Recursive Estimation Algorithms for AUV Collaborative Navigation in Case of Abnormal Outliers in Measurements

The problem of navigation for multiple autonomous unmanned underwater vehicles is considered, when information about the distances between the vehicles within the group is used as measurements. Two cases are discussed: in the first case, distance measurement errors have a normal distribution, while in the second case they contain abnormal outliers. Three algorithms within the stochastic Bayesian approach have been design to solve the problem: the well-known extended Kalman filter and the recently developed correntropy extended Kalman filter. The third algorithm is a modification of the extended Kalman filter. To construct it, a special procedure described in this paper was used, which aims to reject abnormal outliers in the errors of measuring the distance between underwater vehicles. This procedure is based on comparing the filter residual with the calculated value of the corresponding diagonal elements of the covariance matrix of measurement prediction errors. Their interrelations and differences for all three algorithms are analyzed. By conducting predictive simulation using the method of statistical tests, their accuracy, consistency, and computational complexity were compared. For this purpose, the methodology published earlier by the authors of the paper was used. The results of a comparative analysis of the algorithms were obtained both in the absence and presence of outliers in distance measurement errors.