An iterative algorithm for $l_1$-norm approximation in dynamic estimation problems

In this paper, an approach to state estimation in dynamic systems is considered, which consists in solving an $l_1$-norm approximation problem. An algorithm is proposed for the solution of this problem, the so-called weight and time recursion method, which combines the ideas of weighted variational quadratic approximations and smoothing Kalman filtering. For the iterations of the proposed method, estimates of levels of nonoptimality are computed; this is considered as an extension of earlier results obtained by the authors for the classical least absolute deviation method.