Numerical Differentiation of Noisy Data
Abstract
An algorithm has been developed based on the assumption that a given set of data is representable by a function that is a product of algebraic, trigonometric, and exponential polynomials. The degrees of the underlying polynomials, the optimal data spacing (optimal multiple of stepsize in tabular data), and the parameters of the approximating function are all selected by the algorithm to minimize an objective function that depends on the variance of the deviation between the data and the fitted function and on the degree of ill- conditioning of the problem. The algorithm permits choosing global or local fits. Derivatives of any order are obtained either by differentiating the fitted function or by a closed form relation between te model parameters and coefficients of linear combinations that express derivatives in terms of the observed values of the variable. Thus, the algorithm provides local differentiation formulas using parameters derived from global analysis of the data but in terms of the local values of the function. An appendix compares the accuracy of derivatives obtained for synthetic data with the accuracy of other methods.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1981
- Accession Number
- ADA104631
Entities
People
- C. Masaitis
- G. Francis
Organizations
- Ballistic Research Laboratory