Observability-Based Gaussian Sum Cubature Kalman Filter for Three-Dimensional Target Tracking Using a Single Two-Dimensional Radar

This paper considers the problem of tracking a three-dimensional target under the condition that only a single two-dimensional radar is available. Since a two-dimensional radar can only measure the slant range and azimuth information relative to the target, an unobservability issue arises in this tracking application. Therefore, we first investigate the observability issue of tracking a three-dimensional target with a single two-dimensional radar from two perspectives, including intuitive illustration and quantitative analysis. From the perspective of intuitive illustration, we demonstrate "What is the unobservability issue" and "How does the relative target-radar geometry influence the observability of the tracking system". From the perspective of quantitative analysis, we construct a novel observability metric for this special tracking problem. Second, aiming at improving tracking performance under the unobservability of target height, we propose an observability-based Gaussian sum cubature Kalman filter. Built within the Gaussian sum framework and based on the height-parameterized strategy, this novel algorithm uses a set of independent fifth-degree cubature Kalman filters, each of which can detect the system observability variation and enhance the tracking accuracy by using a Gaussian splitting scheme under low-degree observability. Finally, the effectiveness of the presented filtering algorithm is validated through lots of simulation experiments.