Track-Before-Estimate for Low-Elevation Targets in the Presence of Multipath

The presence of multipath effect leads to significant errors in elevation angle measurements, resulting in performance degradation in subsequent tracking. In this article, a track-before-estimate method is proposed to eliminate the effect of multipath on low-elevation target tracking under specular reflection conditions when the sea surface is smooth relative to the radar wavelength. Based on the understanding that multipath errors are not random noise but definitive measurements arising from multipath propagation, the monopulse ratio is employed rather than the elevation angle as the measurement in the tracking process to provide Cartesian state estimates. Under the specular reflection assumption, an accurate measurement equation is established according to the geometric relationship between the target and the reflection point to describe the relationship between the monopulse ratio and target height. This enables the transformation from the traditional track-after-estimate strategy to track-before-estimate strategy. Under the circumstances that the reflection coefficient is unknown and time-varying, the coefficient can be estimated by incorporating it into the state vector, or alternatively, the wave height can be incorporated into the state vector and estimated instead, indirectly providing an estimate of the reflection coefficient. The unscented Kalman filter is employed to extract Cartesian states and the sea surface reflection coefficient from monopulse ratio measurements. To deal with the filter initialization issue that one monopulse ratio measurement may correspond to multiple initial height estimates, a multiple subfilter strategy is proposed based on the static multiple model framework, where each subfilter corresponds to one possible height estimate. The bisection method is adopted to find out all the possible height estimates from multiple height intervals divided according to the transmitted frequency. Numerical simulations are conducted to evaluate the effectiveness and stability of the proposed track-before-estimate method. Benefiting from the effective utilization of the monopulse ratio measurement in the presence of multipath, superior estimation performance is achieved.