A finite-difference approach to linearization in nonlinear estimation algorithms

Linearizations of nonlinear functions that are based on Jacobian matrices can often not be applied in practical applications of nonlinear estimation techniques. An alternative linearization method is presented in this paper. The method assumes that covariance matrices are determined on a square root factored form. A factorization of the output covariance from a nonlinear vector function is directly determined by “perturbing” the nonlinear function with the columns of the factored input covariance, without explicitly calculating the linearization and with no differentiations involved. This method seems to be superior to the ordinary Jacobian linearization. It is also an advantage that Jacobian matrices do not have to be derived symbolically