Adaptive track detection for multi-static active sonar systems

Multi-static active sonar systems detect contacts of interest by transmitting coherent waveforms and detecting the echoes on one or more receiving sensors. When a target of interest is in a region where its echoes are detectable by moire than one receiver it can, in general, be declared sooner toy combining the measurements from all sensors. The track detection schemes used in active sonar systems are often based on the Wald Sequential Probability Ratio Test (SPRT) [1] and take as input the amplitudes of the target echoes associated to the track and where the statistical models for the amplitude of a target echo usually depend on a signal-to-noise ratio (SNR) parameter. Two popular multi-static track detection schemes accumulate a separate SPRT for each target at each sensor. Tracks are declared using one of two rules: if any of the separate SPRTs for a target exceeds the declare threshold then the target is declared (i.e., the OR detector), if the sum of the separate SPRTs goes over the declare threshold then the target is declared (i.e., the SUM detector). The main problem with both methods is that the track detection problem is composite; the distribution for the target-present case depends on the SNR parameter, which is a priori unknown and different source/receiver combinations win typically observe different values of SNR on the same target. In practice, a fixed design value (e.g., 10 dB) is often chosen so that each sensor will separately achieve the desired probability of detection for SNR values greater than or equal to the design value. However, when combining measurements from two or more sensors, this approach can be suboptimal when only one sensor is observing a value of SNR at or above the design value and the SNR for the other sensors are lower than the design value. Under such conditions, the OR detector will not achieve any significant increase in the probability of target detection over the single high-SNR sensor and will have a higher probability of false alarm. In the same conditions, the SUM detector will have a lower probability of detection than the separate high-SMR sensor. In effect, the OR and SUM detection schemes will only increase overall system probability of detection when the SNR values for more than one sensor are at or above the design value. Thus, achieving a gain in overall probability of detection requires a scheme that can recognize the conditions under which a group of sensors will observe dissimilar target SNR values and adapt the relevant parameters in the distributions used to compute a single SPRT statistic. The Multi-Static Adaptive Track Detector (MSATD) is an SPRT based track detection scheme that uses estimates of target aspect derived from track state estimates and a model of bi-static target strength to adapt the parameters in the distribution for target echo amplitude. Essentially, the SUM detector is modified to use different values for SNR parameter at each sensor. The SNR parameters are determined using a model of bistatic target strength and estimates of the target aspect observed by each sensor computed from the current track state estimate. The theoretical improvement in system track detection performance (i.e., probability of detection and latency) afforded by the proposed method is also presented; theoretically exact expressions for probability of detection and latency are evaluated numerically for all three track detection schemes for a system of one source and two receivers.