Second-Order Kalman Filters using multi-complex step derivatives

Vivek Vittaldev, Ryan P. Russell, Nitin Arora, David Gaylor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

14 Scopus citations


The Second Order Kalman Filter (SOKF) uses a second order Taylor series expansion (TSE) to account for nonlinearities in an estimation problem. In this work, the derivatives required for the SOKF are computed using multicomplex (MCX) derivatives, coded in the Matlab programming language. This method uses function overloading in order to derive or compute the derivatives to machine precision without having to compute the derivatives analytically. Thus, the SOKF can be easily implemented, while at the same time having fewer tuning parameters than other high order filters. The standard SOKF is also extended by combining it with Gaussian Mixture models (GMM), which gives promising results. The filters have been used to estimate the state of a 1 DOF falling body. The results show that the MCX computes the required derivatives just as accurately as an analytical method and the SOKF and GMM modification perform well in terms of accuracy compared to other filters. Despite the ease of use and high accuracy benefits, a current drawback of the MCX method is compute speed. Methods for improving the speed are beyond the current scope and will be addressed in future works.

Original languageEnglish (US)
Title of host publicationSpaceflight Mechanics 2012 - Advances in the Astronautical Sciences
Subtitle of host publicationProceedings of the 22nd AAS/AIAA Space Flight Mechanics Meeting
Number of pages16
StatePublished - 2012
Externally publishedYes
Event22nd AAS/AIAA Space Flight Mechanics Meeting - Charleston, SC, United States
Duration: Feb 2 2012Feb 2 2012

Publication series

NameAdvances in the Astronautical Sciences
ISSN (Print)0065-3438


Other22nd AAS/AIAA Space Flight Mechanics Meeting
Country/TerritoryUnited States
CityCharleston, SC

ASJC Scopus subject areas

  • Aerospace Engineering
  • Space and Planetary Science


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