Methodology for the Thermal Models Development of the Brazilian Inertial System
DOI:
https://doi.org/10.1590/jatm.v18.1430Keywords:
Thermal analysis, Inertial navigation, Hierarchical modelling, System Identification, SISNAV, MATLABAbstract
This work presents a methodology to produce the thermal models of the Inertial Navigation System (Sistema de Navegação Inercial), being developed along with its host micro-satellite launch vehicle by the Brazilian Air Force (Força Aérea Brasileira). The rationale is built upon (i) knowledge gathering about the modelling and identification subject and the intended use of the thermal models, (ii) selection of the model’s “box color,” (iii) determination of the theoretical and/or the experimental setup, and (iv) definition of the necessary procedures, which comprise steps, rules, and metrics for selecting and validating the models. Given the “intended use” aimed at facilitating component replacement and parameter tuning, the light-gray box approach is selected, where each component is modelled individually and subsequently grouped hierarchically as submodels. The theoretical setup utilizes the MATLAB + SIMSCAPE environment, while the experimental setup relies on the open-source electronics platform named Arduino. Finally, the procedure is defined whereby the models’ parameters are progressively tuned, based on comparisons between simulation data and experimental measurements, following the progressive aggregation of the system components. The results demonstrate a good correlation between both data and measurements across all aggregation phases. Future work includes complex scenarios and rocket launch campaign results.
References
Chen C, Pan X (2023) Deep learning for inertial positioning: a survey. IEEE Trans Intell Transp Syst 25 (9). https://doi.org/10.1109/TITS.2024.3381161
El-Sheimy N, Youssef A (2020) Inertial sensors technologies for navigation applications: state of the art and future trends. Satell Navig 1(2):1-17. https://doi.org/10.1186/s43020-019-0001-5
Gonzáles-Bárcena D, Cavia-Fraile S, Torralbo I, Borque C, Arroyo JM, Urdampilleta I, Solyga M, Peyrou-Lauga R (2024) Hierarchical thermal modeling and analysis automatization of Comet Interceptor Probe B2 with ESATAN-TMS. Paper presented 2024 53rd International Conference on Environmental Systems. ICES; Louisville, USA. https://ttu-ir.tdl.org/items/5dc26ddf-fe65-4fe7-adbd-cd4af1fffd55
Incropera FP (2006) Fundamentals of heat and mass transfer. 6th ed. Massachusetts: John Wiley and Sons Inc.
Isermann R, Münchhof M (2010) Identification of dynamic systems: an introduction with applications. Berlin: Springer.
Jacobs ED (1972) Accelerometer. U.S. Patent 3702073. Filed February 28, 1969; issued November 7, 1972 [accessed January the 29th 2026]. https://patents.google.com/patent/US3702073A/en
Lapusan C, Balan R, Hancu O, Plesa A (2016) Development of a multi-room building thermodynamic model using SIMSCAPE library. Energy Procedia 85:491-499. https://doi.org/10.1016/j.egypro.2015.12.258
Lienhard VJH, Lienhard IV JH (2024) A heat transfer textbook. Version 6.00. 6th ed. Cambridge: Phlogiston Press.
Liu H, Cai J, Kim D (2022) A hierarchical gray-box dynamic modeling methodology for direct-expansion cooling systems. Technical report. University of Oklahoma; Lawrence Berkeley National Laboratory. [accessed Jan 29 2026]. https://escholarship.org/uc/item/8kt412bk
Ljung L (1996) Development of system identification. Paper presented 1996 13th World Congress of IFAC. IFAC; San Francisco, USA. https://www.sciencedirect.com/science/article/pii/S1474667017581380
Ljung L (1999) System identification: theory for the user. 2nd ed. New Jersey: Prentice Hall PTR.
Lv Z, Sun Z, Wang L, Liu Q, Zhang J (2025) Multi-level thermal modeling and management of battery energy storage systems. Batteries 11(6). https://doi.org/10.3390/batteries11060219
MathWorks (2024) Build model of battery module with thermal effects. [accessed Jan 29 2026]. https://www.mathworks.com/help/simscape-battery/ug/build-battery-module-thermal-effects.html
MATLAB (2011) MATLAB. Version 7.12.0 (R2011a). Natick, MA: The MathWorks Inc.
McFadden C (2017) The origin of the word engineering. [accessed Oct 25 2025]. https://interestingengineering.com/culture/the-origin-of-the-word-engineering
Mijlad A, Mezouar A, Benyahia S, Kherraz N (2016) Simscape electro-thermal modelling of the pin diode for power circuits simulation. IET Power Electron 9(12):2391-2398. https://doi.org/10.1049/iet-pel.2015.0340
Ramos FO (2011) Automation of H∞ controller design and its observer-based realization (doctoral thesis). Instituto Nacional de Pesquisas Espaciais; Institut Supérieur de l’Aéronautique et de l’Espace. https://bdtd.ibict.br/vufind/Record/INPE_4f67369aef6932e3293f29199f60abcd
Ramos FO (2015) History and current status of SISNAV: a brief report. Paper presented VIII Brazilian Symposium of Inertial Engineering. Instituto Nacional de Pesquisas Espaciais; São José dos Campos, Brazil. https://www.researchgate.net/publication/281068299_History_and_current_status_of_SISNAV_a_brief_report
Tannous PJ, Alleyne AG (2020) Multilevel hierarchical estimation for thermal management systems of electrified vehicles. J Dyn Syst Meas Control 142(11). https://doi.org/10.1115/DSCC2020-3175
The Arduino Team (2024) What is Arduino? [accessed Oct 25 2025]. https://www.arduino.cc/en/about?utm_source=chatgpt.com
Wang Q, Li Y, Niu X (2016) Thermal calibration procedure and thermal characterisation of low-cost inertial measurement units. J Navig 69(2):373–-390. https://doi.org/10.1017/S0373463315000600
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