Altitude Estimation Using Multipath With a Two-Dimensional Radar Over Spherical Earth

This paper presents a target altitude estimation approach based on multipath detections with range and range rate information from a two-dimensional (2-D) airborne radar. Using multipath detections has to deal with the following challenges: first, low probability of detection (PD) of the indirect path signal reflected by the sea surface; second, lack of an analytical expression for the relationship between the target motion parameter/state and the indirect path measurements over spherical earth; and third, unknown range measurement error standard deviation (s.d.) for the indirect path signal. Two estimators are developed: an adaptive multiple model iterated least squares (AMM-ILS) estimator for motion parameter estimation (noiseless target motion) and an AMM unscented Kalman filter (AMM-UKF) for dynamic state estimation (noisy target motion). Altitude estimate accuracy is studied based on simulation data. It shows that the AMM-ILS yields statistically efficient estimates (i.e., optimal and with a quantifiable accuracy), but this is not always true for the AMM-UKF. For a long distant target (e.g., 300 km) with very low indirect path PD (0.1 and 0.2), the AMM-UKF is inconsistent and inefficient statistically, due to biased estimation. The altitude Cramer Rao lower bounds from a 3-D radar with range and elevation measurements are also computed for comparison. The results show that the 2-D radar can provide better altitude estimates than the 3-D radar in most of the cases, except when the 3-D radar has accurate elevation measurement (with error s.d. $\sigma _e=0.5^{\circ }$ ) and the 2-D radar has very low indirect path PD (PD = 0.1).