This paper presents a novel type of Kalman filter for track maintenance in multitarget tracking using thresholded sensor data at high target/clutter densities and low detection levels. The filter is robust against tracking errors induced by crossing tracks, clutter, and missed detections, and the computational complexity of the filter scales well with problem size. There are two key features that differentiate this approach from earlier work. First, to reduce computational load, the filter exploits techniques from statistical field theory to simplify measurement to track association by using a mean-field approximation to sum over associations. Second, to enhance tracking of close together targets, the filter explicitly models the error correlations that occur between such target pairs. These error correlations are caused by measurement to track association ambiguities that arise when target separations are comparable to sensor measurement errors.