Optimal Linear Multilateration Combined With the Kalman Filter for Range-Only Tracking

Abstract

This paper presents the optimal estimation for the extensively concerned linear multilateral positioning issues and further improves the accuracy of range-only tracking significantly. The traditional linear multilateration method has been used to achieve target positioning for range-only measurements, but the completeness of the theory and implementation effect are limited due to the imperfect model and the lack of proper statistical error analysis. Moreover, the performance of the representative nonlinear filters is not satisfactory because of the strong nonlinearity between the range observations and kinematic states of the moving target. This paper reveals the essence of the linear fusion of multiple distance sensors from a geometric perspective. The multi-sensor fusion model is reconstructed in the linear feature space by transforming the likelihood function into the probability function and separating the expectation of the compound random variable and residual. After that, a new linear multilateration method is developed based on the precise derivation of statistical characteristics corresponding to the linear fusion model, and also minimizing the squared Mahalanobis distance is introduced to replace minimizing the mean square error. The first-order moment, as a pseudo-measurement used to improve the positioning accuracy, and the second-order moment, as the covariance of the pseudo-measurement noise, are provided by this method, which has been proved to be best linear unbiased according to the Gauss–Markov theorem. Combined with the pseudo-measurement, a standard linear Kalman filter is capable of tracking the maneuvering target. Several simulations and experiments verify the superior performance of the proposed method.