In this paper we address the problem of tracking a signal through successive intervals of matched-filter processing. The common approach to this problem is to locate candidate detections in the matched-filter output at each interval, to associate successive detections in state space, to estimate successive states through a Kalman filter application, and to rank association sequences (tracks) with respect to kinematic consistency. However, if a signature model is available and matched-filter statistics are known, the matched-filter output can be converted to a likelihood function that can drive recursive Bayesian processing for the signal state distribution (and no-signal probability). The field tracker described here follows this processing, compromising the optimality of the Bayesian approach only through the discreteness of the state-space domain. The field approach has a detection capability superior to that of an association approach for low SNR signals, and it is highly compatible with parallel processing. An application to the detection and tracking of a constant-velocity signal in 4-D state space (2-D position, 2-D velocity) is provided by way of illustration, and it demonstrates the ability to achieve a conclusive detection of a 3.5-dB-per-update target in ten updates. A number of application alternatives are described that extend the concept to multiple-target scenarios, refined velocity estimates, connection to velocity-independent processing steams, and computationally efficient means of estimating kinematic variables and signal amplitude through auxiliary fields.