Approximating the Poisson Scan and (λ-σ) acoustic detection model with a Random Search formula

Random Search is one of the most well-known model for area search. However, because of its simplicity, it has inherent limitations. For example, it assumes that the searcher and target search areas are identical and that the searcher uses a perfect cookie-cutter sensor. In this study, we develop a MATLAB simulation of area search with acoustic sensors modeled by the Poisson Scan model and the Lambda-Sigma model. Detection time results are compared to those given by the much simpler Random Search formula. Random Search was found to closely approximate the more complex models if detection range was selected correctly. Guidelines for selecting the Random Search detection range were developed. There are two primary contributions of this paper. The first is the demonstration that initial detection times for area search simulations using both the Poisson Scan and Lambda-Sigma acoustic detection models are approximately exponentially distributed, allowing the simulation results to be closely approximated by the venerable Random Search formula. The second one is the observation that the best-fit cookie-cutter detection range used in the Random Search formula can be accurately predicted using the simulation model parameters, λ, σ, and the detection range.