Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Electrical and Computer Engineering


This paper deals with a state model of clock noises with an emphasis on the realization of the flicker noise process. To model clock noises, an approximation of the flicker noise (1/f noise) is obtained using a continued fraction expansion method. A general approach is given for obtaining a sequential approximation. It is shown that the approximant is a rational transfer function in s and uniformly converges to the 1/f noise, as the order of the approximant increases. The generated approximation is stable and has many interesting properties, including pole-zero relationships. It agrees well with the ideal flicker noise process over a finite frequency range or time interval;Based on the approximation, plus the white noise and random-walk noise, the state-space model of clock noises is constructed. The model can be easily expanded if higher or lower order noise processes are added. A noise process with odd powers in f can be obtained using the approximation followed by a number of cascaded integrators and differentiators;From the state-space model, the Kalman filter is constructed. The general form of Q-matrix for a truth model is obtained. Suboptimal error analysis is performed with respect to the truth model. Study shows that in the 2-state suboptimal model, the choice of Q-matrix is not sensitive to the presence of the flicker noise process in the long-term estimation and prediction of the clock noises. This agrees with the fact that the random-walk noise dominates the other two noise processes for large time intervals. A simple choice of the Q-matrix for the 2-state suboptimal model is just to take most upper left (2 x 2) submatrix of the already developed higher-order truth model Q-matrix;The optimal prediction error can be analytically obtained using the Bode-Shannon method. As time goes on, optimal prediction error is far less than that of the truth model. A numerical example is presented for this;It is briefly discussed that the truth and suboptimal clock models with appropriate Q-matrices can be applied to Global Positioning System.



Digital Repository @ Iowa State University,

Copyright Owner

In Soo Ahn



Proquest ID


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105 pages