Parameter Estimation of Short-period Low Order Equivalent System for Fighter Aircraft Under Extreme Flight Conditions

Sayogyo Rahman Doko; Rianto Adhy Sasongko

doi:doi:10.11648/j.ajae.20261201.11

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Parameter Estimation of Short-period Low Order Equivalent System for Fighter Aircraft Under Extreme Flight Conditions

Sayogyo Rahman Doko^*

, Rianto Adhy Sasongko

Published in American Journal of Aerospace Engineering (Volume 12, Issue 1)

Received: 29 July 2025 Accepted: 5 January 2026 Published: 30 January 2026

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Abstract

This paper presents the estimation of Low Order Equivalent System (LOES) parameters for the longitudinal short-period mode of a fighter aircraft, using high-fidelity nonlinear simulation data of the F-16. The complex flight dynamics of such aircraft, effectively a High Order System (HOS) due to the presence of flight controls and component dynamics, require simplified equivalent systems for evaluating flying qualities against military standards. This study focuses on estimating LOES short period parameters using nonlinear flight simulation data under extreme flight conditions defined by high angles of attack up to 30 degrees. LOES parameters were identified through a hybrid approach combining time-domain regression and frequency-domain parameter estimation using a Maximum Likelihood Estimation (MLE) algorithm, resulting accurate identifications characterized by low standard deviations. Model validation confirms that LOES output closely matches HOS nonlinear data using inputs in the time domain, with a coefficient of determination R² metric above 77% and fit error below 0.2. Additionally, the LOES model effectively represents nonlinear system responses in the frequency domain, yielding relatively low MIL cost and maintaining mismatch errors within the Maximum Unnoticeable Added Dynamics (MUAD) boundary.

Published in	American Journal of Aerospace Engineering (Volume 12, Issue 1)
DOI	10.11648/j.ajae.20261201.11
Page(s)	1-11
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), 2026. Published by Science Publishing Group

Keywords

Equivalent System, Flight Dynamics, Flight Simulations, Parameter Estimation, System Identification

References

[1]	Morelli, Eugene A. “Identification of low order equivalent system models from flight test data.” No. NASA/TM-2000-210117. 2000.
[2]	Military Standard—"Flying Qualities of Piloted Aircraft”. MIL-STD-1797A, Jan. 1990.
[3]	Morelli, Eugene A. "Low-order equivalent system identification for the Tu-144LL supersonic transport aircraft." Journal of Guidance, Control, and Dynamics 26, no. 2 (2003): 354-362. https://doi.org/10.2514/2.5053
[4]	Stachowiak, Susan J., and John T. Bosworth. “Flight test results for the f-16xl with a digital flight control system”. No. NASA/TP-2004-212046. 2004.
[5]	Y. Qiao, G. Li, S. Zhai and Q. Jia, "A Rapid Evaluation Method for Flying Quality," 2023 42nd Chinese Control Conference (CCC), Tianjin, China, 2023, pp. 1200-1204. https://doi.org/10.23919/CCC58697.2023.10240135
[6]	Cao, Rui, Haidong Shen, Yanbin Liu, and Yuping Lu. "The LOES-based control scheme of aerospace vehicle under flying quality constraints." Acta Astronautica 177 (2020): 258-269. https://doi.org/10.1016/j.actaastro.2020.07.035
[7]	Lee, Daero, Jisoo Sim, Kwangho Han, Chongsup Kim, and Gi Ok Koh. "Angle-of-attack command longitudinal control for supersonic advanced trainer aircraft." International Journal of Aeronautical and Space Sciences 22, no. 1 (2021): 120-128. https://doi.org/10.1007/s42405-020-00279-2
[8]	Ji, Chang-ho, Chongsup Kim, and Byoung Soo Kim. 2023. "Flight Control Law for Stabilizing Transient Response of the Aircraft during Gun Firing" Aerospace 10, no. 4: 365. https://doi.org/10.3390/aerospace10040365
[9]	Kumar, R. and A. K. Ghosh. "Nonlinear Aerodynamic Modeling from Flight Data at High Angles of Attack Using Neural-Gauss-Newton Method," AIAA 2015-2707. AIAA Atmospheric Flight Mechanics Conference. June 2015. https://doi.org/10.2514/6.2015-2707
[10]	Klein, Vladislav, Thomas R. Ratvasky, and Brent R. Cobleigh. “Aerodynamic parameters of high-angle-of attack research vehicle (HARV) estimated from flight data”. No. NASA-TM-102692. 1990.
[11]	Weiss, S., D. Rohlf, and Ermin Plaetschke. "Parameter identification for X-31A at high angles of attack." Fourth High Alpha Conference: Volume 1. Vol. 1. No. NASA-CP-10143-VOL-1. National Aeronautics and Space Administration, 1994.
[12]	Sinha, Manoranjan, et al. "High angle of attack parameter estimation of cascaded fins using neural network." Journal of Aircraft 50.1 (2013): 272-291. https://doi.org/10.2514/1.C031912
[13]	Ignatyev, Dmitry I., and Alexander N. Khrabrov. "Neural network modeling of unsteady aerodynamic characteristics at high angles of attack." Aerospace Science and Technology 41 (2015): 106-115. https://doi.org/10.1016/j.ast.2014.12.017
[14]	M. B. Tischler and R. K. Remple. “Aircraft and rotorcraft system identification: engineering methods with flight-test examples.” American Institute of Aeronautics and Astronautics, 2006.
[15]	V. Klein and E. A. Morelli, "Aircraft system identification: theory and practice." American Institute of Aeronautics and Astronautics, 2006. https://doi.org/10.2514/4.861505
[16]	R. Jategaonkar, "Flight vehicle system identification: A time domain methodology". American Institute of Aeronautics and Astronautics, 2006. https://doi.org/10.2514/4.866852
[17]	Wood, J. R., and J. Hodgkinson. "Definition of Acceptable Levels of Mismatch for Equivalent Systems of Augmented CTOL Aircraft." Report Number 1600 (1980): A6792.
[18]	Hodgkinson J. Aircraft handling qualities, 1999.
[19]	Russell, Richard S. Non-linear F-16 simulation using Simulink and Matlab. University of Minnesota (2003).
[20]	L. T. Nguyen, Simulator study of stall/post-stall characteristics of a fighter air plane with relaxed longitudinal static stability, vol. 12854. National Aeronautics and Space Administration, 1979.

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APA Style

Doko, S. R., Sasongko, R. A. (2026). Parameter Estimation of Short-period Low Order Equivalent System for Fighter Aircraft Under Extreme Flight Conditions. American Journal of Aerospace Engineering, 12(1), 1-11. https://doi.org/10.11648/j.ajae.20261201.11

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ACS Style

Doko, S. R.; Sasongko, R. A. Parameter Estimation of Short-period Low Order Equivalent System for Fighter Aircraft Under Extreme Flight Conditions. Am. J. Aerosp. Eng. 2026, 12(1), 1-11. doi: 10.11648/j.ajae.20261201.11

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AMA Style

Doko SR, Sasongko RA. Parameter Estimation of Short-period Low Order Equivalent System for Fighter Aircraft Under Extreme Flight Conditions. Am J Aerosp Eng. 2026;12(1):1-11. doi: 10.11648/j.ajae.20261201.11

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@article{10.11648/j.ajae.20261201.11,
  author = {Sayogyo Rahman Doko and Rianto Adhy Sasongko},
  title = {Parameter Estimation of Short-period Low Order Equivalent System for Fighter Aircraft Under Extreme Flight Conditions},
  journal = {American Journal of Aerospace Engineering},
  volume = {12},
  number = {1},
  pages = {1-11},
  doi = {10.11648/j.ajae.20261201.11},
  url = {https://doi.org/10.11648/j.ajae.20261201.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajae.20261201.11},
  abstract = {This paper presents the estimation of Low Order Equivalent System (LOES) parameters for the longitudinal short-period mode of a fighter aircraft, using high-fidelity nonlinear simulation data of the F-16. The complex flight dynamics of such aircraft, effectively a High Order System (HOS) due to the presence of flight controls and component dynamics, require simplified equivalent systems for evaluating flying qualities against military standards. This study focuses on estimating LOES short period parameters using nonlinear flight simulation data under extreme flight conditions defined by high angles of attack up to 30 degrees. LOES parameters were identified through a hybrid approach combining time-domain regression and frequency-domain parameter estimation using a Maximum Likelihood Estimation (MLE) algorithm, resulting accurate identifications characterized by low standard deviations. Model validation confirms that LOES output closely matches HOS nonlinear data using inputs in the time domain, with a coefficient of determination R2 metric above 77% and fit error below 0.2. Additionally, the LOES model effectively represents nonlinear system responses in the frequency domain, yielding relatively low MIL cost and maintaining mismatch errors within the Maximum Unnoticeable Added Dynamics (MUAD) boundary.},
 year = {2026}
}

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TY  - JOUR
T1  - Parameter Estimation of Short-period Low Order Equivalent System for Fighter Aircraft Under Extreme Flight Conditions
AU  - Sayogyo Rahman Doko
AU  - Rianto Adhy Sasongko
Y1  - 2026/01/30
PY  - 2026
N1  - https://doi.org/10.11648/j.ajae.20261201.11
DO  - 10.11648/j.ajae.20261201.11
T2  - American Journal of Aerospace Engineering
JF  - American Journal of Aerospace Engineering
JO  - American Journal of Aerospace Engineering
SP  - 1
EP  - 11
PB  - Science Publishing Group
SN  - 2376-4821
UR  - https://doi.org/10.11648/j.ajae.20261201.11
AB  - This paper presents the estimation of Low Order Equivalent System (LOES) parameters for the longitudinal short-period mode of a fighter aircraft, using high-fidelity nonlinear simulation data of the F-16. The complex flight dynamics of such aircraft, effectively a High Order System (HOS) due to the presence of flight controls and component dynamics, require simplified equivalent systems for evaluating flying qualities against military standards. This study focuses on estimating LOES short period parameters using nonlinear flight simulation data under extreme flight conditions defined by high angles of attack up to 30 degrees. LOES parameters were identified through a hybrid approach combining time-domain regression and frequency-domain parameter estimation using a Maximum Likelihood Estimation (MLE) algorithm, resulting accurate identifications characterized by low standard deviations. Model validation confirms that LOES output closely matches HOS nonlinear data using inputs in the time domain, with a coefficient of determination R2 metric above 77% and fit error below 0.2. Additionally, the LOES model effectively represents nonlinear system responses in the frequency domain, yielding relatively low MIL cost and maintaining mismatch errors within the Maximum Unnoticeable Added Dynamics (MUAD) boundary.
VL  - 12
IS  - 1
ER  -

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Author Information

Sayogyo Rahman Doko

Faculty of Mechanical and Aerospace Engineering, Institut Teknologi Bandung, Bandung, Indonesia;Department of Flight Physics, Indonesian Aerospace, Bandung, Indonesia

Contact Email

http://orcid.org/0009-0002-7147-9277
Rianto Adhy Sasongko

Department of Flight Physics, Indonesian Aerospace, Bandung, Indonesia

Contact Email

http://orcid.org/0000-0003-0334-7352

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Plain Text BibTeX RIS

APA Style

Doko, S. R., Sasongko, R. A. (2026). Parameter Estimation of Short-period Low Order Equivalent System for Fighter Aircraft Under Extreme Flight Conditions. American Journal of Aerospace Engineering, 12(1), 1-11. https://doi.org/10.11648/j.ajae.20261201.11

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ACS Style

Doko, S. R.; Sasongko, R. A. Parameter Estimation of Short-period Low Order Equivalent System for Fighter Aircraft Under Extreme Flight Conditions. Am. J. Aerosp. Eng. 2026, 12(1), 1-11. doi: 10.11648/j.ajae.20261201.11

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AMA Style

Doko SR, Sasongko RA. Parameter Estimation of Short-period Low Order Equivalent System for Fighter Aircraft Under Extreme Flight Conditions. Am J Aerosp Eng. 2026;12(1):1-11. doi: 10.11648/j.ajae.20261201.11

Copy | Download

@article{10.11648/j.ajae.20261201.11,
  author = {Sayogyo Rahman Doko and Rianto Adhy Sasongko},
  title = {Parameter Estimation of Short-period Low Order Equivalent System for Fighter Aircraft Under Extreme Flight Conditions},
  journal = {American Journal of Aerospace Engineering},
  volume = {12},
  number = {1},
  pages = {1-11},
  doi = {10.11648/j.ajae.20261201.11},
  url = {https://doi.org/10.11648/j.ajae.20261201.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajae.20261201.11},
  abstract = {This paper presents the estimation of Low Order Equivalent System (LOES) parameters for the longitudinal short-period mode of a fighter aircraft, using high-fidelity nonlinear simulation data of the F-16. The complex flight dynamics of such aircraft, effectively a High Order System (HOS) due to the presence of flight controls and component dynamics, require simplified equivalent systems for evaluating flying qualities against military standards. This study focuses on estimating LOES short period parameters using nonlinear flight simulation data under extreme flight conditions defined by high angles of attack up to 30 degrees. LOES parameters were identified through a hybrid approach combining time-domain regression and frequency-domain parameter estimation using a Maximum Likelihood Estimation (MLE) algorithm, resulting accurate identifications characterized by low standard deviations. Model validation confirms that LOES output closely matches HOS nonlinear data using inputs in the time domain, with a coefficient of determination R2 metric above 77% and fit error below 0.2. Additionally, the LOES model effectively represents nonlinear system responses in the frequency domain, yielding relatively low MIL cost and maintaining mismatch errors within the Maximum Unnoticeable Added Dynamics (MUAD) boundary.},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Parameter Estimation of Short-period Low Order Equivalent System for Fighter Aircraft Under Extreme Flight Conditions
AU  - Sayogyo Rahman Doko
AU  - Rianto Adhy Sasongko
Y1  - 2026/01/30
PY  - 2026
N1  - https://doi.org/10.11648/j.ajae.20261201.11
DO  - 10.11648/j.ajae.20261201.11
T2  - American Journal of Aerospace Engineering
JF  - American Journal of Aerospace Engineering
JO  - American Journal of Aerospace Engineering
SP  - 1
EP  - 11
PB  - Science Publishing Group
SN  - 2376-4821
UR  - https://doi.org/10.11648/j.ajae.20261201.11
AB  - This paper presents the estimation of Low Order Equivalent System (LOES) parameters for the longitudinal short-period mode of a fighter aircraft, using high-fidelity nonlinear simulation data of the F-16. The complex flight dynamics of such aircraft, effectively a High Order System (HOS) due to the presence of flight controls and component dynamics, require simplified equivalent systems for evaluating flying qualities against military standards. This study focuses on estimating LOES short period parameters using nonlinear flight simulation data under extreme flight conditions defined by high angles of attack up to 30 degrees. LOES parameters were identified through a hybrid approach combining time-domain regression and frequency-domain parameter estimation using a Maximum Likelihood Estimation (MLE) algorithm, resulting accurate identifications characterized by low standard deviations. Model validation confirms that LOES output closely matches HOS nonlinear data using inputs in the time domain, with a coefficient of determination R2 metric above 77% and fit error below 0.2. Additionally, the LOES model effectively represents nonlinear system responses in the frequency domain, yielding relatively low MIL cost and maintaining mismatch errors within the Maximum Unnoticeable Added Dynamics (MUAD) boundary.
VL  - 12
IS  - 1
ER  -

Copy | Download