Autonomous Tracking and State Estimation with Generalised Group Lasso
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We address the problem of autonomous tracking and state estimation for marine vessels, autonomous vehicles, and other dynamic signals under a (structured) sparsity assumption. With the aim of improving the tracking and estimation performance with respect to classical Bayesian filters and smoothers, we formulate such problems as a generalised L_2-penalised minimisation problem, namely a dynamic generalised group Lasso problem. We first derive batch tracking and estimation methods based on a multi-block alternating direction method of multipliers algorithmic framework. For the case when the number of time points is large (e.g., thousands), we present three effective methods which solve the primal minimisation problem by augmented recursive smoothers. These smoothers are mathematically equivalent to the corresponding batch methods, but allow for low complexity implementations. The proposed methods can deal with large-scale problems without pre-processing for dimensionality reduction, which makes them attractive to address large-scale tracking and estimation problems with sparsity-inducing priors. Additionally, we establish convergence results for the proposed methods. By simulated and real-data experiments including multi-sensor range measurement problems, marine vessel tracking, autonomous vehicle tracking, and audio signal restoration, we show the effectiveness of the proposed methods.
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