New developments in nonlinear filtering using differential algebra

This dissertation presents five different solutions to the nonlinear filtering problem. Three filtering techniques present a different systematic generalization of the linear update structure associated with the extended Kalman filter for high order polynomial estimation of nonlinear dynamical systems. The minimum mean-square error criterion is used as the cost function to determine the optimal polynomial update during the estimation process. Furthermore, both the propagated and posterior probability density functions (PDFs) can be represented through Taylor expansion polynomials, giving an accurate approximation of the shape of the distribution, and providing the base for a new Maximum A Posteriori estimation technique. The high order series representation is implemented using differential algebra (DA) techniques. Differential algebra has been presented as an efficient tool to map PDFs, propagate central moments, and reduce computational burden on Monte Carlo based filtering techniques. Each proposed algorithm has been tested on strongly nonlinear applications, where the most common filters in the literature fail to provide a correct estimate.