reanalyzing all data from X-ray pulsarsavailable in the public XMM-Newton, Chandraand RXTE data archives was therefore a require-ment to reduce systematic uncertainties that wouldhave been introduced otherwise. The result is adatabase containing the energy dependent X-raypulse profiles, templates and relevant timing andspectral properties of all X-ray pulsars that havebeen detected so far (Prinz, 2010; Breithuth, 2012).

According to the harmonic content of an X-raypulse the templates were obtained by fitting the ob-served pulse profiles by series of Gaussian and si-nusoidal functions. The database further includesinformation on the local environment of a pulsar,i.e., whether it is surrounded by a plerion, super-nova remnant or whether it is located in a crowdedsky region like a globular cluster. The latter hasa severe impact on the detectability of the X-raypulses as it reduces theS/N ratio of the pulsedemission by the DC emission from backgroundsources. This in turn is important for the selectionof the optimal pulsars that emit pulses, e.g., in thehard band (above≈ 3 keV) in order to blend awaythe softer emission from a supernova remnant orplerion.

The pulse profile templates allow us to mea-

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sure pulse arrival times with high accuracy evenfor sparse photon statistics by using a least-squarefit of an adequately adjusted template. The errorof pulse-arrival-time measurements is dominatedby the systematic uncertainty that comes with thelimited temporal resolution of the observed pulseprofiles used to construct the templates. The sta-tistical error in fitting a measured profile by a tem-plate was found to be much smaller in all cases.Assuming that the temporal resolution of the de-tector is not the limiting factor, the temporal reso-lution of a pulse profile is given by the widths ofthe phase bins used to represent the observed X-ray pulse. The bin width, or the number of phasebins applied, is a compromise between maximiz-ing theS/N ratio per phase bin while sampling asmuch of the harmonic content as possible. De-noting the Fourier-power of thei-th harmonic byRi and takingm as the optimal number of har-monics deduced from the H-test (De Jager et al.,1989), an exact expression for the optimal numberof phase bins is given byM = 2.36(∑m

i=1 i2R2i )

1/3

(Becker & Trumper, 1999). This formula com-promises between information lost due to binning(i.e., zero bin width to get all information), and theeffect of fluctuations due to finite statistics per bin(i.e., bin width as large as possible to reduce thestatistical error per bin). The total error (bias plusvariance) is minimized at a bin width of 1/M. Weapplied this in the reanalysis of pulse profiles inour database. Pulsed fractions were computed byapplying a bootstrap method (Becker & Trumper,1999), which again leads to results that are not bi-ased by the observers “taste” on where to assumethe DC level in a profile.

The minimal systematic phase uncertainty forthe pulse profile templates in our database is of theorder of 0.001 (Bernhardt et al., 2010). This un-certainty multiplied by the rotation periodP of thepulsar yields the uncertainty in pulse arrival timedue to the limited information we have on the exactX-ray pulse profile. Multiplying this in turn by thespeed of light yields the spacecraft’s position erroralong the line of sight to the pulsar. It is evident by

the linear dependence onP that millisecond pul-sars are better suited for navigation than those withlarger rotation periods.

The precision of a pulsar-based navigation sys-tem thus strongly depends on the choice of pulsarsand the accuracy of pulse arrival measurements,which is subject to the quality of the available tem-plates, accuracy of the on-board clock and clockcalibration. As mentioned above, in order to ob-tain three-dimensional position information, tim-ing of at least three different pulsars has to be per-formed. The spatial arrangement of these pulsars isanother parameter of the achievable accuracy. Oursimulations show that the systematic error of po-sition determination can be reduced significantlyby choosing a pulsar triple that is optimal in thesense that the pulsars are nearly perpendicular toeach other. Since a pulsar might be obscured bythe sun or a planet and, therefore, its availabilityfor navigation depends on the current position ofthe spacecraft, the optimal pulsar triple has to beselected from a ranking of possible pulsar combi-nations. The following Table 1 represents the rank-ing of pulsar combinations, which according to ouranalysis provide the highest position accuracy viapulsar navigation (Bernhardt et al. 2010).

Rank Pulsar 3-Combination

1 B1937+21 B1821−24 J0030+04512 B1937+21 B1821−24 J1023+00383 B1821−24 J0030+0451 J0437−47154 B1937+21 J1023+0038 J0218+42325 B1821−24 J1023+0038 J0437−47156 B1937+21 J0030+0451 J0218+42327 B1937+21 B1821−24 J0437−47158 B1937+21 J0218+4232 J0437−47159 B1821−24 J0218+4232 J0437−471510 J1023+0038 J0218+4232 J0437−4715

Table 1: Ranking of pulsar 3-combinations accordingto the position accuracy achievable when using themin a navigation system based onf X-ray pulsars . Alllisted sources are solitary millisecond pulsars exceptJ0437−4715, which is in a binary.

For the pulsars ranked highest in Table 1 we

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found position errors of about 5 km as a lower limit(cf. Figure 8). The ranking is independent from aspecific spacecraft orbit, but was obtained underthe assumption that the navigation system is capa-ble of measuring pulse profiles with the same levelof detail and accuracy as the ones used in the sim-ulation. Indeed, this is a severe limitation as thosepulse profiles where obtained by powerful X-rayobservatories like XMM-Newton and Chandra. Itis unlikely, due to weight constraints and powerlimitations, that a navigation system will have sim-ilar capacities in terms of collecting power, tempo-ral resolution and angular resolution.

Figure 8: Spacecraft position error as a function ofpossible pulsar 3-combinations. The diagram showsthe mean position errors and standard deviations for thebest 30 combinations. From Bernhardt et al. (2010).

An improved accuracy can be achieved bymeans of pulse profile templates of better quality.This, in turn, calls for deeper pulsar observationsby XMM-Newton or Chandra as long as these ob-servatories are still available for the scientific com-munity. It would be a valuable task worthwhilethe observing time, especially as it is unclear whatmissions will follow these great observatories andwhether they will provide detectors with sufficienttemporal resolution and on-board clock accuracy.

We extended our simulations in order to con-strain the technological parameters of possiblenavigation systems based on X-ray pulsars. The re-

sult of this ongoing project will be a high-level de-sign of a pulsar navigator that accounts for bound-ary conditions (e.g., weight, cost, complexity andpower consumption) set by the requirements of aspecific spacecraft and mission design.

The chart shown in Figure 9 illustrates the worklogic of our current simulations. Navigator bound-ary conditions (1) and spacecraft orbit (2) are pre-defined and constrain the technology parameters(3) of the navigator’s X-ray detector, mirror systemand on-board electronics. Examples of parame-ters that will be analyzed in the simulations are de-tector technology, temporal and energy resolution,on-board-clock accuracy and stability, mirror tech-nology along with collecting power, angular andspatial resolution, focal length, field of view – justto mention the most important ones. Given theirX-ray emission properties some pulsars may notbe detectable by the navigator because of its lim-ited angular resolution and sensitivity. The prop-erties of the detector and mirror system along withthe trajectory of the virtual navigator thus deter-mine the set of available pulsars (5), from whicha suitable selection has to be made (6) accordingto a predefined ranking of pulsar triples. Using anX-ray-sky simulator (7), which was developed tosimulate observations of the future X-ray observa-tories eROSITA and IXO and which we have mod-ified to include the temporal emission propertiesof X-ray pulsars, we will be able to create X-raydatasets in FITS-format with temporal, spatial andenergy information for the pulsars observed by ourvirtual navigator. The simulated event files havethe same standard FITS-format as those of XMM-Newton and/or Chandra, so that standard softwarecan be used to analyze these data. An autonomousdata reduction will then perform the data analysisand TOA measurement in order to obtain the posi-tion and velocity of the virtual observer (8). Corre-lating the result with the input trajectory (9) yieldsthe accuracy of the simulated measurements for agiven spacecraft orbit (10), and hence the overallperformance of the navigator as a function of thespecified detector and mirror system (11,12).

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Figure 9:Work flow and logic of the simulations performed for a technology requirement study and demonstratorhigh-level design of a pulsar-based navigator.

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6 X-ray Detector and MirrorTechnology for Pulsar-BasedNavigation

The design of an X-ray telescope suitable for nav-igation by X-ray pulsars will be a compromisebetween angular resolution, collecting area andweight of the system. The currently operatingX-ray observatories XMM-Newton and Chandrahave huge collecting areas of 0.43 m2 and 0.08 m2

(at 1 keV), respectively (Friedrich, 2008, and ref-erences therein) and, in the case of Chandra, attainvery good angular resolution of less than 1 arcsec-ond. Their focusing optics and support structures,however, are very heavy. To use their mirror tech-nology would be a show-stopper for a navigationsystem.

In recent years, ESA and NASA have puttremendous effort into the development of low-mass X-ray mirrors, which can be used as ba-sic technology for future large X-ray observatoriesand small planetary exploration missions. Table2 summarizes the angular resolution and mass ofX-ray mirrors used for XMM-Newton and Chan-dra as well as developed for future X-ray missions.The light-weighted mirrors are of special interestfor an X-ray pulsar-based navigator.

Angular Mass per effectiveresolution area (at 1 keV)

Chandra 0.5′′ 18500 kg/m2

XMM-Newton 14′′ 2300 kg/m2

Silicon Pore Optics 5′′ 200 kg/m2

Glass Micropore Optics 30′′ 25 kg/m2

Table 2: Comparison of current and future X-ray-mirror optics. From Bavdaz et al. (2010).

A typical high-resolution X-ray telescope usesfocusing optics based on the Wolter-I design(Wolter, 1952). The incoming X-ray photons arereflected under small angles of incidence in or-der not to be absorbed and are focused by dou-ble reflection off a parabolic and then a hyper-

bolic surface. This geometry allows for nestingseveral concentric mirror shells into each other inorder to enlarge the collecting area and thereby im-prove the signal-to-noise ratio. A novel approachto X-ray optics is the use of pore structures in aWolter-I configuration (Bavdaz et al., 2003, 2010;Beijersbergen et al., 2004b). X-ray photons thatenter a pore are focused by reflections on the wallsinside the pore. In contrast to traditional X-ray op-tics with separate mirror shells that are mountedto a support structure, pore optics form a mono-lithic, self-supporting structure that is lightweight,but also very stiff and contains many reflecting sur-faces in a compact assembly. Two different typesof pore optics have been developed, based on sili-con and glass.

• Silicon Pore Optics (Collon et al., 2009,2010; Ackermann et al., 2009) use commer-cially available and mass produced siliconwafers (Figure 10a) from the semiconduc-tor industry. These wafers have a surfaceroughness that is sufficiently low to meetthe requirements of X-ray optics. A chemo-mechanical treatment of a wafer results in avery thin membrane with a highly polishedsurface on one side and thin ribs of very ac-curate height on the other side. Several ofthese ribbed plates are elastically bent to thegeometry of a Wolter-I system, stacked to-gether to form the pore structure and finallyintegrated into mirror modules (Figure 10a).Silicon Pore Optics are intended to be used onlarge X-ray observatories that require a smallmass per collecting area (on the order of 200kg/m2) and angular resolution of about 5 arc-seconds or better.

• Glass Micropore Optics(Beijersbergen et al., 2004a; Collon et al.,2007; Wallace et al., 2007) are made frompolished glass blocks that are surrounded bya cladding glass with a lower melting point.In order to obtain the high surface quality

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a.

b.b.

c.

OPTICAL AXIS

Figure 10: Silicon pore optics (a) and glass micro-pore optics (b) represent novel developments for light-weighted X-ray mirrors of the next generation of X-rayobservatories. Both mirror types will be used in Wolter-I configuration (c) to focus X-rays in a double reflec-tion. Images from Bavdaz et al. (2003, 2004, 2010).

required for X-ray optics, the blocks arestretched into small fibers, thereby reducingthe surface roughness. Several of these fiberscan be assembled and fused into multi-fiberbundles. Etching away the glass fiber coresleads to the desired micropore structure, in

which the remaining cladding glass forms thepore walls (Figure 10b). The Wolter-I ge-ometry is reproduced by thermally slumpingseparate multi-fiber plates. Glass MicroporeOptics are even lighter than Silicon PoreOptics, but achieve a moderate angularresolution of about 30 arcseconds. They areespecially interesting for small planetary ex-ploration missions, but also for X-ray timingmissions that require large collecting areas.The first implementation of Glass MicroporeOptics on a flight program will be in theMercury Imaging X-ray Spectrometer on theESA/JAXA mission BepiColombo, plannedto launch in 2014 (Fraser et al., 2010).

Today’s detector technology, as in use on XMM-Newton and Chandra, is not seen to provide a de-tector design that is useful for a navigation sys-tem based on X-ray pulsars. Readout noise, lim-ited imaging capability in timing-mode and out-of-time events invalidate CCD-based X-ray detectorsfor application as X-ray-pulsar navigator. Detec-tors like those on RXTE that need gas for oper-ation are also not suitable, given the limited livetime due to consumables. However, there are noveland promising detector developments performed insemiconductor labs for the use in the next genera-tion of X-ray observatories. Two challenging ex-amples, which are of potential interest for naviga-tion, are:

• Silicon Drift Detectors (SDDs) have onlylimited imaging capability but provide an en-ergy resolution and are capable of managinghigh counting rates of more than 10 Crab (1Crab count rate≈ 200000 cts/s). A detec-tor based on this technology was proposedfor the High Time Resolution Spectrometeron IXO (Barret et al., 2010). The detectortechnology itself has a high technical readi-ness. SDD-modules developed in the Semi-conductor Lab of the Max Planck Society areworking already in the APXS (Alpha Par-ticle X-ray Spectrometer) on-board NASA’s

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Mars Exploration Rovers Spirit and Oppor-tunity and on the comet lander ROSETTA(Lechner et al., 2010). Detectors based on anSDD technology could be of use, e.g., in de-signing a navigator for a very specific orbit,for which it is sufficient to navigate accord-ing to the signals of pulsars that emit theirpulses in the hard X-ray band mostly so thatthe missing imaging capability does not causeany restrictions on theS/N ratio of the pulsedemission.

• Active Pixel Sensors (APS) are an alterna-tive and perhaps more flexible technology(cf. Figure 11), which was the proposed tech-nology for the Wilde Field Imager on IXO(Struder et al., 2010) and the Low-Energy De-tector (LED) on Simbol-X (Lechner, 2009).This detector provides images in the energyband 0.1–25 keV, simultaneously with spec-trally and time resolved photon counting. Thedevice, which is under development in theMPE Semiconductor Laboratory, consists ofan array of DEPFET (Depleted p-channelFET) active pixels, which are integrated ontoa common silicon bulk. The DEPFET con-cept unifies the functionalities of both sen-sor and amplifier in one device. It has a sig-nal charge storage capability and is read outdemand. The DEPFET is used as unit cellof Active Pixel Sensors (APSs) with a scal-able pixel size from 50µm to several mm anda column-parallel row-by-row readout with ashort signal processing time of≤ 4µsec perrow. As the pixels are individually address-able the DEPFET APS offers flexible readoutstrategies from standard full-frame mode touser-defined window mode.

The typical weight and power consumption ofthese detectors can be estimated from the proto-types proposed for IXO and Simbol-X. The IXOWide Field Imager with its 17 arcmin field of viewand 1024× 1024 pixel design had an energy con-sumption of≤ 22 W. The Low Energy Detector on

Figure 11:Mechanical sample of an Active Pixel (here6-inch wafer-scale) detector. Plotted over one hemi-sphere is the logical layout of the detector. It consistsof roughly 1024×1024 pixels of 100×100µm2 size.From Lechner et al. (2010).

Simbol-X had 128×128 pixels and an energy con-sumption of≤ 8 W. Power consumption includingelectronics, filter wheel and temperature controlwas ca. 250 W. The mass of the focal plane, in-cluding shielding and thermal interface, was about15 kg but could be reduced in a more specific de-sign of an X-ray-pulsar navigator.

7 Concluding Remarks

The knowledge of how to use stars, planets andstellar constellations for navigation was fundamen-tal for mankind in discovering new continents andsubduing living space in ancient times. It is fas-cinating to see how history repeats itself in that aspecial population of stars may play again a funda-mental role in the future of mankind by providinga reference for navigating their spaceships throughthe Universe (cf. Figure 12).

In the paper we have shown that autonomousspacecraft navigating with pulsars is feasible whenusing either phased-array radio antennas of at least150 m2 antenna area or compact light-weighted X-ray telescopes and detectors, which are currentlydeveloped for the next generation of X-ray obser-vatories.

Using the X-ray signals from millisecond pul-

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Figure 12:Artist’s impression of Rosetta, if it navigated in deep space using pulsar signals. The characteristictime signatures of pulsars are used as natural navigation beacons to determine the position and velocity of thespacecraft.

sars we estimated that navigation would be possi-ble with an accuracy of±5 km in the solar systemand beyond. The error is dominated by the inaccu-racy of the pulse profiles templates that were usedfor the pulse peak fittings and pulse-TOA measure-ments. As those are known with much higher ac-curacy in the radio band, it is possible to increasethe accuracy of pulsar navigation down to the me-ter scale by using radio signals from pulsars fornavigation.

The disadvantage of radio observations in a nav-igator, though, is the large size and mass of thephased-antenna array. As we saw in§ 4, the an-tenna area is inversely proportional to the squareroot of the integration time; i.e., the same signalquality can be obtained with a reduced antennasize by increasing the observation time. However,the observing time is limited by the Allen variance

of the receiving system and, therefore, cannot be-come arbitrarily large. In addition, irradiation fromthe on-board electronics requires an efficient elec-tromagnetic shielding to prevent signal feedback.This shielding will further increase the navigatorweight in addition to the weight of the antenna.

The optimal choice of the observing band de-pends on the boundary conditions given by a spe-cific mission. What power consumption and whatnavigator weight might be allowed for may deter-mine the choice for a specific wave band.

In general, however, it is clear already today thatthis navigation technique will find its applicationsin future astronautics. The technique behind it isvery simple and straightforward, and pulsars areavailable everywhere in the Galaxy. Today≈ 2200pulsars are known. With the next generation of ra-dio observatories, like the SKA, it is expected to

17

detect signals from about 20 000 to 30 000 pulsars(Smits et al., 2009).

Finally, pulsar-based navigation systems can op-erate autonomously. This is one of their mostimportant advantages, and is interesting also forcurrent space technologies; e.g., as augmentationof existing GPS/Galileo satellites. Future appli-cations of this autonomous navigation techniquemight be on planetary exploration missions and onmanned missions to Mars or beyond.

Acknowledgments

WB acknowledges discussion with David Cham-pion (MPIfR), Horst Baier and Ulrich Walter(TUM). MGB acknowledges support from andparticipation in the International Max Planck Re-search School on Astrophysics at the Ludwig Max-imilians University of Munich, Germany.

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