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Discrete Stochastic Processes and Optimal Filtering by Roger Ceschi, Jean-Claude Bertein

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6.6. Geometric interpretation

Let us give another expression to the cost function at instant K.

We have found: image with image and image and Wiener solution of image.

The cost can be put in the form:

images

or image

Let us state image (the origin of the axes is at present image); it becomes:

images

and easily: image: the factor K representing the instant where we are considering the gradient.

Let us simplify the preceding expressions to find simple geometric interpretations by changing the base.

Matrix R being symmetric, we say that it is diagonalizable ...

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