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On the Equivalence between Kalman Filter at Steady State and DPLL

Bidon, Stéphanie and Roche, Sébastien On the Equivalence between Kalman Filter at Steady State and DPLL. (2023) Signal Processing. (Unpublished)

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Fundamental results in the literature previously showed that a class of Kalman filter converges to a digital phase lock loop (DPLL) structure at the second and third order. We generalize these results at any order and give the closed-form linear relation, and its inverse, between the steady-state Kalman gains and the loop filter constants. Both relations are simple and only involve Stirling numbers of the first and second kind. This new result may help in a deeper understanding of the equivalence between Kalman filter and DPLL and be of practical interest in high dynamic scenarios.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > Airbus (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
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Deposited On:23 Aug 2022 09:14

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