Robust Non-Linear State Estimation for Underwater Acoustic Localization : Expanding on Gaussian Mixture Methods

Abstract: Robust state estimation solutions must deal with faulty measurements, called outliers, and unknown data associations, which lead to multiple feasible hypotheses. Take, for instance, the scenario of tracking two indistinguishable targets based on position measurements, where each measurement could refer to either of the targets or even be a faulty reading. Common estimation methods model the state as having a unimodal distribution, so they are called unimodal methods. Likewise, multimodal methods model the state as a multimodal distribution. Difficult problems, such as autonomous underwater vehicle (AUV) navigation relying on acoustic localization, frequently involve recurring outliers. In these situations, the correct hypothesis only emerges as the most likely one when a substantial number of measurements are considered. Robust solutions for these problems need to consider multiple hypotheses simultaneously, which, in turn, calls for the representation of multimodal distributions. In this work, a novel approximate inference method is presented, called the Gaussian mixture sum-product algorithm (GM-SPA), as it implements the sum-product algorithm (SPA) for Gaussian mixtures. The GM-SPA can exactly represent under-constrained linear measurements and approximate important non-linear models, such as range measurements and 2D pose kinematics. The outlier robustness of the GM-SPA is tested and compared against the particle filter (PF) and multimodal incremental smoothing and mapping (MMiSAM), both of which are non-parametric methods. Robustness, accuracy, and run-time are improved in simulation tests. The test problems include 1D localization with unknown data association, 3D linear target tracking with correlated outliers, and 2D range-only pose estimation with Gaussian mixture noise.