Steady-State Performance of Kalman Filter for DPLL |
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Authors: | QIAN Yi CUI Xiaowei LU Mingquan FENG Zhenming |
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Affiliation: | aDepartment of Electronic Engineering, Tsinghua University, Beijing 100084, China |
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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. |
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Keywords: | Kalman filter digital phase-locked loop (DPLL) steady-state performance |
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