Multipath estimation based on modified ε-constrained rank-based differential evolution with minimum error entropy

Multipath is one of the dominant error sources for high-precision positioning systems, such as global navigation satellite systems (GNSS). The minimum mean square error (MSE) criterion is usually employed for multipath estimation under the assumption of Gaussian noise. For non-Gaussian noise as appeared in most practical applications, alternative solutions are required for multipath estimation. In this work, a multipath estimation algorithm is proposed based on the minimum error entropy (MEE) criterion under Gaussian or non-Gaussian noises. A key advantage of using MEE is that it can minimize the randomness of error signals, however, the shift-invariance characteristics in MEE may lead to a bias of the estimation result. To mitigate such a bias, an improved estimation strategy is proposed by integrating the second-order central moment of the estimation error together with the prior information of multipath parameters as a constraint. The multipath estimation problem is thus formulated as a constrained optimization problem. A modified ε-constrained rank-based differential evolution (εRDE) algorithm is developed to find the optimal solution. The effectiveness of the proposed algorithm, in terms of reducing the multipath estimation error and minimizing the randomness in the error signal, has been examined through case studies with Gaussian and non-Gaussian noises

Improved Minimum Entropy Filtering for Continuous Nonlinear Non-Gaussian Systems Using a Generalized Density Evolution Equation

This paper investigates the filtering problem for multivariate continuous nonlinear non-Gaussian systems based on an improved minimum error entropy (MEE) criterion. The system is described by a set of nonlinear continuous equations with non-Gaussian system noises and measurement noises. The recently developed generalized density evolution equation is utilized to formulate the joint probability density function (PDF) of the estimation errors. Combining the entropy of the estimation error with the mean squared error, a novel performance index is constructed to ensure the estimation error not only has small uncertainty but also approaches to zero. According to the conjugate gradient method, the optimal filter gain matrix is then obtained by minimizing the improved minimum error entropy criterion. In addition, the condition is proposed to guarantee that the estimation error dynamics is exponentially bounded in the mean square sense. Finally, the comparative simulation results are presented to show that the proposed MEE filter is superior to nonlinear unscented Kalman filter (UKF)