The application of matrix differential calculus for the derivation of simplified expressions in approximate non-linear filtering algorithms

It is shown hew matrix differential calculus can be used to obtain simplifi ed expressions for higher-order terms that appear in standard approximate n on-linear filtering algorithms such as the first-order bias-corrected filte r, the truncated second-order filter, and the modified Gaussian second-orde r filter. These terms are much simpler and more compact than the standard e xpressions given in the literature; particularly, no element-by-element com putations are necessary. For comparison, the approximate version of the Dau m filter is also included. (C) 2000 Elsevier Science Ltd. All rights reserv ed.