A CFAR detector commonly used for the detection of unresolved targets normalizes the background vaiiance by dividing the detection filter output by the local sample standard deviation. A number of researchers have measured the experimental false alarm probability of this detector and found it to be higher than the probability predicted by a Gaussian density funclion. This is the case even when the filter output statistics are known to be Gaussian distributed. A number of attempts have been made to heuiistically construct distribulions which exhibit the heavy tails associated with the measured false alarm probability (eg. sum oftwo Gaussian densities or the modified gamma density).This paper presents a first principles derivalion of the detector false alarm density function based upon the assumption that the filter output is Gaussian distributed. The resulting false alarm density function is veiy nearly Gaussian out to about 3.5 standard deviations. Past 3.5 standard deviations the tails ofthe derived density function are markedly heavier than the corresponding Gaussian tails. The parameters of this new density function are easily estimated from the filter output. The analytic results are validated using a ChiSquare goodness-of-fit test and experimental measurements of the false alarm density.

This paper considers the problem of tracking dim unresolved ground targets and helicopters in heavy clutter with a ground based sensor. To detect dim targets the threshold must be set low which results in a large number of false alarms. The tracker typically uses the target dynamics to prevent the false alarms from forming false tracks. The interesting aspect of this problem is that the targets may be or may become stationary. The tracks of stationary targets are difficult to discriminate from tracks formed by persistent false alarms.

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Problems associated with integrating, debugging and validating real time software systems are well known. Closed ioop tracking systems contain functional elements that illustrate the most difficult aspects of integrating, debugging, and ultimately validating the performance of real time software. Among these are severe real time constraints for line of sight control processing, image processing, inter-processor and peripheral communication. In addition, these highly complex algorithms are running on the target processors that are seldom tested end-to-end prior to system integration.The problem is exacerbated by unavailable or intermittently available hardware during the development and the integration phase of a typical program. Even with fully integrated hardware and software, performance validation is difficult because operational conditions of the platform and targets cannot be adequately represented in a laboratory setting without costly equipment to support hardware-inthe-loop simulation. The pressure to reduce cost and algorithm development to real-time software cycle time further aggravates the problem by limiting the time available for gaining confidence in the algorithms and software before they are committed to integration. This paper discusses a simulation approach that has streamlined the real-time software development process for a closed loop image-based tracking system. The MATLAB/SIMULINK simulation consists of elements constructed from common source modules shared with the deliverable system. The simulation has provided a tool to support algorithm development for the fundamental system components, including a system controller, a servo controller, and an image processor. In addition, the simulation has provided a testbed for verification of system performance. The context for this application is the low rate initial production phase of a tactical airborne avionics system that includes an image-based tracking system.

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