Probability of Position and Motion Parameters Estimation for a Radio Beacon in Passive Search and Rescue Systems

In this article, the method to estimate the range to the beacon in passive search and rescue systems is proposed. The range to the beacon is determined by applying a set of Kalman filters to the bearing measurements with different hypotheses of the beacon motion and subsequent selection of the hypothesis with the minimum sum of residual errors in target range estimation. The expressions for the expectation and standard deviation of the prediction errors are derived and the probability of selection the correct hypothesis is given. The proposed method allows to evaluate the measurement time, required to determine the range to the beacon with probability 0.9...0.95, which agrees well with statistical analysis of multiple data sets.