Maximum likelihood least squares‐based iterative methods for output‐error bilinear‐parameter models with colored noises

Abstract

This article is concerned with the parameter identification of output-error bilinear-parameter models with colored noises from measurement data. An auxiliary model least squares-based iterative method is developed through the overparameterization model. It examines the difficulty of estimating the overparameterized vector, which usually presents a heavy computational burden in the identification process. To overcome this drawback, a parameter separation technique is introduced and the nonlinear model is reformulated as a refined identification model through eliminating the crossmultiplying terms. In this regard, a parameter separation least squares-based iterative (PS-LSI) algorithm is derived by avoiding estimating the redundant parameters. On the basis of the PS-LSI algorithm, we derive a maximum likelihood least squares-based iterative method to further improve the numerical accuracy. The identification is dependent on the formulation of a pseudolinear regression relationship, which contains two linear prefilters constructed from the system and noise models. The performance of this proposed method is confirmed by the numerical simulations as well as direct comparisons with other existing algorithms.

Hierarchical recursive signal modeling for multifrequency signals based on discrete measured data

“…The simulation results verify that the hierarchical estimation methods based on the separation have better performance than the modeling methods without separation. The proposed methods in this paper can combine other identification methods 61‐65 to investigate the parameter estimation problems of other linear and nonlinear models and control systems and can be applied to other fields 66‐73 such as signal processing, prediction and engineering application systems 74‐79 and so on.…”

Three‐stage least squares‐based iterative estimation algorithms for bilinear state‐space systems based on the bilinear state estimator

“…In the future work, we will further investigate whether these algorithms can be applied to systems with missing data. The iterative algorithm in this paper is proposed for bilinear stochastic systems but the idea can be extended to other linear and nonlinear stochastic systems with colored noises [66][67][68][69][70][71][72][73][74][75] and can be applied to other literatures [76][77][78][79][80][81][82][83] such as signal modeling, pattern cognition, information processing, and engineering application systems.…”

Parameter estimation for a multi‐input multi‐output state‐space system with unmeasurable states through the data filtering technique

“…3). The proposed approaches in this paper can combine other mathematical tools and strategies [43][44][45][46][47][48] to study the parameter estimation algorithms of other linear stochastic systems and non-linear stochastic systems with different structures and disturbance noises [49][50][51][52][53][54] and can be applied to literatures [55][56][57][58][59][60][61][62][63] such as paper-making systems. Remark 3: For the SO-F-PC-GSG algorithm, the initial values of the parameter vectors to be estimated can be arbitrary.…”