A Reference Recursive Recipe for Tuning the Statistics of the Kalman Filter
M. Ananthasayanam · InTech eBooks · 2018
The philosophy and the historical development of Kalman filter from ancient times to the present is followed by the connection between randomness, probability, statistics, random process, estimation theory, and the Kalman filter. A brief derivation of the filter is followed by its appreciation, aesthetics, beauty, truth, perspectives, competence, and variants. The menacing and notorious problem of specifying the filter initial state, measurement, and process noise covariances and the unknown parameters remains in the filter even after more than five decades of enormous applications in science and technology. Manual approaches are not general and the adaptive ones are difficult. The proposed reference recursive recipe (RRR) is simple and general. The initial state covariance is the probability matching prior between the Frequentist approach via optimization and the Bayesian filtering. The filter updates the above statistics after every pass through the data to reach statistical equilibrium within a few passes without any optimization. Further many proposed cost functions help to compare the present and earlier approaches. The efficacy of the present RRR is demonstrated by its application to a simulated spring, mass, and damper system and a real airplane flight data having a larger number of unknown parameters and statistics.