Incorporation of Range and Range-Rate Evidence Into Acoustic Contact Data Fusion-Part II

Data fusion and contact correlation are integral parts of submarine passive sonar systems. With increasing emphasis on automation in sonar applications, acoustic contact correlation procedures provide a powerful tool to aid the operator in processing multiple pieces of evidence and to enhance overall detectability of threats. Geometric evidence, in the form of bearing and range data, is especially critical in arriving at a correct target association. In the present work, Bayesian inference techniques are used to process pieces of geometric evidence through a probabilistic network, alone or in combination. Previous studies indicated that merging bearing and range data in an exact manner increases the probability of a correct target association, but is more difficult to implement in real time than algorithms based on only one type of evidence. Because all bits of uncorrelated data are significant, intermediate methods of at least partial incorporation are worth exploring. The objective of the present work is the evaluation of algorithms based on logical AND/OR techniques in acoustic contact correlation. Specifically, two incoming pieces of bearing and range data were compared according to an appropriate criterion, and one selected over the other to be processed through the Bayesian Inference Network (BIN). Assuming independent Gaussian random variables, expressions for the AND/OR probability density functions of the likelihood ratios were derived in terms of the separate likelihood ratios for bearing and range. These were then used in a set of Fredholm integral equations that were solved recursively for the final probabilities. Calculations were carried out for various bearing and range gate width parameters, as well as a range of signal-to-noise (SNR) ratios. Not surprisingly, results indicated that incorporation of all geometric evidence gives better performance than partial consideration of data in an AND/OR algorithm. In all cases, AND/OR results were comparable, with slight variations between the two logical methods depending on the relative magnitudes of the maximum likelihood ratios for bearing and range. At SNRs over −10 dB, logical AND/OR networks produced results almost as good as the exact method and may be used with relative reliability. At intermediate SNRs (≈ −15 dB), AND/ORing underpredicted the exact method by ≈ 11% and the range-only scheme by ≈ 6%. At SNRs below −20 dB, however, AND/ORing produced results from 12 to 16% worse than the exact method. Complete incorporation of range and bearing evidence into the data fusion process is therefore recommended at low signal-to-noise ratios.