GEOLOCATION OF A KNOWN ALTITUDE OBJECT FROM TDOA AND FDOA MEASUREMENTS

Most satellite systems for locating an object on Earth use only time d ifference of arrival (TDOA) measurements. When there are relative moti ons between an emitter and receivers, frequency difference of arrival (FDOA) measurements can be used as well. Often, the altitude of an obj ect is known (it is zero, for example) or can be measured with an alti meter. Two sets of geolocation solutions are proposed which exploit th e altitude constraint to improve the localization accuracy. One is for TDOAs alone and the other for the combination of TDOA and FDOA measur ements. The additional complexity by imposing the constraint is a one- dimensional Newton's search and the rooting of a polynomial. The covar iance matrices of the new estimators are derived under a small measure ment noise assumption and shown to attain the constrained Cramer-Rao l ower bound (CRLB). When there is a bias error in the assumed altitude, using the altitude constraint will introduce a bias to the solution. Since applying the constraint decreases the variance, there is a trade off between variance and bias in the mean square error (MSE). The maxi mum allowable altitude error such that the constraint solution will re main superior to the unconstraint is given. Simulation results are inc luded to corroborate the theoretical development.