assessing three new gps combined l1/l2c acquisition methods

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[23] Crausaz, A., Gasquet, E., and Sanchis, E. Power MosFet: ESA driving licence. In Proceedings of the 4th European Space Power Conference, ESA SP-369, Sept. 1995, 227—233. Assessing Three New GPS Combined L1/L2C Acquisition Methods This paper presents three new global positioning system acquisition methods that make use of both L1 C/A and L2C signals in a combined way. The methods perform joint estimation of the Doppler frequencies and code delays on L1 and L2 without increasing the coherent integration time. Each method is assessed in terms of theoretical probabilities of false alarm and detection as well as through testing with real intermediate frequency data. The first method is a noncoherent summation of L1 and L2 correlator outputs. The second method implements an independent differential summation of L1/L2 correlator outputs, and the third method uses a noncoherent plus dependent differential summation. While each method provides increased detection performance compared with the standard noncoherent acquisition applied on L1 C/A, the noncoherent plus dependent differential summation method outperforms all of the others in the scenarios investigated. I. INTRODUCTION A. Background and Motivations Global positioning system (GPS) receivers must overcome extreme challenges to provide reasonable performance when operating under harsh conditions. In typical urban canyon and indoor environments, attenuation levels exceeding 20 dB have been observed [1]. The most common solution for this attenuation is to increase the coherent integration time used [2, 3]. For instance, high-sensitivity GPS receivers rely on data bit estimation routines to increase the integration time, while assisted GPS uses known data bits sent from a reference station such that the remote receiver can wipe the navigation message off the incoming signal. Nevertheless, availability or reliability of the needed external information is not always guaranteed and data bit estimation methods remain limited. This paper focuses on the possibility of combining the new L2C signal with the legacy L1 C/A signal in terms of acquisition. The principal contribution of this paper is the development of three novel Manuscript received September 16 2009; revised May 3, 2010 and August 29 2010; released for publication September 16, 2010. IEEE Log No. T-AES/47/3/941795. Refereeing of this contribution was handled by L. Kaplan. 0018-9251/11/$26.00 c ° 2011 IEEE CORRESPONDENCE 2239

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Page 1: Assessing Three New GPS Combined L1/L2C Acquisition Methods

[23] Crausaz, A., Gasquet, E., and Sanchis, E.

Power MosFet: ESA driving licence.

In Proceedings of the 4th European Space Power

Conference, ESA SP-369, Sept. 1995, 227—233.

Assessing Three New GPS Combined L1/L2CAcquisition Methods

This paper presents three new global positioning system

acquisition methods that make use of both L1 C/A and L2C

signals in a combined way. The methods perform joint estimation

of the Doppler frequencies and code delays on L1 and L2

without increasing the coherent integration time. Each method

is assessed in terms of theoretical probabilities of false alarm

and detection as well as through testing with real intermediate

frequency data. The first method is a noncoherent summation of

L1 and L2 correlator outputs. The second method implements

an independent differential summation of L1/L2 correlator

outputs, and the third method uses a noncoherent plus dependent

differential summation. While each method provides increased

detection performance compared with the standard noncoherent

acquisition applied on L1 C/A, the noncoherent plus dependent

differential summation method outperforms all of the others in

the scenarios investigated.

I. INTRODUCTION

A. Background and Motivations

Global positioning system (GPS) receivers must

overcome extreme challenges to provide reasonable

performance when operating under harsh conditions.

In typical urban canyon and indoor environments,

attenuation levels exceeding 20 dB have been

observed [1]. The most common solution for this

attenuation is to increase the coherent integration

time used [2, 3]. For instance, high-sensitivity GPS

receivers rely on data bit estimation routines to

increase the integration time, while assisted GPS uses

known data bits sent from a reference station such that

the remote receiver can wipe the navigation message

off the incoming signal. Nevertheless, availability or

reliability of the needed external information is not

always guaranteed and data bit estimation methods

remain limited.

This paper focuses on the possibility of combining

the new L2C signal with the legacy L1 C/A signal

in terms of acquisition. The principal contribution

of this paper is the development of three novel

Manuscript received September 16 2009; revised May 3, 2010 and

August 29 2010; released for publication September 16, 2010.

IEEE Log No. T-AES/47/3/941795.

Refereeing of this contribution was handled by L. Kaplan.

0018-9251/11/$26.00 c° 2011 IEEE

CORRESPONDENCE 2239

Page 2: Assessing Three New GPS Combined L1/L2C Acquisition Methods

combined acquisition methods and the assessment of

their performance through probabilities of detectionand false alarm using theoretical means and real

observations.

B. L1 C/A and L2C Signals

L2C is located at 1227.60 MHz and transmitted

with a power 1.5 dB lower than the legacy GPS L1

C/A itself located at 1575.42 MHz and transmitted

with a power of ¡158:5 dBW. The L1 C/A signalis composed of a satellite dependent pseudorangingcode of 1023 chips that is clocked at 1.023 MHz

using binary phase shift keying (BPSK), which is

also modulated with a 50-Hz navigation message.

The resulting signal is then used to BPSK modulatethe 1575.42-MHz carrier signal. On the other hand,

the L2C signal contains two pseudoranging codes

called the CM code and the CL code. A data channel

is formed by the 10230 chip CM code clocked at

511.5 kHz and modulated by a 50-Hz navigationmessage. Unlike the legacy L1 C/A, exactly one CM

code is present within one navigation data bit, thereby

removing the need for data bit synchronization. The

L2C navigation message, though also transmitted at50 bits/s, is independent of the L1 C/A navigation

message. The L2C CL code is 767 250 chips in length

and is also clocked at 511.5 kHz for a total length

of 1.5 s. The CL code is dataless. Because the L2

frequency also carries the military P(Y) signal, thedevelopment of L2C was limited to a single biphase

carrier. Therefore the two channels (CM and CL)

are time multiplexed, resulting in a 1.023-MCps

signal used to BPSK modulate the 1227.6-MHzcarrier. The CM and CL channels share the total L2C

power of ¡160 dBW equally. However, because of

its extreme length, the CL code is usually ignored

during correlation, which leads to a signal degradationof 3 dB, pushing L2C 4.5 dB lower than L1 C/A in

terms of acquisition [4].

C. Constraints Affecting Acquisition Process

During the acquisition process, a range of possible

Doppler frequencies and code delays must be

searched. However, if the estimated Doppler used to

remove the carrier is too far from the true Doppler,

the signal is averaged out. Therefore, the Dopplerbin size is dependent on the correlation time. The

relation commonly used to determine the number

of Doppler bins needed to cover a Doppler range of

¡5000 to 5000 Hz to the coherent integration time iswell known and can be expressed as

ND =10000 ¢3 ¢T

2(1)

with ND representing the number of Doppler bins and

T the coherent integration time used [5]. Therefore,

longer coherent integration means smaller Doppler binsize and increased complexity.

However, the fact that the acquisition of L2Cleads immediately to the determination of the databit boundaries remains advantageous. A FFT-basedmethod for CM/CL acquisition was investigated by [6]and used to operate in weak signal environments. Limet al. [7] proposed a fast-acquisition method makinguse of L1 aiding L2 to estimate L2C CM code delaysand carrier Doppler. Tracking performance of theL2C signal through combination of the data and pilotchannels has been analyzed by [8] and [9]. However,the first methods actually performing interfrequencyL1/L2 combinations based on the power duplicationresulting from the presence of two signals was onlyproposed by [10] and [11].The focus of this paper is on the theoretical

assessment of three different L1/L2 combinedacquisition techniques. Because both L1 C/A andL2C are time-synchronized signals transmitted bythe same satellite, one can directly combine themto improve receiver detection properties. However,whereas both L1/L2 signals are synchronized at theirgeneration, the presence of instrumental group delaywithin the satellite and receiver, and the signal transitthrough the ionospheric layer desynchronize thesignals. The instrumental relative group delay is onthe order of 1 ns, which is negligible [12, 13] in termsof acquisition for L1/L2 interfrequency combinations,and the ionospheric effect hardly affects the combinedacquisition either [10, 11].Finally, a direct relation exists between the

Doppler effect of L1 and the Doppler effect onL2 because this effect is mainly due to the relativeuser-satellite motion:

fD1 =f1f2fD2: (2)

The remainder of this paper is organized asfollows. Section II introduces the signal modelused throughout. Section III presents the differentcombined acquisition methods and their theoreticalstatistical properties. Section IV verifies thederivations of Section III using real data.

II. SIGNAL MODEL

After the integrate and dump process, the real andimaginary parts of the correlator output at the kthcoherent integration can be expressed as

I(k) =Ap2¢ d(k) ¢R(dt)

¢ sin(¼¢FDT)¼¢FDT

cos(¼¢FT(2k¡ 1)+Á)

Q(k) =Ap2¢ d(k) ¢R(dt)

¢ sin(¼¢FDT)¼¢FDT

sin(¼¢FT(2k¡ 1)+Á)

(3)

where A is the signal amplitude, d(k) the data bit,¢F the Doppler residual, dt the code misalignmentin chips, R the autocorrelation function, T the

2240 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 3 JULY 2011

Page 3: Assessing Three New GPS Combined L1/L2C Acquisition Methods

coherent integration time, and ' the phase differencebetween the incoming signal and local oscillator atthe beginning of the first coherent integration (k = 1).Note that the independent Gaussian noises present atthe receiver input are also modified by the Dopplerremoval and integrate-and-dump processes. Thenoise present at the output of the correlators remainsindependent and identically distributed for the real andimaginary parts, namely N(0,¾2) with ¾2 = ¾2IF=NS ,where ¾2IF is the noise variance at the intermediatefrequency. This discussion is valid regardless of thesignal considered and, as such, is valid for both L1and L2C real and imaginary parts of the correlatoroutputs.

III. COMBINED ACQUISITION METHODS

A. General Presentation

The proposed acquisition methods arepostcorrelation methods. As such, they use the outputof the correlators as input and differ only after theintegrate-and-dump process takes place. The firstmethod, called NCL1L2, represents the summation ofnoncoherent acquisition performed on L1 and L2. Itsmathematical representation is

SNCL1L2 =

MXk=1

(I2k,L1 +Q2k,L1)+W

2 ¢MXk=1

(I2k,L2 +Q2k,L2)

(4)

with W representing a weight factor applied to L2Ccorrelator output.The second, named DiffL1L2, performs a

summation of differential acquisitions done on L1 andL2. Its mathematical expression is

SDiffL1L2 =

M=2Xk=1

(I2k,L1 ¢ I2k¡1,L1 +Q2k,L1 ¢Q2k¡1,L1)

+W2 ¢M=2Xk=1

(I2k,L2 ¢ I2k¡1,L2 +Q2k,L2 ¢Q2k¡1,L2):

(5)

Finally, the last method is named NCDiffL1L2 andis the summation of the noncoherent and differentialacquisitions on L1 and L2. Its mathematicalrepresentation is

SNCDiffL1L2 =

266664MXk=1

(I2k,L1 +Q2k,L1)

+

MXk=2

(Ik,L1 ¢ Ik¡1,L1 +Qk,L1 ¢Qk¡1,L1)

377775

+W2 ¢

266664MXk=1

(I2k,L2 +Q2k,L2)

+

MXk=2

(Ik,L2 ¢ Ik¡1,L2 +Qk,L2 ¢Qk¡1,L2)

377775 :(6)

The difference between the differential methods

DiffL1L2 and NCDiffL1L2 is that DiffL1L2 uses only

independent correlator outputs during the differential

summation, whereas NCDiffL1L2 uses dependent

correlator outputs during the differential summation

[see indices of (5) and (6)].

B. Theoretical Performance

The following section develops the theoretical

probability density functions under the hypotheses

H0: signal is not present

H1: signal is present

Note that in the following, the cell probabilities

are discussed. Indeed, the cell probabilities strongly

depend on the acquisition method used [14] as

well as the signal fading condition [15]. The

probability density functions derived are then used

in Section IVD to derive the probabilities of false

alarm and detection as well as the ROC used to

evaluate the performance of each method. Based on

(3), the correlator outputs for L1 C/A and L2C can be

expressed as

Ik,L1L2 = A1=2(k) ¢ cos(¼¢F1=2T(2k¡ 1)+Á1=2) +wIk,L1L2Qk,L1L2 = A1=2(k) ¢ sin(¼¢F1=2T(2k¡ 1)+Á1=2) +wQk,L1L2

(7)

with A1=2(k) = (A1=2=p2)d1=2(k) ¢R(dt1=2) ¢

(sin(¼¢F1=2T)¼¢F1=2T), wIk,L1 » wQk,L1 »N(0,¾2), and

wIk,L2 » wQk,L2 »N(0,2¾2).Note that all the noise components are

uncorrelated and that L2C noise variance is twice that

of L1 because the CL code is ignored.

1) NCL1L2 Method:

a) Under H0: The probability density function

(PDF) of the NCL1L2 method under H0 can be

expressed as a summation of independent chi-square

random variables [16] as

p(s) =

266641

2¾2exp

³ ¡s2¾2

´1

(M ¡ 1)!

μ¾2

¾2¡¾22

¶M¢M¡1Xi=0

(2(M ¡ 1)¡ i)!i!(M ¡ 1¡ i)!

μ¾22

¾22 ¡¾2¶M¡1¡i³

s

2¾2

´i37775

+

266641

2¾22exp

μ ¡s2¾22

¶1

(M ¡ 1)!

μ¾22

¾22 ¡¾2¶M

¢M¡1Xi=0

(2(M ¡ 1)¡ i)!i!(M ¡ 1¡ i)!

μ¾2

¾2¡¾22

¶M¡1¡iμs

2¾22

¶i37775(8)

with ¾22 = 2 ¢W2 ¢¾2. The NCL1L2 characteristicfunction under H0 is

ªS(!) =

μ1

(1¡ 2j!¾2) ¢ (1¡ 2j!¾22)¶M

: (9)

b) Under H1: From the previous discussion, one

can deduce that the PDF of the NCL1L2 under H1 is a

CORRESPONDENCE 2241

Page 4: Assessing Three New GPS Combined L1/L2C Acquisition Methods

summation of two independent noncentral chi-squarevariables:

p(s) =1

2¾2

μ¾

¾2

¶2Mμs

¸1

¶M¡1=2exp

μ ¡s2¾2

¶¢ exp

μ¡1=2

μ¸1¾2+¸2¾22

¶¶

¢1Xi=0

1Xl=0

2666664¡ (M + i+ l)

i!l!¡ (M + l)

à ps¸2¾

2

2p¸1¾

42

!l

¢Ãp

s(¾22 ¡¾2)p¸1¾

22

!iI2M+i+l¡1

Ãps¸1

¾21

!3777775

(10)with ¸1 =

PMk=1A1(k)

2 ¼ (M ¢A21=2) and ¸2 =PMk=1A2(k)

2 ¼ (M ¢A22=2) and assuming that ¢F, dt1,and dt2 are small. The NCL1L2 characteristic functionunder H1 is

ªS(!) =

μ1

(1¡ 2j!¾2)(1¡ 2j!¾22)¶M

¢ expμ

j!¸11¡ 2j!¾2

¶¢ exp

μj!¸2

1¡ 2j!¾22

¶:

(11)

2) DiffL1L2 Method: The following derivationis based on the one-frequency-only differentialacquisition from [17].a) Under H0: The PDF under H0 for the DiffL1L2

method is expressed as

fS(s) =

KXi=1

2¡i+1=2kski¡1=2p¼ ¢¡ (i)

2664 aK,i¾¡(2i+1)K(i¡1=2)

μktk¾2

¶+bK,i¾

¡(2i+1)2 K(i¡1=2)

μktk¾22

¶3775(12)

where ¡ is the Gamma function, K is the modifiedBessel function of the second kind, and thecoefficients aK,i and bK,i can be determined using thefollowing recurrence relationship (where ± representsthe Dirac function) derived similarly to that in [18]:

aK,K¡i = μ1aK¡1,K¡i¡1 + μ2aK,K¡i+1 +BK¡1,i(13)

bK,K¡i = μ2bK¡1,K¡i¡1 + μ1bK,K¡i+1 +AK¡1,i(14)

AK¡1,i =

"K¡1Xn=1

μn+12 aK¡1,n

#±(i¡K +1) (15)

BK¡1,i =

"K¡1Xn=1

μn+11 bK¡1,n

#±(i¡K +1) (16)

μ1 = a1,1 =¾2

¾2¡¾22(17)

μ2 = b1,1 =¾2

¾22 ¡¾2: (18)

The characteristic function of DiffL1L2 under H0can be derived based on [16]:

ªS(!) =

μ1

1+¾4!2¢ 1

1+¾42!2

¶M=2: (19)

b) Under H1: A closed form solution for thePDF of SDiffL1L2 was not determined. Its characteristicfunction was used instead to derive the probabilityof false alarm and detection of the DiffL1L2 method.Assuming that the Doppler removal process isperformed perfectly or that the Doppler residual issimilar from one coherent integration to the nextand that the data bit remains unchanged during theacquisition period, one can show using [16] that

ªSDiffL1L2 (!) =ªSIL1+SQ

L1

(!) ¢ªSIL2+S

Q

L2

(!)

=

·1

(1+¾4!2)(1+¾42!2)

¸M=2¢ exp

"j! ˆ 1¡ ˆ 1¾2!22 ¢ (1+¾4!2) +

j! ˆ 2¡ ˆ 2¾22!22 ¢ (1+¾42!2)

#(20)

with ˆ 1 = (M ¢ A21=2) and ˆ 2 = (M ¢ A22=2).At this point, the characteristic function of SDiffL1L2

can be used to numerically determine its probabilitydensity function using the following property of thecharacteristic function:

fSDiffL1L2 (s) =1

Z +1

¡1ªSDiffL1L2 (!) ¢ ej!sd!: (21)

The numerical inverse Fourier transform involvedin (21) was done following the method proposedby [19].3) NCDiffL1L2 Method: Defining

XL1 =

266666666666666666666666666666666666664

I1,L1

Q1,L1

I1,L1 + I2,L1

Q1,L1 +Q2,L1

...

...

Ik,L1 + Ik+1,L1

Qk,L1 +Qk+1,L1

...

...

IM¡1,L1 + IM,L1

QM¡1,L1 +QM,L1

IM ,L1

QM,L1

3777777777777777777777777777777777777752242 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 3 JULY 2011

Page 5: Assessing Three New GPS Combined L1/L2C Acquisition Methods

and

XL2 =W ¢

266666666666666666666666666666666664

I1,L2

Q1,L2

I1,L1 + I2,L2

Q1,L1 +Q2,L2

...

...

Ik,L2 + Ik+1,L2

Qk,L2 +Qk+1,L2

...

...

IM¡1,L2 + IM,L2QM¡1,L2 +QM,L2

IM,L2

QM ,L2

377777777777777777777777777777777775the mathematical representation of the output of the

NCDiffL1L2 becomes

SNCDiffL1L2 =12XTL1XL1 +

12XTL2XL2: (22)

Note that the vectors XL1 and XL2 are independent.

Moreover, as the covariance matrix CXL1 of XL1is a (2 ¢M +2)£ (2 ¢M +2) real symmetric matrix,

it is possible to decompose it using eigenvector

decomposition. The matrix of eigenvectors is then

orthogonal. The aforementioned properties of a real

symmetric matrix are summarized for XL1 and CXL1through

CXL1 =QDL1QT (23)

QT =Q¡1: (24)

When projecting XL1 in the orthogonal basis

defined by Q, the resulting vector YL1 has a diagonal

covariance matrix. Moreover, the norm of YL1 is equal

to the norm of XL1.

A similar derivation can be performed for XL2.

YL1 and YL2 are independent of each other and the

elements composing YL1 or YL2 are independent

between themselves (both vectors having a diagonal

covariance matrix). Moreover, the variance of the

elements of YL1 and YL2 are the elements located on

the diagonal of DL1 and DL2, respectively.

After this development, the characteristic functions

of SNCDiffL1L2 can readily be determined.

a) Under H0: SNCDiffL1L2 is the summation of

(4 ¢M +2) central chi-square random variables with

one degree of freedom. Its characteristic function is

expressed as

ªS(!) =

2M+1Yi=1

μ1

1¡ 2j!DL1(i)

¶1=2μ1

1¡ 2j!DL2(i)

¶1=2:

(25)

DL1(i) represents the ith element of the diagonal of

DL1.

b) Under H1: SNCDiffL1L2 is the summation of

(4 ¢M +2) noncentral chi-square random variables

with one degree of freedom and noncentrality

parameters the square of the mean of the elements of

YL1 and YL2. Its characteristic function is expressed as

ªS(!) =

2M+1Yi=1

μ1

1¡ 2j!DL1(i)

¶1=2¢ exp

μj! ¢ YL1(i)2

1¡ 2j!DL1(i)

¢2M+1Yi=1

μ1

1¡ 2j!DL2(i)

¶1=2¢ exp

μj! ¢ YL2(i)2

1¡ 2j!DL2(i)

¶:

(26)

Once the PDFs and characteristic functions of

each method have been theoretically computed, it is

possible to determine the theoretical probabilities of

false alarm and detection. The theoretical results are

verified using real data, and the performance of each

method is discussed.

IV. RESULTS

A. Correlator Outputs from Real Data

The two signals were collected using a L1/L2

antenna and passed through a variable attenuator. The

signals were then split between a L1/L2 RF front end

and a GPS L1/L2 industrial receiver used for C/N0reference. The C/N0 on L1 during the data collection

was 30 dB¢Hz. Finally, the L1/L2 IF signals werestored on the PC performing the acquisition methods.

B. ROC Curves, Comparison, and Analysis

The ROC curve is defined as the probability of

detection Pd as a function of the probability of false

alarm Pfa. In the specific case investigated here, the

probability of detection is defined as the probability

of detecting the presence of the signal under the H1hypothesis. The probability of false alarm is defined

as the probability of detecting the presence of the

signal under the hypothesis H0.

In the following, the coherent integration length

considered is 1 ms and the number of coherent

integrations needed to combine is M = 4.

Prior to any analysis, the optimal weight W

applied on L2 must be determined for each method.

To do so, the probability of detection for a fixed

probability of false alarm of 0.005 was computed for

a set of weight values ranging from 0 to 1. Indeed,

because the signal power and noise variance are

larger on L2 and the weight applied on L1 is 1, it is

CORRESPONDENCE 2243

Page 6: Assessing Three New GPS Combined L1/L2C Acquisition Methods

Fig. 1. Theoretical and “real data” estimated ROC curves for NCL1L2.

Fig. 2. Theoretical and “real data” estimated ROC curves for DiffL1L2.

expected that the weight to apply on L2 would be

smaller than 1. The optimal weight found is similar

for each method and has a value of 0.55.

Once the optimal weight was determined, the

performance of each method is investigated through

comparison of its ROC curve with the ROC curves of

a noncoherent acquisition on L1, only using the same

number of milliseconds. Because the signal power on

L2 is smaller than on L1, it is expected that the ROC

curves on a noncoherent acquisition on L2 will show

poorer performance than a noncoherent acquisition

on L1. However, it is still shown here to underline

the improvement brought by an L2-only acquisition,

which is most interesting because it removes the need

for data bit synchronization on L2 and also on L1.

Figs. 1—4 show the ROC curve and ROC curve

differences with a noncoherent summation performed

on L1 only for each method.

2244 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 3 JULY 2011

Page 7: Assessing Three New GPS Combined L1/L2C Acquisition Methods

Fig. 3. Theoretical and “real data” estimated ROC curves for NCDiffL1L2.

Fig. 4. Difference between new methods ROC and ROC obtained for noncoherent acquisition on L1 only using real data.

Note that because the Doppler residual was kept

low (about 30 Hz) during the creation of the correlator

outputs, the DiffL1L2 theoretical ROC matches the

ROC obtained with real data very well even though

the Doppler residual was ignored in the theoretical

development. Because one tries to maximize the

probability of detection while minimizing the

probability of false alarm, the fact that the ROC curve

of the DiffL1L2 method passes under the ROC curve of

the L1 noncoherent acquisition has no impact on the

validity of this method.

From the figures, it is clear that each combining

method outperforms the noncoherent acquisition on

L1 only. Moreover, when used to determine the ROC

curves, the theoretical models developed matches

properly the estimated ROC obtained through real

data. Finally, NCDiffL1L2 not only outperforms the

noncoherent acquisition performed on L1 only but

CORRESPONDENCE 2245

Page 8: Assessing Three New GPS Combined L1/L2C Acquisition Methods

also the two other L1/L2 combining acquisition

proposed as shown in Fig. 4.

V. CONCLUSIONS

By combining the GPS signals transmitted on the

L1 and L2 frequency bands, one cannot only profit

from the advantages of L1 (higher signal power) and

L2 (no need for data bit synchronization) but also

improve overall detection capability compared with

using only one signal. Three methods were proposed

to combine L1 C/A and L2C signals at the acquisition

level and all proved to outperform the legacy L1 C/A

noncoherent acquisition. The first method, NCL1L2,

combining the noncoherent acquisition on L1 and

L2, shows promising performance when the proper

weight is applied. An improvement of 8% compared

with the standard noncoherent acquisition on L1 only

was observed. Similarly, for the NCDiffL1L2 method,

combining noncoherent and differential acquisitions

on L1 and L2 significantly improved the probability

of properly detecting the signals. An improvement of

25% is expected for the NCDiffL1L2 method. While

not shown in the earlier discussion, the DiffL1L2method combining differential acquisitions performed

on L1 and L2 is strongly dependent on the residual

Doppler frequency remaining after the Doppler

removal process. Poor performance has been observed

when the residual Doppler error varies over the whole

range of half a Doppler bin size defined by a 1-ms

coherent integration (0—333.33 Hz). However, by

limiting the Doppler error to 100 Hz, performance is

greatly improved and the DiffL1L2 method showed an

improvement of 15% compared with the noncoherent

L1 acquisition. Because limiting the Doppler bin

size allows for increased coherent integration times,

the DiffL1L2 is recommended for longer coherent

integration. Indeed, 2 ms of coherent integration

proved to reduce the range of the residual Doppler

error such that the DiffL1L2 method is no longer

negatively affected by this error. Finally, while the

NCDiffL1L2 method outperforms the noncoherent L1

acquisition, it also shows better performance than the

other two combining methods. However, because of

its complexity compared with the NCL1L2 method, one

would employ it only when appropriate computational

power is available.

CYRILLE GERNOT

KYLE O’KEEFE

GERARD LACHAPELLE

Position, Location and Navigation (PLAN) Research Group

Dept. of Geomatics Engineering

University of Calgary Schulich School of Engineering

2500 University Drive NW

Calgary, Alberta, T2N 1N4

Canada

E-mail: ([email protected])

REFERENCES

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Magnetically Jointed Module Manipulators: NewConcept for Safe Intravehicular Activity in SpaceVehicles

Robots for intravehicular (IVA) support are being studied for

their potential to reduce the workload of astronauts. IVA support

robots must meet strict safety requirements, and they need to be

compact to share limited room with astronauts. A magnetically

jointed module manipulator (MagMo) solves these problems in a

unique manner. The manipulator is not harmful when it contacts

humans unexpectedly, because it disassembles by contact force,

and it can be easily assembled only when it is needed. In this

paper, the basic concept of the MagMo is introduced.

I. INTRODUCTION

About 50 years have passed since the first

human space flight. Manned space utilization is

becoming a mature endeavor, partly because of the

establishment of manned space infrastructure. The role

of the International Space Station (ISS) has steadily

increased, and it has become an established space

base for various types of experiments that may lead

to further space utilization. The Japanese Experiment

Module was attached successfully to the ISS in 2008.

It contains various types of equipment and is ready to

begin operation as part of the space infrastructure.

Astronauts must perform diverse tasks, including

housekeeping tasks to maintain their space vehicle,

as well as different types of experiments. Reducing

and optimizing the astronauts’ workload is a focus

of interest so that a manned space system can be

operated more effectively. A substantial number of

astronaut tasks are simple and do not require the

astronauts’ intelligence.

It has been proposed that robots may be used to

reduce the astronauts’ workload. An autonomous

robot could perform a simple repetitive task that

would not require intelligence. Furthermore, a

teleoperated robot may be able to handle unexpected

situations with the support of ground personnel.

However, even though some functions can be

performed by teleoperations, these robots would

Manuscript received October 3, 2008; revised January 28, 2010;

released for publication September 20, 2010.

IEEE Log No. T-AES/47/3/941797.

Refereeing of this contribution was handled by R. Michelson.

Authors’ addresses: Tokyo University of Science, 2641 Yamasaki,

Noda, Chiba 278-8510 Japan, E-mail: ([email protected]).

0018-9251/11/$26.00 c° 2011 IEEE

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