@article{QIAN2009, 
author = {Yi QIAN and Xiaowei CUI and Mingquan LU and Zhenming FENG},
title = {Steady-State Performance of Kalman Filter for DPLL},
year = {2009},
journal = {Tsinghua Science and Technology},
volume = {14},
number = {4},
pages = {470-473},
keywords = {Kalman filter, digital phase-locked loop (DPLL), steady-state performance},
url = {https://www.sciopen.com/article/10.1016/S1007-0214(09)70104-X},
doi = {10.1016/S1007-0214(09)70104-X},
abstract = {For certain system models, the structure of the Kalman filter is equivalent to a second-order variable gain digital phase-locked loop (DPLL). To apply the knowledge of DPLLs to the design of Kalman filters, this paper studies the steady-state performance of Kalman filters for these system models. The results show that the steady-state Kalman gain has the same form as the DPLL gain. An approximate simple form for the steady-state Kalman gain is used to derive an expression for the equivalent loop bandwidth of the Kalman filter as a function of the process and observation noise variances. These results can be used to analyze the steady-state performance of a Kalman filter with DPLL theory or to design a Kalman filter model with the same steady-state performance as a given DPLL.}
}