Incorporation of Matrix Form in Time-Varying Finite Memory Structure Filter

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    This paper develops a computationally efficient algorithm for the time-varying finite memory filter with matrix form under a weighted least square criterion using only finite observations on the most recent window. Firstly, the time-varying finite memory filter is represented in matrix form as an alternative of recursive form. Secondly, a computationally efficient algorithm is derived to obtain the numerical stability for improving computational reliability and the amenability for the parallel and systolic implementation, which can reduce computational burden. The computationally efficient algorithm is derived from the recursive form of time-varying finite memory filter by applying a square-root strategy. Through computer simulations for a sinusoid signal and diverse window lengths, the proposed algorithm can be shown to be better than the infinite memory filtering based algorithm for the temporarily uncertain system.

     

     


  • Keywords


    Time-varying system, finite memory filter, infinite memory filter, computational efficiency, square-root strategy.

  • References


      [1] R. Faragher, “Understanding the basis of the Kalman filter via a simple and intuitive derivation,” IEEE Signal Processing Magazine, vol. 29, no. 5, pp. 128–132, 2012.

      [2] X. Lu, H. Wang, and X. Wang, “On Kalman smoothing for wireless sensor networks systems with multiplicative noises,” Journal of Applied Mathematics, vol. 2012, pp. 1–19, 2012.

      [3] P. S. Kim and W. H. Kwon, “Receding horizon FIR filter and its square-root algorithm for discrete time-varying systems,” Transaction on Control, Automation, and System Engineering, vol. 2, no. 2, 2000.

      [4] W. H. Kwon, P. S. Kim, S. H. Han, A receding horizon unbiased FIR filter for discrete-time state space models, Automatica 38 (3) (2002) 545–551.

      [5] Y. S. Shmaliy, “Linear optimal FIR estimation of discrete time-invariant state-space models”, IEEE Transactions on Signal Processing, vol. 58, no. 6, 3086-3096, 2010

      [6] Y. S. Shmaliy, L. J. Morales-Mendoza, “FIR smoothing of discrete-time polynomial signals in state space,” IEEE Transactions on Signal Processing, vol. 58, no. 5, 2544-2555, 2010

      [7] P. S. Kim, “A computationally efficient fixed-lag smoother using recent finite measurements,” Measurement, vol. 11, no. 1, pp. 206–210, 2013.

      [8] P. S. Kim, “An alternative FIR filter for state estimation in discrete-time systems,” Digital Signal Processing, vol. 20, no. 3, pp. 935–943, 2010.

      [9] J. J. Pomarico-Franquiz, M. Granados-Cruz, and Y. S. Shmaliy, “Self-localization over RFID tag grid excess channels using extended filtering techniques,” J. Sel. Topics Signal Processing, vol. 9, no. 2, pp. 229–238, 2015.

      [10] P. S. Kim, E. H. Lee, M. S. Jang, S. Y. Kang, “A finite memory structure filtering for indoor positioning in wireless sensor networks with measurement delay,” International Journal of Distributed Sensor Networks 13 (1) (2017) 1–8.

      [11] P. S. Kim, “A design of finite memory residual generation filter for sensor fault detection,” Measurement Science Review 17 (2) (2017) 75–81.

      [12] M. Vazquez-Olguin, Y. Shmaliy, O. Ibarra-Manzano, “Distributed Unbiased FIR Filtering with Average Consensus on Measurements for WSNs,” IEEE Transactions on Industrial Informatics, 2017.

      [13] P. Park, “New square-root algorithms for Kalman filtering,” IEEE Trans. on Automatic Control, vol. 40, no. 5, pp. 895–899, 1995.

      [14] P. Wu, X. Li, and Y. Bo, “Iterated square root unscented Kalman filter for maneuvering target tracking using TDOA measurements,” International Journal of Control, Automation and Systems, vol. 11, no. 3, pp. 761–767, 2013.

      [15] J. L. Steward, A. Aksoy, Z. S. Haddad, “Parallel direct solution of the ensemble square root Kalman filter equations with observation principal components,” Journal of Atmospheric and Oceanic Technology, vol. 34, no. 9, pp. 1867–1884, 2017.

      [16] P. S. Kim, “Time-varying finite memory structure filter to incorporate time-delayed measurements”, Engineering Letters, vol. 26, no. 4, pp. 410–414, 2018.


 

View

Download

Article ID: 29226
 
DOI: 10.14419/ijet.v7i4.38.29226




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.