Evaluation of the probability of correct positioning of the beacon and its motion parameters in passive search and rescue systems

Abstract

In this article, the approach to evaluate the probability of estimating the range of the beacon with a given accuracy is proposed. To determine the range to the beacon, a set of Kalman filters is applied to the beacon bearing measurements according to the given hypotheses about its motion parameters. The calculation of the probability of the correct choice of a hypothesis is presented. The hypothesis with the minimum sum of squared residuals is considered without prediction errors, its expectation and standard deviation, respectively, are. The time, required to determine the range with the probability 0.9..0.95 is calculated according to the proposed method agrees with the results obtained by statistical analysis, performed over multiple data sets. The results of the simulation of the “frequency” graph are shown.