Minimizing effects of the Kalman gain on Posterior covariance Eigenvalues, the characteristic polynomial and symmetric polynomials of Eigenvalues

Johannes Krotz

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arXiv · 2404.10191

Minimizing effects of the Kalman gain on Posterior covariance Eigenvalues, the characteristic polynomial and symmetric polynomials of Eigenvalues

Johannes Krotz

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Abstract

The Kalman gain is commonly derived as the minimizer of the trace of theposterior covariance. It is known that it also minimizes the determinant of the posterior covariance. I will show that it also minimizes the smallest Eigenvalue $\lambda_1$ and the chracteristic polynomial on $(-\infty,\lambda_1)$ and is critical point to all symmetric polynomials of the Eigenvalues, minimizing some. This expands the range of uncertainty measures for which the Kalman Filter is optimal.

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Johannes Krotz. 2024-04-16. Minimizing effects of the Kalman gain on Posterior covariance Eigenvalues, the characteristic polynomial and symmetric polynomials of Eigenvalues. https://arxiv.org/abs/2404.10191

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