Robust estimation based on the least absolute deviations method and the Лalman filter

We propose a new approach for solving the filtering problem in linear systems based on incomplete measurements, where the characteristics of the dynamic noise are not known exactly, and measurements may contain anomalous non-Gaussian errors. The proposed algorithm is based on the idea of using the adaptive Kalman filter and the generalized least absolute deviations method jointly. With numerical modeling, we show that, compared to the classical optimal linear filtering method, our solution has lower sensitivity to short-term outliers in measurements and provides a quick adjustment of the parameters of the system dynamics. The proposed algorithm can be used to solve onboard navigation and tracking problems on aircrafts. To implement the method of least absolute deviations, we use an efficient $L_1$-optimization algorithm.