Maximum likelihood geolocation using a ground moving target indicator (GMTI) report

The ground moving target indicator (GMTI) radar sensor [1] plays an important role in surveillance and precision tracking of ground targets. The measurements of a GMTI sensor are range, azimuth, and range-rate, which are nonlinear functions of the target state. An initial estimate of the target state and associated covariance are required in the tracking filter using the first GMTI report. The sensor position and terrain data (digital terrain elevation data (DTED) and geoid undulation [2],[3]) are also used to determine the initial estimate. Current approaches [4],[5] determine the three-dimensional location of the target using the observed range, azimuth, and terrain data in a deterministic manner. Given the observed range, azimuth, and sensor position, the locus of possible target locations is a circle with the center at the sensor position. In the deterministic approach, the intersection of the circle with the observed surface of the Earth gives the target location. In realistic scenarios, the sensor position and terrain data contain errors which are not negligible compared with the GMTI measurement errors. The deterministic estimate of the target position does not take into account the covariances for various error sources. In this paper we first develop the generalized maximum likelihood (ML) parameter estimation algorithm using a general nonlinear measurement error model and error models for consider variables which are used in the measurement equation but are not estimated. An example of a consider variable is the sensor position. We then apply the generalized ML algorithm to the three-dimensional target location estimation problem that not only uses the GMTI measurement error model but also the error models for the sensor position and terrain data. Since the estimation problem is nonlinear, an initial estimate of the target position is required. The target position obtained from the deterministic approach is used as an initial estimate for the NIL estimator. We present numerical results for the ML estimate of the target position and covariance using the terrain data, WGS84 EGM96 geoid undulation data [2],[3], and simulated GMTI measurements.