Multirate, multiresolution, recursive Kalman filter
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An approach to the decomposition of a signal into orthogonal components at different resolution levels is presented in this paper. It is shown that a signal generated by the standard state-space stochastic model can be decomposed into innovations at the different sampling frequencies associated to different levels of resolution. The main result is that these innovations are all uncorrelated with each other. A multiresolution multirate (MRMR) Kalman filter is then introduced which allows multiple MRMR observations to be combined in an optimal fashion.
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