Finite Impulse Response Filtering Algorithm with Adaptive Horizon Size Selection and Its Applications

It is known, that unlike the Kalman filter (KF) finite impulse response (FIR) filters allow to avoid the divergence and unsatisfactory object tracking connected with temporary perturbations and abrupt object changes. The main challenge is to provide the appropriate choice of a sliding window size for them. In this paper, the new finite impulse response (FIR) filtering algorithm with the adaptive horizon size selection is proposed. The algorithm uses the receding horizon optimal (RHOFIR) filter which receives estimates, an abrupt change detector and an adaptive recurrent mechanism for choosing the window size. Monotonicity and asymptotic properties of the estimation error covariance matrix and the RHOFIR filter gain are established. These results form a solid foundation for justifying the principal possibility to tune the filter gain using them and the developed adaptation mechanism. The proposed algorithm (the ARHOFIR filter) allows reducing the impact of disturbances by varying adaptively the sliding window size. The possibility of this follows from the fact that the window size affects the filter characteristics in different ways. The ARHOFIR filter chooses a large horizon size in the absence of abrupt disturbances and a little during the time intervals of their action. Due to this, it has better transient characteristics compared to the KF and RHOFIR filter at intervals where there is temporary uncertainty and may provide the same accuracy of estimates as the KF in their absence. By simulation, it is shown that the ARHOFIR filter is more robust than the KF and RHOFIR filter for the temporarily uncertain systems

Receding Horizon Unbiased FIR Filters and Their Application to Sea Target Tracking

Finite impulse response (FIR) state estimation algorithms have been much discussed in literature lately. It is well known that they allow overcoming the Kalman filter divergence caused by modeling uncertainties. In this paper, new receding horizon unbiased FIR filters ignoring noise statistics for time-varying discrete state-space models are proposed. They have the following advantages. First, the proposed filters use only known means of state vector components at starting points of sliding windows. This allows us to take into account priory statistical information (on average) about specified movements of the system. Second, the iterative version of the filter has a Kalman-like form. Besides, its initialization does not include a training cycle in a batch form. Such filters may have a wide range of applications. In this paper, position and speed estimation of sea targets using angle measurements in azimuth and elevation is considered as an example