Robust Kalman Filter for RTK Positioning under Signal-Degraded Scenarios

Haoqing Li, Daniel Medina, Jordi Vilà-Valls, and Pau Closas

Abstract: Location-based services, alongside with the modern applications on Intelligent Transportation Systems require reliable, continuous and precise navigation, positioning and timing information for their successful operation and implantation in the market. Global Navigation Satellite Systems (GNSS) constitute the backbone and main information supplier for Positioning, Navigation and Timing (PNT) data [1, 3, 4]. Despite offering a fairly good open sky positioning performance, standard differential code-based GNSS techniques can only achieve metre-level accuracy. Therefore, the accuracy potential for this approach is nearly exhausted and the transition techniques based on carrier phase observations is required in order to reach below decimetre-level positioning accuracies. Depending on the set of correction data, two kind of phase-based positioning techniques can be distinguished. First, Precise Point Positioning (PPP) reaches high accuracy by modelling GNSS system errors, such as ionospheric or tropospheric delays. PPP performance relies on GNSS satellite clock and orbit corrections, generated from a global network of stations. Although no nearby base station is required, which may be an advantage for some applications, the convergence time for the atmospheric corrections require from 5 to 20 minutes [10], excessive for safety-critical applications. Second, Real Time Kinematic (RTK) is a relative positioning procedure, where the position of a - potentially moving - receiver is determined with respect to a stationary base station of accurately known coordinates [5]. Thus, whenever the communication channel from the base station to the vehicle is sufficient, centimetre-level positioning accuracy can be reached almost immediately. Besides the interest of PPP techniques, this work focuses on RTK positioning and the challenges on urban navigation, where multipath effects can heavily deteriorate the navigation solution. In RTK, the typical process to convert observables into position, velocity, and time (PVT) estimates involves some sort of state estimation problem. This is in general approach by solving a least-squares (LS) problem, or its recursive version resulting in the implementation of variants of the Kalman filter (KF). In such LS problem, both code and phase pseudoranges are exploited, then a vector of double-difference ambiguities must be estimated together with the targeted receiver position. Given the integer nature of such ambiguities, a possible solution is to use a three step approach. These are applied sequentially: i) float solution determination, ii) integer ambiguity fixing, and iii) state reconstruction. In the initial step, either a LS or KF-type method is considered, the ambiguities and other unknowns are estimated as real numbers (therefore, the results is often referred to as the float solution). Then, the estimated float ambiguities and the corresponding covariance matrix are used to obtain the integer ambiguities estimates. Finally, the computed integer ambiguities are used to improve the positioning solution. Such estimate is typically implemented, again, within the LS framework in order to obtain the so-called fixed solution. The three steps approach for RTK described earlier is known to provide acceptable estimation performance under nominal conditions, which is not the case in urban environments, typically affected by multipath and non-line-ofsight (NLOS) propagation conditions. These harsh propagation conditions are the main source of errors for precise navigation, since the locality of the effect prevents augmentation systems from assisting meaningfully against such channel effects. As a consequence, counter measuring signal reflections can be better done locally at the receiver in either the baseband processing (i.e., in the calculation of observables) or the navigation side (i.e., when producing the PVT solution). In this work, we focus on the later, where the usual RTK pipeline described earlier is enhanced in order to provide additional robustness to local effects. The result is a new RTK technique that is resilient to, for instance, multipath conditions. The key point is to improve the performance of the float solution estimation, where the multipath-contaminated satellite links are detected, enabling the guidance of the integer ambiguity search and enhancing its success ratio. To achieve such goal, we propose to use a robust KF with outlier detection and rejection capabilities, which is based on concepts from Variational Bayes (VB) inference methods. VB inference is an efficient approximating method to estimate posterior probabilities. The main idea of this method is to come up with a tractable distribution to approximate posterior distribution of latent variables by minimizing KullbackLeibler divergence. The reason why VB inference is needed is that latent variables is designed to detect and reject outliers, which is also the differnece of standard KF and this robust KF. The basic difference between standard KF and VB inference-based KF is the model assumed. In standard KF, only Additive White Gaussian Noise (AWGN) is considered and therefore Gaussian distribution is assumed, in which standard KF is optimal. However, in VB inference-based KF, multipath is also considered in addition to AWGN. With new model built, latent variables is assumed to mitigate multipath’s influence, which is why VB infernce is applied. The new approach is validated using real data on a challenging propagation environment. The real data used in this work was recorded during a measurement campaign on 16th May 2017 (DOY 208, UTC 12:00-13:30) conducted in Koblenz (Germany) on the Moselle river. The data was collected on board of a vessel, which travelled through the river with several bridges and a waterway lock, then affected by severe multipath and NLOS conditions. The evaluation comprises the positioning accuracy of the proposed algorithm, alongside with the fixing rate. The fixing rate defines the probability of finding the correct set of integer ambiguities, based on an empirical method aiming to deice whether the estimated set of integer ambiguities can be considered sufficiently more likely than any other integer candidates [8]. The reported results show the added robustness when adding a robust KF in the RTK pipeline.
Published in: Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019)
September 16 - 20, 2019
Hyatt Regency Miami
Miami, Florida
Pages: 3717 - 3729
Cite this article: Li, Haoqing, Medina, Daniel, Vilà-Valls, Jordi, Closas, Pau, "Robust Kalman Filter for RTK Positioning under Signal-Degraded Scenarios," Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019), Miami, Florida, September 2019, pp. 3717-3729.
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