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This paper investigates an approach to quantify the problem of cross correlation between the prediction and observation noise of an inertial navigation system (INS), which utilizes a linear Kalman filter (KF). Cross correlation is shown being introduced by use of the transformation matrix to transform body frame velocity observations into navigation frame. The effect of the cross-correlation term on the error covariance matrix and subsequently on the convergence of the filter is evaluated theoretically. With the cross-correlation term being formulated from the prediction and observation noise, it is incorporated into the KF and thus the relevant filter equations have been updated accordingly. A simulation is produced to evaluate the effect of the cross-correlation term. The theoretical formulation and numerical simulations present the importance of incorporating this term into the filter and navigation system. If this term was ignored, the error covariance estimates associated with the positional estimates would be too small and the filter would be Â¿over confidentÂ¿.