Adaptive-Gain Kinematic Filters of Orders 2-4

The kinematic filter is a common tool in control and signal processing applications dealing with position, velocity and other kinematical variables. Usually the filter gain is given a fixed value determined due to dynamic and measurement conditions. Most studies provide analytical solutions for optimal gains in particular scenarios. In practice, due to a lack of information (or under timevarying conditions) these recipes are mostly inapplicable and the kinematic filter requires appropriate adaptation tools instead. In its simplest form, the problem may be formulated as the gain adaptation under the tracking index uncertainty. We suggest a simple adaptive-gain kinematic filter based on minimization of the innovation variance which is known to give the optimal Kalman gain. The study deals with commonly used kinematic models of order 2-4. As shown, for any order of the kinematic filter its transfer function matches the moving-averaging (MA) model parameterized by the filter gain. In this view, the adaptive kinematic filter may be implemented in a variety of forms either based on the MA identification or by a direct gain adaptation. Optimal closed-form solutions may be incorporated into the adaptive filter as constraints. With the optimally constrained gain-vector components, the multipleparameter adaptive filter is translated into a beneficial single-parameter version. The simulation study demonstrates behavior of suggested filters in a wide range of conditions. Index Terms kinematic/tracking filter, adaptive gain, timeseries identification