A high order method for estimation of dynamic systems, part I: Theory
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An analytical approach to propagate neighboring initial conditions through nonlinear dynamical systems is considered for developing an estimation framework (called the J* Moment Extended Kalman Filter (JMEKF)). This forms an important component of a class of architectures under investigation to study the interplay of major issues in nonlinear estimation such as model nonlinearity, measurement sparsity and initial condition uncertainty in the presence of low process noise. Utilizing the analyticity of the model, an approximate solution for the departure motion dynamics about a nominal trajectory is derived in the form of state transition tensors. The solution of the state transition tensor equations are subsequently utilized in evaluating the evolution of statistics of the departure motion as a function of the statistics of initial conditions. The statistics thus obtained are used in the determination of a state estimate assuming a Kalman update structure. Central to the state transition tensor integration about a nominal, is the high order sensitivity calculations of the nonlinear models (dynamics and measurement), being automated by OCEA (Object Oriented Coordinate Embedding Method), a computational tool generating the partials without user intervention. Working in tandem is a vector matrix representation structure of tensors of arbitrary rank facilitating faster and more accurate computations. High order moment update equations are derived to incorporate the statistical effects of the innovations process more rigorously, improving the effectiveness of the estimation scheme. Numerical examples evaluate the gain of the proposed methodology.
author list (cited authors)
Majji, M., Turner, J. D., & Junkins, J. L.