Robust Multi-Carrier, Multi-Satellite Vector Phase Locked Loop with Wideband Ionospheric Correction and Integrated Weighted RAIM

Current GNSS receivers have independent Phase Locked Loops (PLLs) for each satellite and frequency. The introduction of new GPS signals on L5 and the development of new satellite constellations (Galileo, Compass) increases the number of PLLs and, thus, the probability of a loss of lock of one PLL. This probability becomes especially critical during ionospheric scintillations with frequent deep amplitude fades of more than 20 dB. The outage of a PLL on one frequency prevents the computation of an ionosphere-free combination at this instant, and thus, degrades the positioning accuracy. Therefore, a Multi-Carrier, Multi-Satellite Vector-PLL (MC-MS-VPLL) has been recently suggested to improve both accuracy and robustness of carrier tracking. The individual PLLs are coupled by transforming the tracking errors at the discriminator outputs into a position drift, a clock drift, ionospheric drifts and tropospheric drifts. These quantities are fed into loop filters whose bandwidths are adapted to the dynamics of the receiver, of its clock and of the atmospheric delays. The MC-MS-VPLL assigns a low weight to satellites during deep amplitude fades and a high weight for a high power level. This enables robust carrier tracking even during severe ionospheric scintillations as the stronger signals are helping to track the weaker signals. There exist two threats of a MC-MS-VPLL that are addressed in this paper: The first one is ionospheric dispersion within the wideband Galileo E5 signal (51 MHz bandwidth) which causes ripples in the code signal and a power shift in correlation result from the real part to the imaginary part. If no wideband correction is applied, the phase tracked by an independent PLL is biased by 14 for 100 TECU, and this bias can not be mapped to the ionospheric delay tracked by a MC-MS-VPLL. A correction term is derived for the mitigation of these wideband ionospheric effects. Secondly, the joint tracking means that any failure on one or more satellites or frequencies (e.g. phase jump on satellite clock, low elevation multipath) affects the tracking of all satellites and frequencies. A Receiver Autonomous Integrity Monitoring (RAIM) is integrated into the MCMS-VPLL to detect and exclude severely biased satellites from the joint tracking. The weighted sum of squared error test statistic is computed from the carrier tracking errors given by the discriminator outputs. INTRODUCTION The joint tracking of all satellites goes back to Spilker who has proposed a Vector Delay Locked Loop (DLL) for code delay tracking in [1]. The tracking errors were originally transformed into a position drift and a clock drift by weighted least-square estimation which does not consider ionospheric and tropospheric delays and other biases like multipath as individual parameters. The benefit of the VDLL is the adaptive weighting of satellites, i.e. the stronger signals help to track the weaker signals. The vector tracking of carrier phase is more challenging due to its higher precision and the existence of an unknown integer ambiguity for each satellite and frequency. Zhodzishsky, Yudanov, Veitsel and Ashjaee have first applied vector tracking to carrier phase in [2]. The tracking errors at the discriminator outputs were transformed into position errors and clock drifts by weighted least-square estimation. The atmospheric delays were not considered as individual parameters in the filtering which motivated Zhodzishsky et al. to use both individual and joint loop filters, and to combine both results in the oscillators. They attempted to separate the parameters by different filter bandwidths, i.e. a large bandwidth was chosen for the position and clock filters due to its higher dynamics and a small bandwidth was selected for the individual loop filters. However, the atmospheric errors are also present in the position and clock filters, and the position and clock drifts also occur to a certain degree in the individual filters. Consequently, this “Co-Op tracking” reduces the tracking error of an individual PLL but is still sub-optimal as the physically different error sources are not completely separated. In the MC-MS-VPLL of [3], the authors have coupled individual PLLs by transforming the tracking errors of the discriminator outputs into a position drift, a receiver clock drift, ionospheric delay drifts and a tropospheric zenith delay drift. These quantities are fed into loop filters whose bandwidths are adapted to the dynamics of the receiver, of its clock and of the ionospheric and tropospheric delays. Note that the MC-MS-VPLL is not limited to measurements from a single constellation. The joint tracking of satellites from multiple constellations further improves the tracking performance as position drift, clock drift and tropospheric zenith delay drift are equal for all constellations. The MC-MS-VPLL can also be extended to include measurements from several antennas. The objectives of this paper are two-fold: First, two strategies are proposed to mitigate the wideband ionospheric effects that have been analysed by Gao et al. in [4]. Both require an estimate of the ionospheric delay which is not biased by wideband ionospheric effects. The ionospheric dispersion within the E5 band results in a complex correlation result which shifts the phase but does not cause an additional delay in the estimated code delay. Thus, the intra-band ionospheric dispersion differs from the classical code-carrier divergence which motivates the computation of the ionospheric delay from a linear combination of code measurements. The estimated ionospheric delay at a given reference frequency enables the computation of a phase shift for each frequency, and thus the equalization of wideband ionospheric effects in frequency domain. This method requires an FFT of the downconverted signal and an IFFT after the application of the wideband correction. Alternatively, the phase correction can be determined from a look-up table and applied before the tracking, which improves the efficiency of the first method as it does not require the FFT and IFFT. It is shown that the phase correction increases linearly with the TEC, and that the gradient of the phase correction w.r.t. TEC equals 8/100 TECU for a bandwidth of 30 MHz and 14/100 TECU for a bandwidth of 50 MHz. These rather low gradients indicate that a rough estimate of TEC (+/-5 TECU) is sufficient to correct wideband ionospheric effects. The second threat of a VPLL (multipath and other failures affecting a subset of satellites or frequencies) requires the integration of a fault detection method. The weighted RAIM of Walter and Enge [5] has been chosen due to its efficiency. Large phase jumps on one or more satellites result in an unstable behaviour of the MC-MS-VPLL as the phase errors can not be mapped into one of the tracked parameters (position, clock drift, ionospheric and tropospheric delays). Another error might occur in the weighting matrix which partially compensates the gain obtained from the joint tracking. It is shown that the MC-MS-VPLL achieves a lower tracking error than independent tracking loops even if the low elevation satellites suffer from an up to five times larger standard deviation than considered in the weighting matrix. For fault detection, a Weighted Sum of Squared Error (WSSE) test statistic is computed from the range residuals using the discriminator outputs. This WSSE is related to the average WSSE in the absence of biases, e.g. due to multipath. The ratio is called WSSE amplification due to multipath and it enables the detection of a failure if a predefined threshold is exceeded. It is shown that the WSSE is very sensitive to multipath and that the WSSE amplification is substantially larger than the amplification of the standard deviation of the estimated phase. Therefore, a failure can already be detected when the benefit of joint tracking is still larger than the degradation due to an erroneous weighting matrix. WSSE amplification of up to 100 has been observed for severe multipath from a single reflector. Moreover, protection levels are computed from the discriminator outputs in the presence of multiple biases. The HPL and VPL depend on the largest position biases that do not exceed the threshold of the WSSE test statistics for a given probability of false alert. PRINCIPLES OF VECTOR PHASE LOCKED LOOP Fig. 1 shows the functional diagram of a MultiCarrier Single-Satellite (MC-SS)-VPLL. The received signal rm(ti) on frequencym ∈ {1, . . . ,M} at time instant ti is modeled in baseband as rm(ti) = x(tm − τm) · emi + ηm(ti), (1) with the code signal x(tm − τm), the code delay τm, the received phase φm(ti) and the noise ηm(ti). The received signal is multiplied by the oscillator generated signal emi, and correlated with a local copy of the code signal x(tm − τm). The non-linear discriminators (see Kaplan and Hegarty [6]) extract the carrier tracking errors ∆φm(ti) = φm(ti) − φm(ti) from the correlation result. The tracking errors are modeled as