Abstract: Existing localization methods using second order changing rate of time of arrival (TOA) can not achieve a high precise estimation when the acceleration of the observing station is small. A new locating method is proposed by estimating the TOA changing rate for each duration slice of the observation. A biased estimator is used to reduce the root mean square error (RMSE) by ignoring the relative acceleration. Firstly, Newton iterative method is adopted to get a rough estimation of the position based on the biased estimation. Secondly, the position bias can be calculated approximately with the coarse estimation. Finally, the location is revised by eliminating the calculated position bias from the rough estimation. The location errors before and after correction are induced consisting of the random and biased portion. The numerical simulations demonstrate that the localization based on TOA changing rate is more precise than the one based on second order changing rate of TOA, and the correction procedure can modify the position estimation efficiently. The location precision is better than that of the conventional unbiased method.

Key words: passive location, single channel, time of arrival (TOA) changing rate, biased estimation, bias correction