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2계층 Frobenius norm 유한 임펄스 응답 필터 기반 디지털 위상 고정 루프 설계

Design of Digital Phase-locked Loop based on Two-layer Frobenius norm Finite Impulse Response Filter

  • 김신 (조선대학교 전자공학부) ;
  • 신성 (조선대학교 전자공학부) ;
  • 유성현 (조선대학교 전자공학부) ;
  • 최현덕 (전남대학교 ICT융합시스템공학과)
  • 투고 : 2023.12.29
  • 심사 : 2024.02.17
  • 발행 : 2024.02.29

초록

디지털 위상 고정 루프는 디지털 위상 검출기, 디지털 루프 필터, 디지털 제어 발진기, 분배기 등으로 이루어진 일반적인 회로로 전기 및 회로 분야 등 다양한 분야에서 널리 사용된다. 디지털 위상 고정 루프의 성능 향상을 위해 다양한 수학적인 알고리즘 등을 활용한 상태 추정기가 사용된다. 전통적인 상태 추정기로는 무한 임펄스 응답 상태 추정기의 칼만 필터를 활용해왔으며, 무한 임펄스 응답 상태 추정기 기반 디지털 위상 고정 루프는 초기값의 부정확성, 모델 오차, 다양한 외란 등의 예상치 못한 상황에서 급격한 성능 저하가 발생할 수 있다. 본 논문에서는 새로운 디지털 위상 고정 루프를 설계하기 위해 2계층 Frobenius norm 기반 유한 임펄스 상태 추정기를 제안한다. 제안한 상태 추정기는 첫 번째 층의 추정 상태를 이용하여 두 번째 층에서 상태 추정을 하는데, 이때 첫 번째 층의 추정 상태와 누적된 측정값과 결합하여 설계하였다. 새로운 유한 임펄스 응답 상태 추정기 기반 디지털 위상 동기 루프의 강인한 성능을 검증하기 위해 잡음 공분산 정보가 부정확한 상황에서 무한 임펄스 응답 상태 추정기와 비교하여 시뮬레이션을 수행하였다.

The digital phase-locked loop(DPLL) is one of the circuits composed of a digital detector, digital loop filter, voltage-controlled oscillator, and divider as a fundamental circuit, widely used in many fields such as electrical and circuit fields. A state estimator using various mathematical algorithms is used to improve the performance of a digital phase-locked loop. Traditional state estimators have utilized Kalman filters of infinite impulse response state estimators, and digital phase-locked loops based on infinite impulse response state estimators can cause rapid performance degradation in unexpected situations such as inaccuracies in initial values, model errors, and various disturbances. In this paper, we propose a two-layer Frobenius norm-based finite impulse state estimator to design a new digital phase-locked loop. The proposed state estimator uses the estimated state of the first layer to estimate the state of the first layer with the accumulated measurement value. To verify the robust performance of the new finite impulse response state estimator-based digital phase locked-loop, simulations were performed by comparing it with the infinite impulse response state estimator in situations where noise covariance information was inaccurate.

키워드

과제정보

본 논문은 교육부와 한국연구재단의 재원으로 지원을 받아 수행된 3단계 산학연협력 선도대학 육성 사업(LINC 3.0)의 연구결과입니다.

참고문헌

  1. P. Driessen, "DPLL bit synchronizer with rapid acquisition using adaptive Kalman filtering techniques," IEEE Transactions on Communications, vol. 42, no. 9, Sept. 1994, pp. 2673-2675  https://doi.org/10.1109/26.317406
  2. S. R. Al-Araji, Z. M. Hussain, and M. A. Al-Qutayri, Digital Phase Lock Loops: Architectures and Applications. New York, NY, USA: Springer, 2006. 
  3. S. You, J. Pak, C. Ahn, P. Shi, and M. Lim, "Unbiased Finite-Memory Digital Phase-Locked Loop," in IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 63, no. 8, Aug. 2016, pp. 798-802.  https://doi.org/10.1109/TCSII.2016.2531138
  4. C. Ahn, P. Shi, and S. You, "A New Approach on Design of a Digital Phase-Locked Loop," in IEEE Signal Processing Letters, vol. 23, no. 5, May 2016, pp. 600-604.  https://doi.org/10.1109/LSP.2016.2542291
  5. S. Kim, S. Shin, and S. You, "Localization Algorithms for Mobile Robots in a Wireless Communication Environment with Presence of Data Missing," J. of the Korea Institute of Electronic Communication Sciences, vol. 18, no. 4, Aug. 2023, pp. 601-608. 
  6. G. Song, H. Choi, and N. Ko, "Attitude Estimation of Unmanned Vehicles Using Unscented Kalman Filter," J. of the Korea Institute of Electronic Communication Sciences, vol. 14, no. 1, 2019, pp. 265-273. 
  7. W. Kwon and S. Han, Receding Horizon Control: Model Predictive Control for State Models. London: Springer-Verlag, 2005. 
  8. A. H. Jazwinski, Stochastic Processes and Filtering Theory. New York: Academic, 1970. 
  9. Y. S. Shmaliy, S. Zhao, and C. Ahn, "Unbiased Finite Impluse Response Filtering: An Iterative Alternative to Kalman Filtering Ignoring Noise and Initial Conditions," in IEEE Control Systems Magazine, vol. 37, no. 5, Oct. 2017, pp. 70-89.  https://doi.org/10.1109/MCS.2017.2718830
  10. S. You, D. Pae, and H. Choi, "A Digital Phase-locked Loop design based on Minimum Variance Finite Impulse Response Filter with Optimal Horizon Size," J. of the Korea Institute of Electronic Communication Sciences, vol. 16, no. 4, Aug. 2021, pp. 591-598. 
  11. W. Kwon, P. Kim, and P. Park, ''A receding horizon Kalman FIR filter for discrete time-invariant systems,'' in IEEE Transactions on Automatic Control, vol. 44, no. 9, Sept. 1999, pp. 1787-1791.  https://doi.org/10.1109/9.788554
  12. W. Kwon and Han, Receding Horizon Control: Model Predictive Control for State Models. Cham, Switzerland: Springer, 2015. 
  13. S. You, C. Ahn, Y. S. Shmaliy, and S. Zhao, "Minimum Weighted Frobenius Norm Discrete-Time FIR Filter With Embedded Unbiasedness," in IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 65, no. 9, Sept. 2018, pp. 1284-1288.  https://doi.org/10.1109/TCSII.2018.2810812
  14. C. Ahn, Y. S. Shmaliy, and S. Zhao, ''A new unbiased FIR filter with improved robustness based on frobenius norm with exponential weight,'' IEEE Transactions on Circuits Systems II, Express Briefs, vol. 65, no. 4, Apr. 2018, pp. 521-525.  https://doi.org/10.1109/TCSII.2017.2749006
  15. S. You, C. Ahn, Y. S. Shmaliy, and S. Zhao, "Fusion Kalman and Weighted UFIR State Estimator With Improved Accuracy," in IEEE Transactions on Industrial Electronics, vol. 67, no. 12, Dec. 2020, pp. 10713-10722.  https://doi.org/10.1109/TIE.2019.2958278
  16. J. Pak, C. Ahn, M. Lim, and M. Song, "Indoor Localization Using Unscented Kalman/FIR Hybrid Filter," Journal of Institute of Control, Robotics and Systems, vol. 21, no. 11 2015, pp. 1057-1063.  https://doi.org/10.5302/J.ICROS.2015.15.0149
  17. I. Choi, J. Pak, C. Ahn, S. Lee, M. Lim, and M. Song, "Arbitration algorithm of FIR filter and optical flow based on ANFIS for visual object tracking," Measurement, vol. 75, 2015 pp. 338-353. https://doi.org/10.1016/j.measurement.2015.07.020