Incorporation of Matrix Form in Time-Varying Finite Memory Structure Filter
DOI:
https://doi.org/10.14419/ijet.v7i4.38.29226Keywords:
Time-varying system, finite memory filter, infinite memory filter, computational efficiency, square-root strategy.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.
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 modelsâ€, 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 measurementsâ€, Engineering Letters, vol. 26, no. 4, pp. 410–414, 2018.
How to Cite
License
Authors who publish with this journal agree to the following terms:- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution Licensethat allows others to share the work with an acknowledgement of the work''s authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal''s published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Accepted 2019-05-13