Introduction: An underwater surveillance system composed of a single source and receiver couple is called a bistatic sonar. The sensing zone of a bistatic sonar is typically modeled as the interior of a Cassini oval. A Cassini oval is a type of quartic plane curve which can be defined as the set of points in the twodimensional plane such that the product of the distances to two fixed points is constant.The Cassini oval is symmetrical about the xaxis and the yaxis. Depending on the distance between its foci, it can take the shape of (1) a single convex that looks like an ellipse, (2) a nonconvex oval with a dent on top and bottom, (3) Lemniscate of Bernoulli, or (4) two mirror imaged disjoint ovals. No closed form expressions exist to compute the exact area of a Cassini oval, but it can be computed by numerical integration or Willis (2005)’s approximation. In this study, we consider a randomly deployed source and receiver and seek to develop equations to approximate the expected area coverage of a bistatic sonar deployed in a rectangular sea zone. For this purpose we adopt simple analytic geometry and use Monte Carlo simulations to verify our results. Purpose: The purpose of this research is to derive equations which can be used to approximate the area covered by a randomly deployed bistatic sonar. Such approximations are especially useful for planners in decision making problems which require back of the envelope type analysis. Scope: The scope of this study includes a bistatic sonar which is composed of a single source and receiver. It considers deployment tactics that are conducted uniform randomly to rectangular sea area. Although our motivation comes primarily from underwater detection systems, some aspects of our approach are generalizable to radar or similar geolocation systems. The research has lasted approximately two months. Limitations: The scope of this study does not incorporate practical issues such as depth, drift, mobile sensors, mobile targets, reverberation, etc. Method: To achieve our objectives, we first mapped the coverage problem to a twodimensional geometry problem. In particular, since the area of a Cassini shaped bistatic sensing zone depends on the distance between the two sensors, we approximated this measure by mapping it to the distance between two random points in a rectangle. Next, using this approximation, we developed a formula to approximate the area of the randomly deployed bistatic sonar sensing zone. The analytic results are verified with Monte Carlo simulations. Findings: The simulation results showed that the approximations developed using analytic geometry are reliable and can be used by decisionmakers and planners to measure the expected performance of a search operation using bistatic sonars. The results also revealed that, as the size of the area that the sensors are deployed increases, the expected coverage also decreases. Conclusion: The results obtained both through our analytic derivations and Monte Carlo simulations showed that the expected area coverage of bistatic sonars can be computed by analytic techniques. The results gained in this study can be used by planners in order to approximate and measure the effectiveness of their sensors in searching areas as well as utilizing them for a better performance.
Anahtar Kelimeler: Bistatic Sonar, Area Coverage, Simulation
