Optimal and sub-optimal fusion of α-β target tracks

This paper considers the optimal and sub-optimal fusion of position measurements to track a maneuvering target. The sub-optimal technique allows α-β filters to operate on measurements separately, yielding distinct target tracks. These tracks are then fused into one via a linear combiner. Derived in closed-form is the inter-relational performance between the α-β filters and the MSE optimal coefficients of the linear combiner. The optimal technique uses a Kalman filter to derived an α-β Matrix Fusion Tracker in closed-form. The α-β Matrix Fusion Tracker is a set of optimal α-β fusion tracking parameters based solely on measurement errors, measurement update time and target maneuverability. It is shown that the α-β Matrix Fusion Tracker is equivalent to a steady-state Kalman filter with stationary noise processes. Furthermore, it is shown that the measurement fusion process can be reduced to a single optimal α-β filter operating on the combined measurement from two measurement inputs. This technique results in the derivation of the α-β Fusion Tracker. Numerical examples are presented to show the relative performance between optimal and sub-optimal fusion techniques and also to verify all derived results.