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

Xubao Zhang

doi:doi:10.11648/j.jeee.20221005.12

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

Xubao Zhang

Published in Journal of Electrical and Electronic Engineering (Volume 10, Issue 5)

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), 2024. 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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[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.
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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.
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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

Xubao Zhang

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

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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

Copy | Download

@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}
}

Copy | Download

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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