Next Article in Journal
Influence of Contextual Factors on Soundscape in Urban Open Spaces
Previous Article in Journal
A Deeper Insight on the Stability of Water-Induced Reconstruction of Anatase (001) Surface
Article Menu

Article Versions

Export Article

Open AccessArticle
Appl. Sci. 2018, 8(12), 2523; https://doi.org/10.3390/app8122523

Correct Stability Condition and Fundamental Performance Analysis of the α-β-γ-δ Filter

Department of Intelligent Systems Design Engineering, Graduate School of Engineering, Toyama Prefectural University, Imizu, Toyama 939-0398, Japan
*
Author to whom correspondence should be addressed.
Received: 26 October 2018 / Revised: 29 November 2018 / Accepted: 5 December 2018 / Published: 6 December 2018
(This article belongs to the Section Computer Science and Electrical Engineering)
PDF [2090 KB, uploaded 6 December 2018]   |   Review Reports

Abstract

This paper theoretically analyzes the fundamental performance of a fourth-order steady-state moving object tracking filter, called an α - β - γ - δ filter. The α - β - γ - δ filter considers estimations of jerk (time-derivative of acceleration) in the motion of targets. First, regarding the stability conditions of the α - β - γ - δ filter, we prove that there are unstable cases even when the conventionally derived stability conditions are satisfied, and then we derive the correct stability conditions. Next, we analytically derive performance indices that indicate the steady-state errors for targets with typical motions. Based on the derived indices, the optimal performance of the α - β - γ - δ filter is theoretically analyzed and compared with that of the traditional second- and third-order steady-state tracking filters, i.e., α - β and α - β - γ filters. Numerical analyses and simulations are used to verify the advantages and disadvantages of the α - β - γ - δ filter over the above-mentioned filters. The practicality of the use of jerk for the tracking filtering problem is revealed in this paper.
Keywords: α-β-γ-δ filter; jerk tracking; fourth-order tracking filter; stability condition; performance index α-β-γ-δ filter; jerk tracking; fourth-order tracking filter; stability condition; performance index
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Shibata, T.; Saho, K. Correct Stability Condition and Fundamental Performance Analysis of the α-β-γ-δ Filter. Appl. Sci. 2018, 8, 2523.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Appl. Sci. EISSN 2076-3417 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top