On the Probability of Cross-Radar Assignment Error

If two radar sensors observe the same target their measurements can be combined to produce a fused target-state estimate that is of higher quality than that from one radar alone. If there are multiple targets whose information is shared, a necessary first step to fusion is to 'assign' each measurement from the first sensor to that at the other in such a way that both refer to the same underlying object, a task generally accomplished by minimizing a global cost involving distance. An assignment error occurs when the measurement originated by target i at the first radar is wrongly associated to a measurement originated by target j (not i) at the second radar. Naturally, when such an error occurs the result is fusion of information describing disparate objects, resulting in degraded estimation performance and poor self-assessment in terms of posterior uncertainty. Here we address the issue, and derive approximate assignment error probability. Remarkably, performance depends only upon the parameters combined to a single scalar constant.