Numerical differentiation on irregular grids

In this article, we propose a multidimensional numerical differentiation method from irregularly sampled data, in a noisy environment. The method extends to irregular grids our previous work and it relies on the same spirit as the algebraic numerical differentiators due to M. Mboup et al. (“Numerical differentiation with annihilators in noisy environment,” Numerical Algorithm, 50, pp. 439-457, 2009). We provide a least squares interpretation of the developed estimators as well as a discrete implementation scheme. Several numerical simulations are presented to asses the performance of the proposed differentiators.