For the practical application of single beacon navigation system, effective sound velocity (ESV) setting error, measurement outliers and unknown noise statistical parameters are the major sources of positioning error. Although the unknown ESV of single beacon navigation system has been well studied, the other two sources are less concerned. The performance of existing state-of-art navigation methods will deteriorate when there are measurement outliers or noise statistical parameters setting error. This paper aims to fill the gap. We model the process and measurement noise of each state and measurement component based on their own stochastic properties, so that, the influence of measurement outliers can be incorporated into stochastic model. The unknown noise statistical parameters are regarded as random variables and the variational Bayesian approximation method is used to estimate them along with the navigation state. The corresponding robust adaptive single beacon navigation method is proposed. Moreover, the simulation and field data demonstrate that the proposed method is superior to the existing state-of-art navigation methods in the presence of measurement outliers and unknown noise statistical parameters.
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