Nonlinear static filtering and prediction considering quadratic terms

The parameters are considered as normal random quantities in filtering and prediction, and the observation equations usually are nonlinear ones. The nonlinear equations should be deployed in Taylor‘s formula, adopting to first power of term, by linear static filtering and prediction, and transformed into linear equations, and then the tested estimating values and their variances according to some statistical methods such as maximum tested estimation. The formulas of nonlinear static filtering and prediction,adapting to quadratic and cross terms by Taylor‘s progression formula, and the computation formulas were also deduced that filtering the corresponding function nonlinear signals and predicting the signals with nonlinear function. Meanwhile, it is been testified that the formula of static filtering and prediction is a special case of nonlinear filtering formulas.