Hierarchical maximum likelihood generalized extended stochastic gradient algorithms for bilinear‐in‐parameter systems
Haibo Liu, Jun‐Wei Wang, Xiangxiang Meng
Abstract
Abstract In this article, we use the maximum likelihood principle and the multi‐innovation identification theory to study the identification issue of a bilinear‐in‐parameter system with autoregressive moving average noise. A maximum likelihood multi‐innovation stochastic gradient algorithm is derived to estimate the model parameters, which uses not only the current innovation but also the past innovations to improve the parameter estimation accuracy. The maximum likelihood multi‐innovation stochastic gradient algorithm has higher parameter estimation accuracy than the stochastic gradient algorithm. The simulation examples indicate that the proposed methods work well.
Topics & Concepts
Estimation theoryIdentification (biology)Bilinear interpolationMaximum likelihoodAutoregressive modelExpectation–maximization algorithmMaximum likelihood sequence estimationMathematicsAlgorithmRestricted maximum likelihoodComputer scienceApplied mathematicsMathematical optimizationStatisticsBiologyBotanyControl Systems and IdentificationAdvanced Control Systems OptimizationFault Detection and Control Systems