Abstract
For non-linear systems (NLSs), the state estimation problem is an essential and important problem. This paper deals with the nonlinear state estimation problems in nonlinear and non-Gaussian systems. Recently, the Bayesian filter designer based on the Bayesian principle has been widely applied to the state estimation problem in NLSs. However, we assume that the state estimation models are nonlinear and non-Gaussian, applying traditional, typical nonlinear filtering methods, and there is no precise result for the system state estimation problem. Therefore, the larger the estimation error, the lower the estimation accuracy. To perfect the imperfections, a projection filtering method (PFM) based on the Bayesian estimation approach is applied to estimate the state. First, this paper constructs its projection symmetric interval to select the basis function. Second, the prior probability density of NLSs can be projected into the basis function space, and the prior probability density solution can be solved by using the Fokker–Planck Equation (FPE). According to the Bayes formula, the proposed estimator utilizes the basis function in projected space to iteratively calculate the posterior probability density; thus, it avoids calculating the partial differential equation. By taking two illustrative examples, it is also compared with the traditional UKF and PF algorithm, and the numerical experiment results show the feasibility and effectiveness of the novel nonlinear state estimation filter algorithm.
Highlights
Published: 16 September 2021In recent years, the state estimation problems of the dynamic system have become very important in various applications of nonlinear systems (NLSs), such as underwater navigation positioning, mechanical equipment fault diagnosis, signal processing, space target orbit prediction, target tracking, etc. [1,2,3].The earliest applied state estimation method is the Kalman filter method
Steps of PFM-PSI (Projection Filter Method based on Projection Symmetric Interval) in the n-dimensional system can be obtained as:
Using PFM-PSI (Projection Filter Method based on Projection Symmetric Interval), the interval of time is chosen as 1 s
Summary
The state estimation problems of the dynamic system have become very important in various applications of nonlinear systems (NLSs), such as underwater navigation positioning, mechanical equipment fault diagnosis, signal processing, space target orbit prediction, target tracking, etc. [1,2,3]. The KF method is only suitable for the state estimation model in linear and Gaussian systems. The state estimation problems of many actual physical systems are nonlinear and non-Gaussian models. The performance of UKF will become unstable This is not suitable for general methods of state estimation problems. There is another popular Bayesian estimation algorithm based on the Particle Filter method (PF) in NLSs [10], known as a complex technique based on the sequential. PF can deal with a set of nonlinear, non-Gaussian state estimation problems It still has some shortcomings, such as computational complexity and sample degradation. In [22], a projection filter method has been proposed, which can only solve the problem of low-dimensional state estimation.
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