A Geometric Transversals Approach to Analyzing the Probability of Track Detection for Maneuvering Targets

There is considerable precedence in the sensor tracking and estimation literature for modeling maneuvering targets by Markov motion models in order to estimate the target state from multiple, distributed sensor measurements. Although the transition probability density functions of these Markov models are routinely outputted by tracking and estimation algorithms, little work has been done to use them in sensor coordination and control algorithms. This paper presents a geometric transversals approach for representing the probability of track detection by multiple, distributed sensors, as a function of the Markov model transition probabilities. By this approach, the Markov parameters of maneuvering targets that may be detected by the sensors are represented by three-dimensional cones that are finitely generated by the sensors fields-of-view in a spatiotemporal Euclidian space. Then, the problem of deploying a sensor network for the purpose of maximizing the expected number of target detections can be formulated as a nonlinear program that can be solved numerically for the optimal sensor placement. Numerical results show that the optimal sensor placements obtained by this geometric transversals approach significantly outperform greedy, grid, or randomized sensor deployments.