Abstract
Bayes'rule can be directly applied to estimation using noisy non-linear measurements in real systems. This requires an on-line computer to implement numerical computation of conditional probability distributions and their statistics: suitable machines are now routinely available for distributions of low dimensionality.
Practical numerical problems can arise in connection with grid-scaling, prediction, and dimensionality. Gaussian approximation is well known as a way to avoid the first two of these: numerical results are included which demonstrate the power of this approximation. The main contribution of the paper is a novel linearisation which avoids the curse of dimensionality in Wiener systems where several random variables are observed through a noisy non-linear function of their weighted sum.
The work was motivated by case studies and is justified by examples from simulations and experimental studies. Analysis to guarantee reliability of the method is not yet available.
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