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.

Considering the difficulty in measuring the P-band electromagnetic parameters of porous materials such as graphene foam (GF), this paper proposes a free-space frequency-domain technology to measure the electrical properties of finite-plate materials from multiple perspectives. First, the multiangle reflectance of the sample was measured with the arch method; second, an electromagnetic simulation model consistent with the sample size was established, and the reflectance of different angles was calculated using the method of moments (MoM). Finally, the genetic algorithm (GA) was optimized for the electromagnetic parameters such that the reflective difference between the electromagnetic simulation model and the test obtained was minimized. The validity of the method was verified by reconstructing the electromagnetic parameters of a 1 m×1 m×0.03 m absorbing material at 0.5 GHz. The unique advantage of this method is that it solves the problem of inversion of electromagnetic parameters based on the multiangle reflectivity of an absorbing material plate within three times the wavelength. Because the electromagnetic simulation model can automatically divide the appropriate mesh size according to the size of the electromagnetic parameters, this method is suitable for high-loss and low-loss materials. In addition, this method avoids the special processing requirements regarding the shape size of the absorbing material, which has a wide application scope and low cost.

Aiming at the state estimation problem of non-linear systems (NLSs), the traditional typical nonlinear filtering methods (e.g., Particle Filter, PF) have large errors in system state, resulting in low accuracy and high computational speed. To perfect the imperfections, a new Bayesian estimation method based on particle flow velocity (PFV-BEM) is proposed in this paper. Firstly, the state update is carried out according to the projection principle to calculate the prior information of the state and select its particle points. Secondly, the particle flow velocity defined, which describes the evolution process of random samples from the prior distribution to the posterior distribution. The posterior information of the state is calculated by solving the parameters related the particle flow velocity. Finally, the estimated mean and standard deviation of the state are solved. Simulation experiments use one-dimensional general nonlinear examples and multi-target motion tracking as examples, it is compared with PF, the simulation results show the feasibility of the novel Bayesian estimation algorithm.