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Lattice Predictors for a Stagger-Period Sequence: Their Theory and Application

Received: 23 August 2022     Accepted: 13 September 2022     Published: 21 September 2022
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Abstract

This paper proposes a new structure of lattice predictors, which applies to a stagger-period sequence. To deal with the sequence’s time-varying periods, the stagger-period lattice predictor has a linear time-variant processing structure, whose reflection coefficients and delay units need to match the input sequence periods for optimality. The staggered lattice predictor’s operation is relatively complex, of ∑M forward and backward reflection coefficients, M its order; and a uniform-period lattice predictor consists of M forward and backward coefficients. Based on Burg’s uniform-period lattice algorithm, we propose the staggered Forward and Backward Error Minimum algorithm to determine this predictor’s reflection coefficients and prove its optimality in the sense of minimum mean square error. By means of staggered forward and backward transversal predictors, we also propose the staggered Levinson-Durbin relations and prove it holds in the Appendix; these relations play an important role in researching the staggered lattice predictor. For practical application, we present a corresponding reflection coefficient estimation, the staggered Arithmetic Mean method, which substitutes for the ensemble mean with the limited-sample mean, and minimizes the estimate’s variance in the least square error sense. Through many computer simulations, we investigate convergence performance and learning characteristic of this type of predictor with three observation goals: the reflection coefficient, prediction error, and frequency response; the investigations reveal relationships between the convergence performance, learning characteristic and the balance factor, length of averaging window. In order to apply the staggered lattice predictor to an actual field, we illustrate a moving target indicator for Doppler radar with a stagger-period pulse emission and pulse compression waveform technology. Our simulation tests demonstrate that the staggered block lattice filter with essential artificial intelligence (AI) can efficiently detect weak targets submerged in the stationary and nonstationary clutters. The AI includes five heuristic strategies based on radar professionals’ knowledge to preserve targets and reject false alarms.

Published in Journal of Electrical and Electronic Engineering (Volume 10, Issue 5)
DOI 10.11648/j.jeee.20221005.12
Page(s) 184-198
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Lattice Predictor, Stagger-Period Signal Processing, Lattice Prediction Convergence, Moving Target Indicator, Artificial Intelligence

References
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[2] Hanoch Lev-Ari, Thomas Kailath, and John Cioffi. (1984). Least-squares adaptive lattice and transversal filters: a unified geometric theory. IEEE Transactions on Information Theory, 30 (2), 222-236.
[3] Takafumi Takemoto, Naoto Sasaoka, Kensaku Fujii, and Yoshio Itoh. (2010). Speech enhancement system based on lattice filter and system identification. 10th International Symposium on Communications and Information Technologies, 441-446, doi: 10.1109/ISCIT.2010.5664880.
[4] Gediminas Simkus, Martin Holters, and Udo Zolzer. (2013). Ultra-low latency audio coding based on DPCM and block companding. 14th International Workshop on WIAMIS, Paris, 1-4, doi: 10.1109/WIAMIS.2013.6616143.
[5] Kensaku Fujii, Masaaki Tanaka, Naoto Sasaoka, and Yoshio Itoh. (2007). Method estimating reflection coefficients of adaptive lattice filter and its application to system identification. The Acoustical Society of Japan, Acoust. Sci. & Tech. 28 (2), 98-104.
[6] Rui Zhu, Feiran Yang, and Jun Yang. (2016). A gradient-adaptive lattice-based complex adaptive notch filter. EURASIP Journal on Advances in Signal Processing, 2016: 79, 1-11, doi: 10.1186/s13634-016-0377-4.
[7] B. M. Keel and E. G. Baxa. (1990). Adaptive least square complex lattice clutter rejection filters applied to the radar detection of low altitude windshear. International Conference on ASSP, 1496-1472, doi: 10.1109/ICASSP.1990.115677.
[8] Dmitri N. Moisseev, Cuong M. Nguyen, and V. Chandrasekar. (2008). Clutter suppression for staggered PRT waveforms. J. Atmos. Oceanic Technol. 25, 2209-2218. doi: 10.1175/2008JTECHA1096.1.
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[13] Zhang Xubao. (2021). Finite impulse response filters for stagger-period signals, their designs and applications. European Journal of Information Technologies and Computer Science 1 (1), 1-11. doi: http://dx.doi.org/10.24018/compute.2021.1.1.3.
[14] J. Makhoul. (1977). Stable and efficient lattice methods for linear prediction. IEEE Trans. on ASSP, 25 (5), 423-428.
[15] C. J. Gibson and S. Haykin. (1980). Learning characteristics of adaptive lattice filtering algorithms. IEEE Trans. ASSP, 28 (6), 681-691.
[16] Rohit Negi and P G Poonacha. (1998). Convergence and bias in the LSG algorithm for adaptive lattice filters. Sadhana in India, 23, Part l, 83-91.
[17] Michael L. Honig and David G. Messerschmitt. (1981). Convergence properties of an adaptive digital lattice filter. IEEE Transactions on ASSP, 29 (3), 642-653.
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  • APA Style

    Xubao Zhang. (2022). Lattice Predictors for a Stagger-Period Sequence: Their Theory and Application. Journal of Electrical and Electronic Engineering, 10(5), 184-198. https://doi.org/10.11648/j.jeee.20221005.12

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    ACS Style

    Xubao Zhang. Lattice Predictors for a Stagger-Period Sequence: Their Theory and Application. J. Electr. Electron. Eng. 2022, 10(5), 184-198. doi: 10.11648/j.jeee.20221005.12

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    AMA Style

    Xubao Zhang. Lattice Predictors for a Stagger-Period Sequence: Their Theory and Application. J Electr Electron Eng. 2022;10(5):184-198. doi: 10.11648/j.jeee.20221005.12

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  • @article{10.11648/j.jeee.20221005.12,
      author = {Xubao Zhang},
      title = {Lattice Predictors for a Stagger-Period Sequence: Their Theory and Application},
      journal = {Journal of Electrical and Electronic Engineering},
      volume = {10},
      number = {5},
      pages = {184-198},
      doi = {10.11648/j.jeee.20221005.12},
      url = {https://doi.org/10.11648/j.jeee.20221005.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.jeee.20221005.12},
      abstract = {This paper proposes a new structure of lattice predictors, which applies to a stagger-period sequence. To deal with the sequence’s time-varying periods, the stagger-period lattice predictor has a linear time-variant processing structure, whose reflection coefficients and delay units need to match the input sequence periods for optimality. The staggered lattice predictor’s operation is relatively complex, of ∑M forward and backward reflection coefficients, M its order; and a uniform-period lattice predictor consists of M forward and backward coefficients. Based on Burg’s uniform-period lattice algorithm, we propose the staggered Forward and Backward Error Minimum algorithm to determine this predictor’s reflection coefficients and prove its optimality in the sense of minimum mean square error. By means of staggered forward and backward transversal predictors, we also propose the staggered Levinson-Durbin relations and prove it holds in the Appendix; these relations play an important role in researching the staggered lattice predictor. For practical application, we present a corresponding reflection coefficient estimation, the staggered Arithmetic Mean method, which substitutes for the ensemble mean with the limited-sample mean, and minimizes the estimate’s variance in the least square error sense. Through many computer simulations, we investigate convergence performance and learning characteristic of this type of predictor with three observation goals: the reflection coefficient, prediction error, and frequency response; the investigations reveal relationships between the convergence performance, learning characteristic and the balance factor, length of averaging window. In order to apply the staggered lattice predictor to an actual field, we illustrate a moving target indicator for Doppler radar with a stagger-period pulse emission and pulse compression waveform technology. Our simulation tests demonstrate that the staggered block lattice filter with essential artificial intelligence (AI) can efficiently detect weak targets submerged in the stationary and nonstationary clutters. The AI includes five heuristic strategies based on radar professionals’ knowledge to preserve targets and reject false alarms.},
     year = {2022}
    }
    

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  • TY  - JOUR
    T1  - Lattice Predictors for a Stagger-Period Sequence: Their Theory and Application
    AU  - Xubao Zhang
    Y1  - 2022/09/21
    PY  - 2022
    N1  - https://doi.org/10.11648/j.jeee.20221005.12
    DO  - 10.11648/j.jeee.20221005.12
    T2  - Journal of Electrical and Electronic Engineering
    JF  - Journal of Electrical and Electronic Engineering
    JO  - Journal of Electrical and Electronic Engineering
    SP  - 184
    EP  - 198
    PB  - Science Publishing Group
    SN  - 2329-1605
    UR  - https://doi.org/10.11648/j.jeee.20221005.12
    AB  - This paper proposes a new structure of lattice predictors, which applies to a stagger-period sequence. To deal with the sequence’s time-varying periods, the stagger-period lattice predictor has a linear time-variant processing structure, whose reflection coefficients and delay units need to match the input sequence periods for optimality. The staggered lattice predictor’s operation is relatively complex, of ∑M forward and backward reflection coefficients, M its order; and a uniform-period lattice predictor consists of M forward and backward coefficients. Based on Burg’s uniform-period lattice algorithm, we propose the staggered Forward and Backward Error Minimum algorithm to determine this predictor’s reflection coefficients and prove its optimality in the sense of minimum mean square error. By means of staggered forward and backward transversal predictors, we also propose the staggered Levinson-Durbin relations and prove it holds in the Appendix; these relations play an important role in researching the staggered lattice predictor. For practical application, we present a corresponding reflection coefficient estimation, the staggered Arithmetic Mean method, which substitutes for the ensemble mean with the limited-sample mean, and minimizes the estimate’s variance in the least square error sense. Through many computer simulations, we investigate convergence performance and learning characteristic of this type of predictor with three observation goals: the reflection coefficient, prediction error, and frequency response; the investigations reveal relationships between the convergence performance, learning characteristic and the balance factor, length of averaging window. In order to apply the staggered lattice predictor to an actual field, we illustrate a moving target indicator for Doppler radar with a stagger-period pulse emission and pulse compression waveform technology. Our simulation tests demonstrate that the staggered block lattice filter with essential artificial intelligence (AI) can efficiently detect weak targets submerged in the stationary and nonstationary clutters. The AI includes five heuristic strategies based on radar professionals’ knowledge to preserve targets and reject false alarms.
    VL  - 10
    IS  - 5
    ER  - 

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Author Information
  • Electronic Engineering Department, Xi’an Electronic Science and Technology University, Xi’an, China

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