Derivative Estimation from Coarse, Irregular, Noisy Samples: An MLE-Spline Approach
Konstantin E. Avrachenkov and Leonid B. Freidovich
我们解决粗糙、非均匀采样和高斯噪声下的数值分化。 获得具有高阶导数上L_2-norm约束的最大可能性估计器,产生基于spline的解决方案。 我们引入了二次延展线的非标准参数化,并开发了递归在线算法。 两种配方 - 二次和零序 - 提供平滑度和计算速度之间的权衡。 在粗采样和高噪声下,模拟显示比高增益观察者和超扭曲的差异化性能更高,使采样率较高的系统受益。
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 observ...