Abstract
This paper presents a method for the realization of nonlinear estimators based on an optimal quadrature approximation. The optimal quadrature formula is obtained by solving a set of nonlinear algebraic equations induced from a monospline subject to a set of interpolatory conditions. All the weights of the optimal quadrature formulas derived from monosplines which do not involve the derivatives of the integrand at the end points are positive. This guarantees the positiveness of the quantized density functions in numerical approximation of Bayesian recursive computations. The numerical errors associated with the optimal quadrature approximation to Bayesian recursive computations are discussed. Finally methods of quantizing and updating the prediction and filtering densities are derived.
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