AN OPTIMUM SEARCH IN RANGE AND RANGE RATE,
JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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Signals from a target being tracked in range x and range rate y are lost as a result of noise or jamming at t O. At time t t sub o signals are again available and a search can be undertaken to reacquire the target whose coordinates are assumed to be given by the equations, x sub T u sub T v sub T t and y sub T v sub T. In formulating the search problem the unknown constants u sub T and v sub T are replaced by the stationary random variables u and v which have a known joint probability density distribution, rhou, v. The non-stationary random variable, x, and the stationary random variable, y, are then defined in terms of u, v and t by the equations, x u vt and y v. A search for the target, either in the xy-plane for the moving point x sub T, y sub T or in the uv-plane for the fixed point u sub T, v sub T, is said to be optimum if the target is found in the least time possible or, what is equivalent, if the mean cumulative acquisition time is a minimum. In this report the optimum search in the uv-plane is obtained for an arbitrary distribution, rhou, v. Also, an example of the optimum search is offered for the case where u and v are independent random variables with normal probability density distributions. The example includes the optimum searches in the uv- and xy-planes.
- Statistics and Probability
- Active and Passive Radar Detection and Equipment