Abstract The use of kinematic measurements for target classification has been explored recently by several authors. This paper formulates the general framework for optimal Bayesian estimation of target state and class. Since target class is a non-evolutionary attribute, the solution is conceptually based on a static multiple-class filter. When applied to linear/Gaussian estimation using acceleration limits, the class-matched filters can be aggregated into a single IMM filter, thus reducing the described general solution to the joint tracking and classification approach presented in earlier publications.