Recursive adaptive algorithms for fast and rapidly time-varying systems

In this paper, some new schemes are developed to improve the tracking performance for fast and rapidly time-varying systems. A generalized recursive least-squares (RLS) algorithm called the trend RLS (T-RLS) algorithm is derived which takes into account the effect of local and global trend variations of system parameters. A bank of adaptive filters implemented with T-RLS algorithms are then used for tracking an arbitrarily fast varying system without knowing a priori the changing rates of system parameters. The optimal tracking performance is attained by Bayesian a posteriori combination of the multiple filter outputs, and the optimal number of parallel filters needed is determined by extended Akaike´s Information Criterion and Minimum Description Length information criteria. An RLS algorithm with modification of the system estimation covariance matrix is employed to track a time-varying system with rare but abrupt (jump) changes. A new online wavelet detector is designed for accurately identifying the changing locations and the branches of changing parameters. The optimal increments of the covariance matrix at the detected changing locations are also estimated. Thus, for a general time-varying system, the proposed methods can optimally track its slowly, fast and rapidly changing components simultaneously.