Joint Estimation of States and Parameters for an Input Nonlinear State-Space System with Colored Noise Using the Filtering Technique

Abstract

This paper concerns the state and parameter estimation problem for an input nonlinear state-space system with colored noise. By using the data filtering and the over-parameterization technique, we transform the original nonlinear state-space system into two identification models with filtered states: one containing the system parameters and the other containing the noise model's parameters. A combined state and parameter estimation algorithm is developed for identifying the state-space system. The key is that the estimation of system parameters uses the estimated states, and the estimation of states uses the preceding parameter estimates. A simulation example is provided to show that the proposed algorithm can work well.

The parameter estimation algorithms based on the dynamical response measurement data

“…The accuracy, the computation complexity, and the robustness [21][22][23] are main aspects of the identification algorithm performance. 24,25 Many identification algorithms focus on enhancing the accuracy and robust and reducing the complexity. [26][27][28] Wang and Ding [29][30][31] considered the filtering algorithm to reduce the algorithm's complexity.…”

Combined state and parameter estimation for Hammerstein systems with time delay using the Kalman filtering

“…The proposed algorithms are different from the least squares algorithm in 1 study, 32 which decomposes the bilinear cost function into 3 linear functions by using the hierarchical identification principle and uses the state observer to get the estimates of the unknown states. Also, the proposed algorithms are different from the overparameterization-based recursive least squares algorithm in 1 study, 33 which ignores the process noise in the model structure and the influence of the measurement noise in the process of updating the estimates of the system states. The main contributions of this paper are as follows.…”

“…In fact, there is another model which is called the over-parameterization model to deal with the product term of b and γ. For example, the method in [33] expresses the parameter vector as…”

Adaptive filtering‐based multi‐innovation gradient algorithm for input nonlinear systems with autoregressive noise

“…The proposed algorithms are different from the least squares algorithm in [32], which decomposes the bilinear cost function into three linear functions by using the hierarchical identification principle and uses the state observer to get the estimates of the unknown states. Also, the proposed algorithms are different from the over-parameterization based recursive least squares algorithm in [33], which ignores the process noise in the model structure and the influence of the measurement noise in the process of updating the estimates of the system states. The main contributions of this paper are as follows.…”