In this paper, we introduce a new method for tracking multiple objects. The method combines Kalman filtering and the Expectation Maximization (EM) algorithm in a novel way to deal with observations that obey a Gaussian mixture model instead of a unimodal distribution that is assumed by the ordinary Kalman filter. It also involves a new approach to measuring the object locations using a series of morphological operations with binary masks. The benefit of this approach is that soft assignment of the measurements to corresponding objects can be performed automatically using their a posteriori probabilities. This is a general approach for multi-object tracking, and there are basically various ways to segment the objects, but in this paper we use simple color features simply to demonstrate the feasibility of the concept.