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.
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.
This article presents the expressions which allow evaluating the potential accuracy of radio source location by the method of «imaginary base» when using the linear model of changing the bearing on it. The concept of the method of «imaginary base» is to be used in solving the triangulation problem not only of measuring bearing, but also their extrapolated values at a certain time interval. Potential characteristics is determined by accuracy, dynamic and geometrical factors, bearing measurement and extrapolation times. The article shows that when using a linear model, there are limitations both on the time of measuring bearing and on the time of extrapolation. It will be because of the increase in the variance of the error of estimating the distance. Limiting of series decomposition members number of non-linear bearing change dependence from time there are. It depends on the speed of changing bearing (depends on the range and speed) and the initial bearing (depends on the track angle). Extrapolation over long time intervals is possible only at long distances and at relatively low speeds.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.