Study On Adaptive Parameter Identification Lgorithm For Systems With Multiplicative Noise

A real engineering system is not only influenced by the additive noise, but alsoby some more complex factors, such as energy decreasing, nonlinear distortion,time-varying and so on, and all these down to one thing—multiplicative noise, so it isvery important to study on the systems with multiplicative noise (SMN). Statefiltering for SMN needs accurate system models and priori noise statistics, or far fromoptimal result, the filtering system may even be divergent. To solve this problem, anadaptive filtering algorithm for SMN is of great concern. The main study of thedissertation is the adaptive algorithm for SMN with the dynamic noise covariance andmeasurement noise covariance unknown. There are many achievements in the area ofadaptive Kalman filter for the linear system at home and abroad, however, the studyon adaptive algorithm for SMN is at the initial stage. The dissertation puts forwardthree methods to identify the covariance of the dynamic noise and measurement noisebased on previous result. The main study of the dissertation is as follows:1. Adaptive covariance identification algorithm for SMN is studied. Based onKronecker products, the innovation is proven to be stable during the steady state, andthe innovation series is approximated to be stationary stochastic process. A recursivealgorithm is developed in the sense of linear minimum variance under the Kalmanfiltering algorithm, thus forming a case of adaptive filtering algorithm for SMN withunknown noise covariance. Besides, the algorithm is optimized through the weightedalgorithm according to the difference between the practical value of innovationcovariance and the theoretical one. This algorithm is very simple, easy to implementon the computer, and validated through computer simulation.2. Adaptive gain identification algorithm is studied. Based on the state filteringalgorithm, a gain identification algorithm is developed in independent white noisescondition, with the convergence demonstrated under the theory of the matrix norminequality, matrix calculus, the stability of systems. The identification result will tendto the optimal value. Simulation result validate the algorithm.3. Adaptive fading factor filter algorithm is studied. According to Kalmanadaptive fading factor algorithm, the algorithm is developed which can adapt thedynamic noise covariance and measurement noise covariance by generating two fading factors matching each variance. The algorithm is very simple and easy toimplement on the computer. By using F-test, the algorithm can follow the change ofthe noise covariance, which has more practical value. At last the computer simulationis made to demonstrate the validity of the algorithm.