A new approach to multi-target data association is presented. In this new approach, the problem of correctly associating measurements to the object from which they originate is viewed as an impulse optimization. In the systems considered, a single sensor attempts to measure a pre-specified object of interest. Interpolating the discrete set of measurements, it is possible to compute a "measurement trajectory." The action of the sensor randomly measuring a system target other than the object of interest is viewed as an impulse in the measurement trajectory. It is possible to correctly associate measurements by determining the times at which the impulses occur. The main contribution of the work presented in this paper is to provide a method for estimating the total number of impulses.