Abstract
Navigation problems are generally solved applying least-squares (LS) adjustments. Techniques based on LS can be shown to perform optimally when the system noise is Gaussian distributed and the parametric model is accurately known. Unfortunately, real world problems usually contain unexpectedly large errors, so-called outliers, that violate the noise model assumption, leading to a spoiled solution estimation. In this work, the framework of robust statistics is explored to provide robust solutions to the global navigation satellite systems (GNSS) single point positioning (SPP) problem. Considering that GNSS observables may be contaminated by erroneous measurements, we survey the most popular approaches for robust regression (M-, S-, and MM-estimators) and how they can be adapted into a general methodology for robust GNSS positioning. We provide both theoretical insights and validation over experimental datasets, which serves in discussing the robust methods in detail.
Highlights
Global navigation satellite systems (GNSS) play a fundamental role on prospective applications of intelligent transportation systems (ITS), as the main source of positioning information [1]
This assumption is generally fulfilled for nominal GNSS open-sky conditions, positioning on signal-degraded scenarios constitutes a challenge for maximum likelihood (ML) estimators such as the least-squares (LS) [3]
This paper focuses on the single point positioning (SPP) problem, purposely does not consider precise point positioning (PPP) or real-time kinematic (RTK) approaches, which typically involve more complex estimates and the application of different methodologies [34,35,36] to the ones investigated here
Summary
Global navigation satellite systems (GNSS) play a fundamental role on prospective applications of intelligent transportation systems (ITS), as the main source of positioning information [1]. Most positioning techniques are based on maximum likelihood (ML) estimation, since it provides optimal solutions under the assumption of Gaussian distributed observation noise. This assumption is generally fulfilled for nominal GNSS open-sky conditions, positioning on signal-degraded scenarios constitutes a challenge for ML estimators such as the least-squares (LS) [3]. The application of robust estimators to compute position, velocity, and time (PVT) solutions in satellite-based navigation has appealed numerous authors, both for memory-less SPP [27,28,29,30]. With additional analysis of the robust methods, the definition of the loss-of-efficiency concept for robust PVT estimation, and additional experimental discussions using real data in a vehicular scenario.
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