An enhanced linear Kalman filter (EnLKF) algorithm for parameter estimation of nonlinear rational models

Abstract

Abstract:In this study an enhanced Kalman Filter formulation for linear in the parameters models with inherent correlated errors is proposed to build up a new framework for nonlinear rational model parameter estimation. The mechanism of Linear Kalman Filter (LKF) with point data processing is adopted to develop a new recursive algorithm. The novelty of the Enhanced Linear Kalman Filter (EnLKF in short and distinguished from Extended Kalman Filter (EKF)) is that it is not formulated from the routes of extended Kalman Filters (to approximate nonlinear models by linear approximation around operating points through Taylor expansion) and also it includes LKF as its subset while linear models have no correlated errors in regressor terms. No matter linear or nonlinear models in representing a system from measured data, it is very common to have correlated errors between measurement noise and regression terms, the EnLKF provides a general solution for unbiased model parameter estimation without extra cost to convert model structure. The associated convergence is analysed to provide a quantitative indicator for applications and reference for further research. Three simulated examples are selected to bench-test the performance of the algorithm. In addition, the style of conducting numerical simulation studies provides a user-friendly step by step procedure for the readers/users with interest in their ad hoc applications. It should be noted that this approach is fundamentally different from those using linearization to approximate nonlinear models and then conduct state/parameter estimate.

Biased compensation recursive least squares-based threshold algorithm for time-delay rational models via redundant rule

“…Since the time-delay τ is unknown, those elements in ϕ(t) are also unknown, then the LS proposed in [10] and the enhanced linear Kalman filter algorithm proposed in [12] cannot be applied for this time-delay rational model. To overcome this difficulty is using the redundant rule proposed in [26].…”

“…Recently, Zhu proposed an error back propagation parameter estimation algorithm for a class of rational models, by combining an orthogonal correlation test method, the model structure and the associate parameters can be estimated simultaneously [11]. Zhu et al also proposed an enhanced linear Kalman filter algorithm for parameter estimation of nonlinear rational models, in which the proposed algorithm is an online algorithm [12]. However, all the rational models in above literature are non-time-delay systems, when the rational models have unknown time-delays, those methods mentioned in above literature are invalid.…”

Neural Computing Enhanced Parameter Estimation for Multi-Input and Multi-Output Total Non-Linear Dynamic Models

“…At present, a variety of model structure detection techniques and parameter estimation algorithms are developed for non-linear models, including the orthogonal model structure detection and parameter estimation program [ 6 ], the generalized least square estimator [ 7 , 8 ], the prediction error estimator [ 9 , 10 ], the Kalman filter estimator [ 11 , 12 ], the genetic algorithm estimator [ 12 , 13 ], the artificial neural network estimator [ 14 , 15 , 16 , 17 ], etc. However, most of these algorithms are parameter estimators for polynomial non-linear models.…”

Control of Complex Nonlinear Dynamic Rational Systems

“…The major work on rational model identification is summarised in the following categories: linear least squares (LLS) algorithms for parameter estimation-extended LLS estimator [10], recursive LLS estimator [11], orthogonal LLS structure detector and estimator [12], fast orthogonal algorithm [13], and implicit least squares algorithm [14], and nonlinear least squares algorithms-prediction error estimator [15] and globally consistent nonlinear least squares estimator [16]. Other algorithms include the following categories: back propagation (BP) algorithm [17] and enhanced linear Kalman filter (EnLKF) [18].…”

“…The challenging issue is that classical recursive least Figure 3: Uncertain U-model control system. 6 Complexity squares estimation algorithms give biased estimates and recursive rational model estimators need noise variance information in advance [11,18].…”