Abstract
A stochastic gradient (SG)-based particle filter (SG-PF) algorithm is developed for an ARX model with nonlinear communication output in this paper. This ARX model consists of two submodels, one is a linear ARX model and the other is a nonlinear output model. The process outputs (outputs of the linear submodel) transmitted over a communication channel are unmeasurable, while the communication outputs (outputs of the nonlinear submodel) are available, and both of the two-type outputs are contaminated by white noises. Based on the rich input data and the available communication output data, a SG-PF algorithm is proposed to estimate the unknown process outputs and parameters of the ARX model. Furthermore, a direct weight optimization method and the Epanechnikov kernel method are extended to modify the particle filter when the measurement noise is a Gaussian noise with unknown variance and the measurement noise distribution is unknown. The simulation results demonstrate that the SG-PF algorithm is effective.
Highlights
The non-standard ARX model which is a standard ARX model mixed with a nonlinear communication output model, can be seen as a networked control system [1], [2]
The iterative algorithms are off-line algorithms which have heavy computational efforts and cannot be used to estimate the parameters recursively by new data, while the recursive least squares (RLS) and stochastic gradient (SG) algorithms can be used as on-line algorithms and can update the parameters based on new data
An SG based particle filter (SG-PF) algorithm is proposed for a non-standard ARX model in this paper
Summary
The non-standard ARX model which is a standard ARX model mixed with a nonlinear communication output model, can be seen as a networked control system [1], [2]. Jin et al investigated an auxiliary model based identification algorithm for multivariable OE-like systems with missing outputs [12]. The Kalman filter and the particle filter apply the measureable data to improve the priori estimates, which makes them be more accurate. These two filters are often used for state-space systems. This paper takes the above described literature into study and develops an SG based particle filter algorithm for an ARX model with nonlinear communication output. 2) Propose a particle filter instead of an auxiliary model for nonlinear non-state-space systems, which can estimate the unknown variables and can increase the estimation accuracy.
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