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Analytical calculation for probability of detection given time-dependent search parameters

The problem solved in this paper is easily stated: given search parameters (p∞, τ) that are known functions of time, calculate how the probability a single observer acquires a target grows with time. This problem has been solved analytically. In this paper we describe the analytical solution and provide derivations of the results. Comparison with perception experiments will be reported in a future publication and hopefully will support the results presented here. The provided solution is applicable to any scenario where the search parameters are changing with time and are specified. In particular, the solution can be used to estimate the probability of target acquisition as a function of time: (1) when the sensor-target range is changing, (2) for a slewed sensor where the target is alternately in and out of the field of view, and (3) for a sensor that switches between wide and narrow fields of view.