Minimizing effects of the Kalman gain on Posterior covariance Eigenvalues, the characteristic polynomial and symmetric polynomials of Eigenvalues
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916208308125696 |
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| author | Krotz, Johannes |
| author_facet | Krotz, Johannes |
| contents | 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 $λ_1$ and the chracteristic polynomial on $(-\infty,λ_1)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10191 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimizing effects of the Kalman gain on Posterior covariance Eigenvalues, the characteristic polynomial and symmetric polynomials of Eigenvalues Krotz, Johannes Statistics Theory 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 $λ_1$ and the chracteristic polynomial on $(-\infty,λ_1)$ 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. |
| title | Minimizing effects of the Kalman gain on Posterior covariance Eigenvalues, the characteristic polynomial and symmetric polynomials of Eigenvalues |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2404.10191 |