Estimation with Applications to Tracking and Navigation
Estimation with Applications to Tracking and Navigation
RLS-weighted Lasso for adaptive estimation of sparse signals
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
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Fixed-interval smoothing of time-varying vector processes is an estimation approach with well-documented merits for tracking applications. The optimal performance in the linear Gauss-Markov model is achieved by the Kalman smoother (KS), which also admits an efficient recursive implementation. The present paper deals with vector processes for which it is known a priori that many of their entries equal to zero. In this context, the process to be tracked is sparse, and the performance of sparsityagnostic KS schemes degrades considerably. On the other hand, it is shown here that a sparsity-aware KS exhibits complexity which grows exponentially in the vector dimension. To obtain a tractable alternative, the KS cost is regularized with the sparsity-promoting l1 norm of the vector process - a relaxation also used in linear regression problems to obtain the least-absolute shrinkage and selection operator (Lasso). The Lasso (L)KS derived in this work is not only capable of tracking sparse time-varying vector processes, but can also afford an efficient recursive implementation based on the alternating direction method of multipliers (ADMoM). Finally, a weighted (W)-LKS is also introduced to cope with the bias of the LKS, and simulations are provided to validate the performance of the novel algorithms.