Factorization of the discrete noise covariance matrix for plans (U) / by J. Chris McMillan.: DR52-17/34-1991E-PDF

"The PLANS (Primary Land Arctic Navigation System), developed at Defence Research Establishment Ottawa (DREO), optimally integrates a directional gyro/gyrocompass, an odometer, a 3-axis strapdown magnetometer, a GPS receiver, a Transit receiver, a baroaltimeter and a digital terrain elevation map, for the purpose of navigating a land vehicle in the Canadian Arctic under potentially adverse conditions. This report derives the exact form of the discrete driving noise covariance matrix Q sub k which is needed to propagate the covariance matrix in the Kalman filter used by PLANS. It is shown that the exact Q sub k does not have a Cholesky UDU super T decomposition. However, a good approximation is shown to have the necessary decomposition for use in the Biermann-Agee-Turner formulation of the Kalman filter. This approximate decomposition is then found. A general result on the preservation of block diagonal form under UDU super T decomposition is also proven"--Abstract, page iii.

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