Chair of Multimedia Telecommunications and Microelectronics

Paweł Kubczak, Jakub Nikonowicz, Łukasz Matuszewski,
Kalman Filter Design for Fast Synchronization of a High-Stability Rubidium Oscillator,
2019 Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA), IEEE, Poznan, Poland, 18-20 Sept. 2019,


The article briefly describes the methodology of designing a Kalman filter that it is used in the phase lock loop (PLL). At the beginning the tools and the experimental environment are discussed, especially the structure of the synchronization loop. First, the characteristic of the 1PPS GNSS reference signal is obtained using superposition by gathering data when the oscillator is locked to GPS. This data is used to calculate a covariance matrix of the measurement noise for the Kalman filter. Next, a signal without noise from a very stable frequency source is applied as a reference signal, and the identification experiment of the oscillator is executed. Based on the identification data, one, two-, three- and four-dimensional space-state models of the rubidium clock are created and the process noise covariance matrix for the Kalman filter is calculated. At the end, the quality of Kalman filter tracking is examined. For this purpose, MSE between the real behavior of the phase and the estimation provided by the filter is calculated. Finally, the optimal dimensionality of the model is discussed. It is also shown how much the estimations of the phase prediction in Kalman filter can be trusted and how to adjust the process noise covariance matrix properly.