A technique for estimating the state of a nonlinear system

A technique for the estimation of the state of a general class of nonlinear systems is discussed. The technique involves linear optimal estimation of the state of a linear approximation to the nonlinear system. The linear approximation to the nonlinear system is derived solely from the nonlinear differential equations and the noise-corrupted observations of some of the components of the state vector of the nonlinear system. An example of optimal estimation of the current position and velocity of a low earth-orbit satellite, using range, elevation and azimuth observations from a ground tracking station, is discussed. Numerical results from a digital simulation of the example are presented.