An Adaptive Minimum Variance Filter for Discrete Linear Systems

The main purpose of this report is to present a technique whereby standard Kalman filters can adapt to unknown noise statistics and hence an improvement on their workability and stability characteristics can be realized. The fundamental concept used herein is one of whitening of the realizations using a moving average filter. Through the execution of this process, details pertaining to the composition of the message process are ascertained. Adaptive filters based on the work of Shellenbarger, Sage, et al. using Bayesian techniques were also derived and their final algorithms presented being careful to mention any assumptions used throughout the development. Finally, simulation results were presented for the scalor case, when both the measurement and the process noise sources were unknown. These runs were quite successful in their accuracy and setting. Although the results obtained were based on linear, stationary systems, they do form a basis to enhance further growth in this complex but important area.