In this paper we describe a refined stochastic model for the errors of the Loran-C radio navigation aid, and show how this model can be used to improve the performance of integrated navigation systems. In addition to the usual propagation errors, Loran-C time of arrival measurements are occasionally plagued with sudden intermittent errors of a particular magnitude and caused by receiver cycle selection errors. These result in sudden large jumps in the calculated position solution. Standard stochastic models, described by linear Ito differential equations driven by Wiener processes, cannot adequately describe the behavior of these cycle selection errors. In this paper the Loran-C error has therefore been modeled as the sum of a diffusion process, representing the normal propagation errors, and a pure jump process of Poisson type, representing the cycle selection errors. A simple integrated navigation system is then described, based on the Loran-C model and the standard dead reckoning (heading and speed) system model. Assuming that the observed process is governed by a linear stochastic difference equation, a recursive linear unbiased minimum variance filter is developed, from which the Loran-C and dead reckoning errors, and hence position and velocity, can be estimated. Finally, a numerical example is presented to illustrate the expected behavior of this proposed filter in comparison with the usual Kalman filter.
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