Fusing quantized observations in multisensor random signal detection

Optimum detection schemes based on fusing quantized data taken from multiple sensors are of great interest in radar and sonar applications. The design and properties of such schemes are considered here for detection of weak random signals in additive, possibly non-Gaussian, noise. Signal-to-noise ratios are assumed unknown and the signals at the different sensors may be statistically dependent. Analytical expressions describing the best way to fuse the quantized observations for cases with any given observation sample size are provided. The best schemes for originally quantising the observations are also studied for the case of asymptotically large observation sample sires. These schemes are shown to minimise the mean-squared error between the best weak-signal test statistic based on unquantized observations and the best weak-signal test statistic based on quantised observations (under signal absent).