ALGORITHM OF VARIATIONAL-WEIGHTED QUADRATIC APPROXIMATIONS FOR LEAST ABSOLUTE DEVIATIONS METHOD IN DYNAMIC SYSTEMS

摘要

The algorithm of weight and time recurrences for the least absolute deviations method (l_1 - norm approximation) is proposed. Some components of the state vector of a linear discrete dynamic system can abruptly change under the influence of rare uncontrolled input pulses in the right-hand side of equations. In this case, the least absolute deviations method gives better results than the widely used least squares method (l_2 - norm approximation). The main attention is paid to the efficiency of this algorithm in case of large amount of measurement data. To make numerical procedure more reliable, a nonoptimality level for current iteration is constructed. An example from inertial navigation illustrates the advantages of the approach presented.