Negative correlation and optimal tracking with Doppler measurements

In target tracking systems that utilize Doppler radar (or sonar), the measurements consist of range, range rate, and one or two angles, When multiple sensors are used in the proper geometry, the final accuracy is determined primarily by each sensor's range estimation accuracy. In this case it is particularly important to extract the most accurate state estimate in the range direction by processing optimally the range and range rate measurements. The usual assumption in the design of tracking filters is that the measurement errors in range and range rate are uncorrelated. However, in the case of the commonly used upsweep chirp (linear FM) waveforms, there can be a significant negative correlation between the range and range rate measurement noises. The purpose of this note is to quantify the performance improvement one can obtain when this correlation is present, as it is in certain waveforms, and accounted for.