Parameter Estimation Method for Generalized Time-varying Systems With Colored Noise Based on the Hierarchical Principle

For generalized time-varying systems with colored noise, the difficulty of identification lies in time-varying parameters and colored noise. The recursive estimation problem of a controlled autoregressive generalized time-varying system with autoregressive moving average noise is studied. By means of the hierarchical principle, the identification model is decomposed into two subsystems with fewer variables and different characteristics, which simplifies the original model and processes the colored noise based on the idea of the auxiliary model. Then a two-stage auxiliary model-based recursive least squares (TS-AM-RLS) algorithm is proposed, which realizes the parameter estimation of the subsystem based on the least squares method. In order to improve the identification accuracy and convergence speed, the scalar innovation is extended to the innovation vector, and a multi-innovation least squares algorithm is proposed by using the multi-innovation identification theory. A numerical experiment is given to illustrate the performances of the proposed algorithms.