Hierarchical multi-innovation stochastic gradient identification algorithm for estimating a bilinear state-space model with moving average noise (Q2087500)

This article considers simultaneous state and parameter estimation of a bilinear control system with linear observations corrupted by a noise that is the output of a rational transfer function fed by zero mean uncorrelated noise. A state estimator is derived based on Kalman filter and then a parameter estimation scheme is proposed using a hierarchical decomposition and stochastic gradient descent, using multiple innovations processes. Consistency of this scheme is established. Supporting numerical experiments are reported.