Error Expressions for Optimal Stationary State Estimation

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Abstract
Explicit expressions are derived for the residual error covariance matrix in optimal causal prediction, filtering and interpolation of a stationary state vector satisfying a linear Ito differential equation with constant coefficients. The estimation is based on the output vector perturbed by noise that is mostly assumed to be white, but extensions to the colored noise case are also indicated. In particular, the error expressions for filtering in white noise provide an explicit solution to a matrix quadratic equation, also known as algebraic Riccati equation. Earlier results obtained by a similar technique are more general (but usually not explicit) expressions for the residual error covariance matrix in linear estimation problems.

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