This paper discusses an issue in the implementation of Kalman filter tracking systems. The issue is the relationship between processing time in generating measurement data, the search area needed for such measurements, and the errors in the measurement data produced, A key observation is that in certain cases (particularly when the underlying model used in the Kalman filter is not asymptotically stable) processing time may be a very real issue. The analysis of several cases shows that a variable precision measurement computation strategy may be of benefit. One of the motivating examples is a tracking system using image-type data. The study is performed for a first-order system and shows the difficulties encountered with multidimensional systems.