Multi‐innovation gradient estimation algorithms for multivariate equation‐error autoregressive moving average systems based on the filtering technique

Abstract

This study concentrates on the parameter estimation of multivariate pseudo-linear autoregressive moving average systems by means of the multi-innovation identification theory and data filtering technique. A multi-innovation stochastic gradient algorithm is derived by introducing the innovation length in the stochastic gradient algorithm. Then, the original system is transformed into two subsystems by using a filter. A filtering-based multi-innovation stochastic gradient algorithm is presented, whose parameter estimation accuracy is higher than the multi-innovation stochastic gradient algorithm. The simulation results confirm that these two algorithms are effective.