A Global Optimal Gaussian Mixture Reduction Approach Based on Integer Linear Programming

In many applications, the Gaussian mixture serves as an important probabilistic representation of the system state. A global optimal Gaussian mixture reduction (GMR) approach based on Integer linear programming (ILP) is developed in this paper. Firstly, a Gaussian base set is constructed with partial merging of components of the original mixture. Secondly, by introducing auxiliary variables reasonably, the original problem of selecting the best candidates from the given Gaussian base set is formulated as an ILP problem. Finally, a global optimal solution to GMR is obtained by solving the ILP problem. The global optimum property enables it as a basis for performance comparison with different GMR algorithms.