The main purpose of this paper is the error analysis of the fixed-point prediction for the linear continuous-time system with the coloured measurement noise. In the first part of this paper we derive an algorithm for the fixed-point prediction with the coloured measurement, noise from the given system. The remaining part presents the error analysis of the fixed-point prediction due to two causes, one of which is misidentifying the coefficients of the system and the covariances of the noises and the other of simplifying the coloured measurement noise by a white measurement noise. For the above cases two differential equations are obtained which govern the actual covariances regarded as the error quantities.