The first stage in any control system is to be able to accurately estimate the system's state. However, some types of measurements are ambiguous (non-injective) in terms of state. Existing algorithms for such problems, such as Monte Carlo methods, are computationally expensive or not robust to such ambiguity. We propose the Box Regularized Particle Filter (BRPF) to resolve these problems. Based on previous works on box particle filters, we present a more generic and accurate formulation of the algorithm, with two innovations: a generalized box resampling step and a kernel smoothing method, which is shown to be optimal in terms of Mean Integrated Square Error. Monte Carlo simulations demonstrate the efficiency of BRPF on a severely ambiguous and non-linear estimation problem, that of Terrain Aided Navigation. BRPF is compared to the Sequential Importance Resampling Particle Filter (SIR-PF), Monte Carlo Markov Chain (MCMC), and the original Box Particle Filter (BPF). The algorithm outperforms existing methods in terms of Root Mean Square Error (e.g., improvement up to 42% in geographical position estimation with respect to the BPF) for a large initial uncertainty. The BRPF reduces the computational load by 73% and 90% for SIR-PF and MCMC, respectively, with similar RMSE values. This work offers an accurate (in terms of RMSE) and robust (in terms of divergence rate) way to tackle state estimation from ambiguous measurements while requiring a significantly lower computational load than classic Monte Carlo and particle filtering methods.
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To perform long-term and long-range missions, underwater vehicles need reliable navigation algorithms. This paper considers multi-beam Terrain Aided Navigation which can provide a drift-free navigation tool. This leads to an estimation problem with implicit observation equation and unknown likelihood. Indeed, the measurement sensor is considered to be a numerical black box model that introduces some unknown stochastic noise. We introduce a measurement updating procedure based on an adaptive kernel derived from Approximate Bayesian Computational filters. The proposed method is based on two well-known particle filters: Regularized Particle Filter and Rao-Blackwellized Particle Filter. Numerical results are presented and the robustness is demonstrated with respect to the original filters, yielding to twice as less non-convergence cases. The proposed method increases the robustness of particle-like filters while remaining computationally efficient.
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