What question did this study set out to answer?

Formulate a solution to the optimum linear smoothing problem by synthesizing two independent optimal linear filters via maximum likelihood estimation.

August 1, 1969IEEE Transactions on Automatic Control

The optimum linear smoother as a combination of two optimum linear filters

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Formulate a solution to the optimum linear smoothing problem by synthesizing two independent optimal linear filters via maximum likelihood estimation.
Applied the maximum likelihood equation for combining two independent statistical estimates to linear smoothing.
Derived analytical equivalence between the dual-filter formulation and existing linear smoother frameworks.
Developed mathematically simplified expressions configured for efficient practical computation.
Proved that an optimal linear smoother is mathematically equivalent to the synthesis of two independent optimal linear filters.
Demonstrated exact agreement with prior classical formulations of linear smoothing problems.
Produced computationally practical algorithmic forms that reduce processing complexity for real-world implementation.

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Implication

Theoretical analysis demonstrates optimum linear smoothing through dual linear filters in dynamic state estimation, indicating streamlined mathematical and practical computation.

Cite This Study

Fraser et al. (1969) studied this question.

synapsesocial.com/papers/6a0a5a7c839f3dcd48b4f45a https://doi.org/10.1109/tac.1969.1099196

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Implication

Theoretical analysis demonstrates optimum linear smoothing through dual linear filters in dynamic state estimation, indicating streamlined mathematical and practical computation.

The optimum linear smoother as a combination of two optimum linear filters

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Discussion

Implication

Cite This Study

The optimum linear smoother as a combination of two optimum linear filters

Key Points

Discussion

Implication

Cite This Study

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