Abstract
We study the Kalman Filter for the linear elastic wave equation over the real line with spatially distributed partial state measurements. The dynamics of the filter are described by a spatial convolution operator with asymptotic exponential spatial decay rate. This decay rate dictates how measurements from different spatial locations must be exchanged to implement the filter: faster spatial decay implies local measurements are more relevant and the filter is more “decentralized”; slower decay implies farther measurements also become relevant and the filter is more “centralized”. Using dimensional analysis, we demonstrate that this decay rate is a function of one dimensionless group defined from system parameters, such as wave speed and noise variances. We find a critical value of such dimensionless group for which the Kalman Filter is completely decentralized.
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