A widely used estimator for multi-target tracking, conventionally referred to as a maximum likelihood estimator, is analyzed. For the problem of locating closely spaced fixed, untagged objects using a noiseless sensor, the conventional estimator's mean and variance estimates are inconsistent, i.e. asymptotically biased. We propose an alternative maximum likelihood estimator that corrects this problem. This estimator uses a coherent sum over report to track associations to evaluate the track likelihood function. The resulting estimator is efficient in the sense that it achieves the Cramer-Rao lower bound (CRLB) on the variance asymptotically. A novel feature of this approach is that it entails estimation of track error correlations in addition to the variance estimates generated in the usual Kalman filter based methods. These motions are used to develop a filter for a pair of uncorrelated Brownian walkers. It successfully estimates the error correlations that must be present in an optimal filter.