Kalman and H Infinity Optimal Filtering for a Class of Kinematic Systems

This paper presents a set of optimal filtering results for a class of kinematic systems with particular application to the estimation of linear quantities in Integrated Navigation Systems for mobile platforms. At the core of the proposed methodology there is a time varying orthogonal Lyapunov coordinate transformation that renders the overall system dynamics linear time invariant (LTI). The design is based on the Kalman or H∞ filtering steady state solutions for an equivalent LTI system and allows for the natural use of frequency weights to explicitly achieve adequate disturbance rejection and attenuation of the noise of the sensors on the state estimates. Afterwards, the resulting solution is converted back to the original coordinate space, yielding a globally stable time varying optimal estimator for the problem at hand. A simple example of practical importance in marine systems is provided that demonstrates the applicability of the proposed design methodologies and simulation results are included to illustrate the filtering achievable performance.