Derivative Estimation from Coarse, Irregular, Noisy Samples: An MLE-Spline Approach
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| Format: | Preprint |
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2025
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| author | Avrachenkov, Konstantin E. Freidovich, Leonid B. |
| author_facet | Avrachenkov, Konstantin E. Freidovich, Leonid B. |
| contents | We address numerical differentiation under coarse, non-uniform sampling and Gaussian noise. A maximum-likelihood estimator with $L_2$-norm constraint on a higher-order derivative is obtained, yielding spline-based solution. We introduce a non-standard parameterization of quadratic splines and develop recursive online algorithms. Two formulations -- quadratic and zero-order -- offer tradeoff between smoothness and computational speed. Simulations demonstrate superior performance over high-gain observers and super-twisting differentiators under coarse sampling and high noise, benefiting systems where higher sampling rates are impractical. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_22176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derivative Estimation from Coarse, Irregular, Noisy Samples: An MLE-Spline Approach Avrachenkov, Konstantin E. Freidovich, Leonid B. Methodology Systems and Control Optimization and Control Probability We address numerical differentiation under coarse, non-uniform sampling and Gaussian noise. A maximum-likelihood estimator with $L_2$-norm constraint on a higher-order derivative is obtained, yielding spline-based solution. We introduce a non-standard parameterization of quadratic splines and develop recursive online algorithms. Two formulations -- quadratic and zero-order -- offer tradeoff between smoothness and computational speed. Simulations demonstrate superior performance over high-gain observers and super-twisting differentiators under coarse sampling and high noise, benefiting systems where higher sampling rates are impractical. |
| title | Derivative Estimation from Coarse, Irregular, Noisy Samples: An MLE-Spline Approach |
| topic | Methodology Systems and Control Optimization and Control Probability |
| url | https://arxiv.org/abs/2507.22176 |