Comparison of Solution via Covariance Matrix and Convolution Integral for INS Position and Velocity Errors Due to Deflections of the Vertical

D. Hsu

Abstract:	Assume that the gravity Deflection of the Vertical (DoV), the deviation of the gravity vector from the normal to the reference ellipsoid, is modeled per level axis as a correlated Markov random process with a specified correlation distance. The position and velocity errors caused by DoV as an equivalent accelerometer input are derived from two completely different approaches: (1) Covariance Matrix Approach: Starts with the matrix linear covariance equation of the dynamic system including initial conditions and measurement statistics. The matrix equation is then solved analytically/numerically to obtain variances of position and velocity errors. (2) Convolution Integral Approach: Expresses the velocity and position error as the convolution integrals of the system transfer functions (h(t) for input-to-velocity, g(t) for input-to-position) with the equivalent accelerometer input function a(i). These integrals are then evaluated to obtain the variance of the position and velocity errors. It can be shown for the steady-state case that the two methods are equivalent and generate identical solutions. However, only the covariance matrix approach is applicable to the transient case. The MATLAB Symbolic Toolbox is used to carry out the tedious algebraic operations and the results are directly utilized in typesetting software as LATEX.
Published in:	Proceedings of the 2003 National Technical Meeting of The Institute of Navigation January 22 - 24, 2003 Disneyland Paradise Pier Hotel Anaheim, CA
Pages:	126 - 132
Cite this article:	Hsu, D., "Comparison of Solution via Covariance Matrix and Convolution Integral for INS Position and Velocity Errors Due to Deflections of the Vertical," Proceedings of the 2003 National Technical Meeting of The Institute of Navigation, Anaheim, CA, January 2003, pp. 126-132.
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In