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The problem of cooperative track detection by a dynamic sensor network arises in many applications, including security and surveillance, and tracking of endangered species. Several authors have recently shown that the quality-of-service of these networks can be statically optimized by placing the sensors in the region of interest (ROI) via mathematical programming. However, if the sensors are subject to external forcing, such as winds or currents, they may be rapidly displaced, and their quality-of-service may be significantly deteriorated over time. The novel approach presented in this paper consists of placing the sensors in the ROI based on their future displacement, which can be estimated from environmental forecasts and sensor dynamic models. The sensor network deployment is viewed as a new problem in dynamic computational geometry, in which the initial positions of a family of circles with time-varying radii and positions are to be optimized subject to sets of algebraic and differential equations. When these equations are nonlinear and time-varying, the optimization problem does not have an exact solution, or global optimum, but can be approximated as a finite-dimensional nonlinear program by discretizing the quality-of-service and the dynamic models with respect to time. Then, a near-optimal solution for the initial sensor positions is sought by means of sequential quadratic programming. The numerical results show that this approach can improve quality-of-service by up to a factor of five compared to existing techniques, and its performance is robust to propagated modeling and deployment errors.