Tampere University of Technology

TUTCRIS Research Portal

Automatic numerical differentiation by maximum likelihood estimation of a linear Gaussian state space model

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review


Original languageEnglish
Title of host publication2019 18th European Control Conference, ECC 2019
Number of pages5
ISBN (Electronic)9783907144008
Publication statusPublished - 1 Jun 2019
Publication typeA4 Article in a conference publication
EventEuropean Control Conference - Naples, Italy
Duration: 25 Jun 201928 Jun 2019


ConferenceEuropean Control Conference


A linear Gaussian state-space smoothing algorithm is presented for off-line estimation of derivatives from a sequence of noisy measurements. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements and non-equally spaced abscissas, and can compute state estimates at points between the data abscissas. The state space model's parameters, including driving noise intensity, measurement variance, and initial state, are determined from the given data sequence using maximum likelihood estimation computed using an expectation maximisation iteration. In tests with synthetic biomechanics data, the algorithm is found to be more accurate compared to a widely used open source automatic numerical differentiation algorithm, especially for acceleration estimation.

Publication forum classification

Field of science, Statistics Finland

Downloads statistics

No data available