{"ID":2889374,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.22176","arxiv_id":"2507.22176","title":"Derivative Estimation from Coarse, Irregular, Noisy Samples: An MLE-Spline Approach","abstract":"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.","short_abstract":"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 a...","url_abs":"https://arxiv.org/abs/2507.22176","url_pdf":"https://arxiv.org/pdf/2507.22176v1","authors":"[\"Konstantin E. Avrachenkov\",\"Leonid B. Freidovich\"]","published":"2025-07-29T19:14:18Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"eess.SY\",\"math.OC\",\"math.PR\"]","methods":"[]","has_code":false}