The global navigation satellite system (GNSS) antenna plays an important role in the positioning output of any GNSS engine. A poor GNSS antenna can pull down the positioning capabilities of any high-end GNSS receiver software. When it comes to the acquisition of one single frequency from GNSS satellites, the design of an antenna doesn’t seem to be complex. But, when it comes to design an antenna, which can receive multiple frequencies in a degraded environmental condition with a well defined phase center, the GNSS antenna design can be cumbersome. Additionally, the size of the antenna is based on hardware limitations and elevation cut-off capabilities to minimize multipath does no good to the situation, which clearly impacts the most largest user class of GNSS: smartphones [1, 2]. A very promising approach to improve the performance of these small antennas is exploit the user motion to realize a larger antenna aperture [3, 4]. However, this approach is extremely complex as the antenna motion has to reconstructed with high accuracy, the clock jitter during the beamforming has to be estimated precisely and proper beamforming strategies need to be selected. All those algorithms shall work with small antenna elements, low-quality oscillators, in urban environments and finally deliver code and carrier measurements that allow to compute an real time kinematics (RTK) fixed solution. We are in the process of developing an tailored software receiver that shall accomplish this task and shall allow to get full insight into the whole processing flow. The receiver itself, including generation of an inertial measurement unit (IMU) based trajectory to capture the antenna motion has been described in [5, 6] showing its capability to deliver precise observations. In [7] the way of estimating the receiver clock jitter from all channels (Co-Op clock tracking loop) is outlined.
Connecting a mass-market low-cost antenna to a GNSS software defined radio (SDR) gives the possibility to influence the whole tool chain. For this reason, we developed a flexible MATLAB-based GNSS receiver (MSRx), which was already presented in previous publications [5–7] and uses precomputed multi-correlator values to speed-up processing and allow a simpler handling of multiple frequencies and constellations within the Matlab framework. In 2022, we reported the status of the MSRx, where inertial navigation system (INS) aided tracking loops have been implemented and validated with real satellite signals. This kind of aiding technique enables to reduce the dynamic of the hosted vehicle from the tracking channels while narrowing the phase locked loop (PLL) bandwidth, i.e. from 9 Hz to e.g 0.1 Hz, which improves tracking sensitivity considerably. In addition to that, multipath is averaged out due to the low loop bandwidth. This concept is very similar to synthetic aperture processing (SAP), where correlation values are projected onto the line-of-sight (LOS) motion in order to purify the correlation values from multipath (i.e. beam-forming in LOS-direction). But such ulra-low bandwidth PLL (ULB-PLL) requires a good oscillator or a cooperative tracking loop (Co-Op) to estimate the receiver clock jitter. In [7] we show the extension of the MSRx to a multi-system and multi-frequency L1/L5 E1/E5a capable deeply coupled GNSS/INS receiver including a Co-Op tracking loop to estimate the receiver clock. Hereby, the receiver clock estimate is realized using a second order clock locked loop (CLL), similar to a PLL or DLL, which takes as input timely synchronized and averaged carrier discriminator values. The in-place receiver clock estimate allows to remove the receiver clock instantaneously inside the PLL. So far, the MSRx receiver was tested with real satellite signals collected during a kinematic vehicle trajectory in Neubiberg, Germany. The corresponding dataset, is called UniBw M-dataset and still not open for public use. As stated before, with our dataset, we were able to achieve RTK-cm accuracy, albeit not all carrier-phase ambiguities could solved, i.e., approx. 15%. The potential error sources that caused this (reminder) float solution have different origins. For instance, the reference trajectory used to generate to Doppler Aiding signals, could attain the tracking loops with time delay, due some buffer issue in the hardware. An other fragile parameter that has to be considered is the lever-arm between the GNSS antenna phase center (APC) and the IMU center of gravity (CoG), as we are targeting a reliable cm-accuracy. It is therefore worth, to look back on the impact of these particular parameters in well controlled signal conditions, which can be realized by a simulation scenario. To this end, based on a kinematic trajectory with moderate dynamic (see Fig. 1), IF samples for dual-frequency multi-GNSS have been simulated. Additionally, IMU observations at 100 Hz sampling rates for the same trajectory were generated with zero time delay, i.e., GPS time stamp, w.r.t. the IF samples stream to compute the external Doppler-aiding information for the MSRx. To validate our implemented Co-Op tracking of the receiver oscillator, both clock bias and drift were simulated as sine and cosine oscillation with an amplitude of 10^-9 s and 10^-9 s/s and a frequency of 0.2 Hz which enables, an ”input-output” closed-loop control of the clock jitters estimation over all tracked channels. A number of improvements of the ULB-PLL have been developed, implemented and tested, since our last publications [7]. This includes monitoring of the ULB-PLL, outlier detection and consistency checks, smoothing methods at loop bandwidth switches, parameter tuning and several bug-fixes of the CLL, an elevation and C/N0 cut-off for satellites for the CLL as well independent Doppler aiding of the DLL in addition to the PLL. Furthermore, it is was an important step to improve the plotting tools such that environmental effects, systematic errors and algorithmic impacts could be identified and understood on carrier phase level, which is fundamental when developing the method. We found that this operational improvements had a huge impact on the finally achieved performance. We introduce a new key performance indicator (KPI) to measure the performance of the ULB-PLL. Previously, the RTK fixing rate was analyzed, but as this KPI has a binary character (either near 0 % or near 100%) we consider now the RMS of the carrier residuals (modulo the wavelength) from a float RTK solution, which provides a more consistent KPI to measure the ULB-PLL performance. We are able to link phase residuals to PLL discriminator time series thereby understanding specific limitations of the algorithm or environment. Assuming the GNSS and inertial sensor share the same origin, i.e., lever-arm is neglected, the evaluation of the simulated dataset with activated external Doppler-aiding for the PLL tracking loops and Co-Op tracking delivers RTK-cm accuracy with 100% fix of all carrier-phase ambiguities. A simulated trajectory is exemplary shown in Fig. 1. The estimated clock bias and drift within the MSRx match very accurate the simulated pattern, which is shown in Fig. 2 and acted as a verification of the implemented algorithms. These findings allow to conduct further sensitivity analysis of the impact of both timing delay of the external Doppler signal and the lever-arm accuracy on our ULB-PLL architecture.
To showcase the flexibly and the performance of our ULB-PLL based MSRx receiver, we make use of the TEX-CUP data set [8] which is a public benchmark dataset collected in the dense urban center of the city of Austin, TX. This data set is dedicated for evaluation of multi-sensor GNSS-based urban positioning with various challenging surrounding conditions. In comparison to other open-source datasets, this dataset provides raw ADC output of wideband IF GNSS data along with tightly synchronized raw IMU and a stereoscopic camera unit. We customized the provided raw data for our needs to make it compatible with our receiver. To be more specific, the IF samples (with L1/L2/L5 signals) from the NTLab front-end were decoded based on the ”ION GNSS software-defined radio metadata standard” as described in [9] and later have been converted to sufficient-statistics data by means of the MuSNAT. In addition, a new INS/GNSS reference trajectory was generated based on the tightly coupling (TC) of the Septentrio receiver with the LORD-MicroStrain IMU and made later on available a 100 Hz sampling rates to perform Doppler-aiding withing the MSRx.
In conclusion, we demonstrated that the ULB-PLL is a consistent framework to provide accurate multi-frequency carrier phase observations even in difficult environments. They are significantly better than the ones provided by a COTS receivers on the same antenna (noting of course, that the ULB-PLL is aided by an IMU). An impression of the significant performance improvement by getting highly consistent carrier-phase observations even in challenging urban areas shall be given by the number of green fixed solutions in Fig. 3. The developed framework can be attached to any conventional GNSS chip that provides multi-correlator values (so-called sufficient statistics) as input.
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