A new iterative algorithm for geolocating a known altitude target using TDOA and FDOA measurements in the presence of satellite location uncertainty

This paper considers the problem of geolocating a target on the Earth surface whose altitude is known previously using the target signal time difference of arrival （TDOA） and frequency difference of arrival （FDOA） measurements obtained at satellites. The number of satellites available for the geolocation task is more than sufficient and their locations are subject to random errors. This paper derives the constrained Cramor-Rao lower bound （CCRLB） of the target position, and on the basis of the CCRLB analysis, an approximately efficient constrained maximum likelihood estimator （CMLE） for geolocating the target is established. A new iterative algorithm for solving the CMLE is then proposed, where the updated target position estimate is shown to be the globally optimal solution to a generalized trust region sub-problem （GTRS） which can be found via a simple bisection search. First-order mean square error （MSE） analysis is conducted to quantify the performance degradation when the known target altitude is assumed to be precise but indeed has an unknown but deterministic error. Computer simulations are used to compare the performance of the proposed iterative geolocation technique with those of two benchmark algorithms. They verify the approximate efficiency of the proposed algorithm and the validity of the MSE analysis.