Recursive LMMSE Fusion for Tracking With Non-Colocated Multi-Radar Measurements

In target tracking, multiple non-colocated radars usually make observations in their own local coordinate systems with different locations and attitudes. However, the fusion center normally performs tracking in a global Cartesian coordinate system, where target motion is usually modeled. As a result, existing recursive linear minimum mean square error (LMMSE) fusion algorithms, in which all radars are assumed to be colocated with the same orientations, are not valid. This paper deals with single target tracking with multiple non-colocated radar measurements. Recursive LMMSE fusion algorithms are proposed for the two-dimensional (2D) and three-dimensional (3D) cases, respectively. In addition, the impact of the locations and attitudes of radars on the fusion mean square error (MSE) is analyzed. For tracking with polar measurements, it is found that the fusion MSE cannot be different if and only if no radar location changes, regardless of attitudes. For tracking with spherical measurements, the same conclusion holds if and only if both the location and the
$\mathrm{z}$
-axis orientation of the coordinate system of each radar remain unchanged. Numerical examples are provided to demonstrate the effectiveness of the proposed recursive LMMSE fusion algorithm.