Tuning of the Kalman Filter Using Constant Gains

Abstract

For designing an optimal Kalman filter, it is necessary to specify the statistics, namely the initial state, its covariance and the process and measurement noise covariances. These can be chosen by minimising some suitable cost function J . This has been very difficult till recently when a near optimal Recurrence Reference Recipe ( RRR ) was proposed without any optimisation but only filtering. In many filter applications after the initial transients, the gain matrix K tends to a constant during the steady state, which points to design the filter based on constant gains alone. Such a constant gain Kalman filter ( CGKF ) can be designed by minimising any suitable cost function. Since there are no covariances in CGKF, only the state equations need to be propagated and updated at a measurement, thus enormously reducing the computational load. Though CGKF results may not be too close to those of RRR, they are acceptable. It accepts extremely simple models and the gains are robust in handling similar scenarios. In this chapter, we provide examples of applying the CGKF by ancient Indian astronomers, parameter estimation of spring, mass and damper system, airplane real flight test data, ballistic rocket, re-entry of space object and the evolution of space debris.