Precise point positioning for mobile robots (797945), страница 2

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CSKmodulation shifts the phase of the LEX code by the number ofchips indicated in the 8-bit encoded message symbol. The ideaproposed in this paper is to decode the LEX messages withoutthe LEX signal tracking loop for estimating the code phase andDoppler frequency of the LEX signal, but with the aid of theconventional L1CA signal simultaneously broadcasted fromthe QZSS. Fig. 3 illustrates the LEX decoding algorithm basedon the L1CA signal. This algorithm requires a code phase andDoppler information computed by the L1CA signal trackingresult to extract the QZSS LEX message.

The algorithm wasexecuted as follows:(i) Acquisition and tracking of the QZSS L1CA signalwere performed. In the signal acquisition, a circularcorrelation based on the fast Fourier transform (FFT) was usedto estimate the rough Doppler frequency and rough codephase of the L1CA signal. In the tracking process, the accurateDoppler frequency and code phase were continuouslyestimated every 1 ms using the frequency lock loop (FLL),phase lock loop (PLL), and delay lock loop (DLL).

During thistime, the LEX code phase, which occurs every 4 ms, wasunknown.(ii) Synchronization of the navigation bit overlaid in L1CAcode was performed. If the navigation bit is synchronized, theambiguity of the LEX code phase (nonshifted phase) can beresolved. We then estimated the LEX Doppler frequency usingthe L1CA Doppler frequency.

The code phase and Dopplerfrequency of the LEX signal were denoted using the L1CAsignal as follows:C LEX = C L1CA + ε(1)d LEX = d L1CA f LEX f L1CA(2)where CL1CA and CLEX are the code phases, dL1CA and dLEX arethe Doppler frequencies in L1CA and LEX, and fL1CA and fLEXare 1575.42 and 1278.75 MHz, respectively.

The variable ε isthe differential code bias (DCB) between QZSS L1CA andLEX signals, and it can be calibrated in advance.′(iii) The LEX code phase (shifted phase) C LEXwasestimated using FFT based on the circular correlationtechnique. The LEX message symbol L can be calculated usingthe nonshifted code phase and estimated code phase using thefollowing equation:′L = N LEX + C LEX − C LEXwhere NLEX = 10,230 was the number of chips of LEX code.370(3)4ms1.2Normalized Power(iv) The error of the estimated message symbol wascorrected by the Reed-Solomon code.

On the basis of theabove, the GPS satellite ephemeris error and clock error canbe extracted from the LEX message using the software GNSSreceiver, without tracking the LEX code.10.80.60.40.203.64GNSS Front End1.2LEX Code PhaseEstimation using FFTSignal AcquisitionInitial Code PhaseInitial Doppler FrequencyCode Phase Doppler Frequency3.6753.683.693.685x 10LEX code phase10230-N byte3.643.6453.653.6553.663.6653.6725From these tests, it was concluded that it is possible todevelop a method to receive the QZSS LEX message using thesoftware GNSS receiver. In the following section, we describethe real-time kinematic PPP that uses the QZSS LEXmessages.Figure 4. Set-up of software GNSS reciver.3.673.6753.683.693.6857x 102025QZSS Elevation AngleLEX Decoding Errors 20151510105500500100015002000Epoch Number2500300003500Figure 6. Relationship between QZSS elevation angle and LEX messagesymbol decoding errors.IV.

PPP WITH LEX MESSAGEThe PPP was introduced by Zumberge et al. as an efficientand robust analysis technique for large GPS receiver networks[6]. PPP can estimate a single receiver position without anyreference station or baseline by fixing satellite positions andclocks to previously determined values. In addition, allpositions are related to a well-defined geodetic datum which isvalid globally. The International GNSS Service (IGS) providesaccurate and high-quality products, including GPS satelliteorbits and clocks, based on the post-mission analysis ofobservations at more than 300 permanent stations worldwide.Furthermore, PPP can be used for high-precision positioningwithout any baseline length limitation.

For these reasons, PPPis anticipated to be a useful and efficient means of localizingmobile robots.For the purpose of the real-time application, there was aquestion of how to get the precise satellite ephemeris andclock to process the PPP. As already mentioned, we used theQZSS LEX signal in this study as the precise ephemeris andclock source using the software receiver. By obtaining theprecise satellite ephemeris and clock from positioning satellitesusing the GNSS receiver, then applications can easilydetermine the high-precision position without any datacommunication. QZSS is suitable for broadcasting the3717LEXFigure 5.

Code phases of L1CA and LEX signals obtained by the proposedmethod.C. ExperimentWe conducted initial tests to evaluate the decoding part ofthe proposed method, using the test setup shown in Fig. 4. Weused a front end (NSL Stereo, UK), GNSS antenna (TrimbleZephyr Model 2, US), and a laptop PC to receive and decodethe LEX message.

Fig. 5 shows the estimated L1CA and LEXcode phases. We computed the LEX message symbol bytaking the difference between the L1CA code phase and LEXcode phase in Fig. 5. The decoding error rate for the LEXmessage was evaluated using the Reed-Solomon errorcorrection code. Fig. 6 shows the relationship between theQZSS elevation angle and the decoded symbol errors. Whenthe number of symbol errors is less than 16, the error can becorrected by the Reed-Solomon code. In this test, the correctLEX message was received when the QZSS elevation anglewas over 13°.

In general GNSS positioning, a 15° elevationmasking is usually used. For this reason, the QZSS elevationangle presented little problem for the GNSS positioning.Laptop PC3.665IF Sample [sample]IF Sample [sample]Figure 3. Flowchart of LEX message extraction aided by L1CA trackingusing software GNSS receiver.Front End(NSL STEREO)3.660.2GPS Clock ErrorEphemeris ErrorGNSSAntenna3.6550.40Reed-Solomon ErrorCorrectionDLL3.65DopplerCode phase0.6Number of Decoding ErrorsPLL10.8LEX MessageComputationSignal TrackingFLLNormalized PowerLEX3.645QZSS Elevation Angle degL1CAL1CA1msaugmentation information because QZSS has a high elevationangle, and it is visible over long periods in Japan.user position rr were estimated simultaneously by the extendedKalman filter (EKF) in this study.We developed the PPP technique based on the QZSS LEXmessages.

In the first step, precise satellite clocks andephemeris were used for correcting the GNSS observations.The GNSS carrier-phase observation was then modeled by Eq.(4) as follows:The state vector x of EKF for state k is denoted as follows:φ = r + I + T + c(dt − dT ) + N + εIn conventional RTK-GPS, the double-differencetechnique can be applied to cancel out most of the correlatederrors in observations. In contrast, PPP uses the observableionosphere-free linear combination (LC) of the dual-frequencycarrier-phase GPS to estimate the user position.

Using theionosphere-free LC, the ionosphere delay can be completelycancelled. The ionosphere-free LC of the dual-frequencycarrier-phase GPS observables was expressed as follows [14]:f1φ1 − f 2φ 2= r + T + c(dt − dT ) + N IF + ε IFf12 − f 22dtN 1IFZTDn N IF]T(7)Here, rr is the 3-D position vector, and n denotes thenumber of satellites. In the EKF prediction step, the equation(4) of state at prediction was as follows:Here φ denotes the carrier phase measurement; r, thegeometric satellite-to-receiver distance; I, the ionosphericdelay; T, the tropospheric delay; c, the velocity of light; dt, theclock bias of the receiver; dT, the clock bias of the satellite; N,the carrier-phase integer ambiguity; and ε, the measurementerror including the multipath effect.φ IF = c[x k = rrT[x k |k −1 = rrT0dt 0ZTDk −1nN 1IFk −1  N IFk−1]T(8)Where the suffix k|k−1 denotes state k predictionsestimated from the k−1 state. The variables rr0 and dt0 are thereceiver position and clock error that are calculated by thesingle-point positioning.

In the kinematic PPP, the receiverposition was reset to the single-point positioning solution inevery epoch.In the EKF observation step, the GPS observation vectorsare denoted as follows:[1z k = φ IF φ IFn]T(9)where φ IF is the ionosphere-free LC carrier phase in Eq. (5).The observation matrix H is denoted by the following(5) equation:where subscripts 1 and 2 refer to the L1 and L2 frequencies,respectively; φIF, the carrier phase of the ionosphere-free LC;ΝIF, the carrier-phase integer ambiguity of ionosphere-freeLC; and εIF, the measurement error, including the L1 and L2multipath effects.Here, the clock bias dT of the satellite can be calculatedfrom the broadcasted clock and LEX clock error information.Once the low-rate clock errors are obtained, higher rate valuescan be acquired by a simple linear interpolation, wherein theyare assumed to be stable for a short period.

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