Recursive estimation algorithm for l1-norm approximation in dynamic systems with nonoptimality levels

State estimation problem for a linear discrete dynamic system is considered. Some components of the state vector can abruptly change under the influence of rare uncontrolled input pulses in the right-hand side of equations. In this case, l₁-norm approximation (least absolute deviations method) gives better results than the standard l₂-norm approximation (least squares method). A recursive estimation algorithm for finding l₁-norm approximation in case of large amount of measurements is presented. To make numerical procedure more reliable, a nonoptimality level for current iteration is constructed. An example from inertial navigation verifies the effectiveness of proposed approach.