Gaussian sum approximations for nonlinear filtering

A sum of weighted gaussian probability density functions can be used to approximate another density function. This representation provides the basis for a procedure for computing the conditional density p(xk|zk) of the state xk of a nonlinear dynamical system given all available measurement data zk. As is well-known, estimates of the state xk for any performance criterion can be determined in a relatively straight forward manner if one has p(xk|zk). Consequently, knowledge of this density function essentiaUy constitutes a solution of the general nonlinear filtering problem.