Recursive instrumental variable method for locating a scanning emitter by a single observer using time of interception

The recursive solution to passive localisation of a scanning emitter using time of interception (TOI) by a single moving observer is investigated in this study. First, the correlated measurement noise in the traditional pseudo-linear model for the scanning emitter localisation is decoupled by introducing the first noise corrupted direction of arrival as a nuisance parameter. A recursive pseudo-linear least square (RPLS) estimator is then developed by transforming the TOI of the scanning emitter into the direction difference of arrival model. However, there is bias in this method due to the correlation between the measurement matrix and the noise. To reduce the bias, the instrumental variable (IV) method is used, and two recursive IV (RIV) estimators, forgetting factor based RIV (F2RIV) and Taylor series expansion based RIV (TSRIV), are proposed. It approximates the IV matrix recursively using the Taylor series expansion in the TSRIV estimator. Simulations show that the TSRIV estimator alleviates the bias compared with the RPLS estimator dramatically and can reach the Cramer-Rao lower bound at moderate measurement noise levels. Moreover, it is more stable and has shorter convergence time than the F2RIV estimator.