Quantum limited optical tracking

Most optical tracking algorithms are based upon a set of intensity measurements from an array of discrete dectector elements. However, as technology progresses, the number of possible detector elements per unit will increase so that in the limit it is reasonable to consider a spatially distributed measurement. In such a limit, the appropriate model is the space-time point process. We present the minimum mean square error (MMSE) estimator structure for the general problem of tracking the centroid of a Gaussian shaped intensity profile based upon such a measurement. Both upper and lower bounds on MSE are presented as well as an indication of operating regimes where the bounds are nearly equal. Thus quantum limited minimum signal levels are established for which acceptable performance can be obtained. The estimator structure and performance are compared to those obtained in the discrete array case in order to study the effects of finite detector size. Finally, Monte Carlo simulation results are presented to verify the bounds and to illustrate the sensitivity of the results to the measurement model assumptions.