Off-grid algorithms for direction of arrival (DOA) estimation have become attractive because of their advantages in resolution and efficiency over conventional ones. In this paper, we propose a grid reconfiguration direction of arrival (GRDOA) estimation method based on sparse Bayesian learning. Unlike other off-grid methods, the grid points of GRDOA are treated as dynamic parameters. The number and position of the grid points are varied iteratively via a root method and a fission process. Then, the grid gets reconfigured through some criteria. By iteratively updating the reconfigured grid, DOAs are estimated completely. Since GRDOA has fewer grid points, it has better computational efficiency than the previous methods. Moreover, GRDOA can achieve better resolution and relatively higher accuracy. Numerical simulation results validate the effectiveness of GRDOA.

A novel spherical simplex Gauss–Laguerre quadrature cubature Kalman filter is proposed to improve the estimation accuracy of nonlinear dynamic system. The nonlinear Gaussian weighted integral has been approximately evaluated using the spherical simplex rule and the arbitrary order Gauss–Laguerre quadrature rule. Thus, a spherical simplex Gauss–Laguerre cubature quadrature rule is developed, from which the general computing method of the simplex cubature quadrature points and the corresponding weights are obtained. Then, under the nonlinear Kalman filtering framework, the spherical simplex Gauss–Laguerre quadrature cubature Kalman filter is derived. A high-dimensional nonlinear state estimation problem and a target tracking problem are utilized to demonstrate the effectiveness of the proposed spherical simplex Gauss–Laguerre cubature quadrature rule to improve the performance.

In order to improve the estimation accuracy of particle filter algorithm in a nonlinear system state estimation problem, a new algorithm based on the second-order divided difference filter to generate the proposed distribution and the differential evolution algorithm for resampling is proposed. The second-order divided difference based on Strling’s interpolation formula is used to generate approximations to nonlinear dynamics, which avoids the evaluation of the Jacobian derivative matrix and is easy to implement. Cholesky factorization is used to ensure the positive definiteness of the covariance matrix. The truncated errors of the local linearization are reduced to a certain extent, and the approximation degree of the proposed distribution to the posterior probability of the system state is improved. The differential evolution algorithm is used to replace the traditional resampling algorithm, which effectively mitigates the problem of particle degradation. Monte Carlo simulation experiments show the effectiveness of the new algorithm.