本論文提出了一個針對嵌入式系統設計工具的功能模擬研究，尤其是針對物聯網 (IoT) 中的周邊裝置。在這類系統中，輸入源主要來自傳感設備。不幸的是，目前的模擬器主要專注於指令集或硬體模擬，而沒有任何幫助設計人員處理主要關注的問題，也就是傳感數據本身的研究。數位傳感器的發展增加了這類問題的重要性，數位傳感器不僅在芯片上執行類比數位轉換 (ADC)，還對數據執行數位信號處理，然而當今的模擬器都不支持這些重要的內部設定。
為了解決這類問題並應用在嵌入式系統的新設計工具上，我們提出了一種以數據為中心的功能模擬器。模擬器模擬數位傳感器支持的通信接口和命令，以便於將數據發送到中央處理器之前對其進行處理。最重要的是，可以預先從實際傳感器收集數據或根據物理定律合成數據，以及用於噪聲注入和環境因子的建模。
本論文通過對數位慣性測量單元 (IMU) 進行案例研究，代表了實現此類模擬器的第一步。我們的模擬器允許設計人員以可重複性的方式提出許多假設，包括不同的採樣率、分辨率、動態範圍、觸發條件、噪聲條件等等，對模擬器進行設定，並加以觀察輸出結果。該模擬器有望成為優化許多物聯網設備的重要工具。

This thesis proposes a case study of functional simulation for a design tool for embedded systems, especially edge devices in the Internet of Things (IoT). In these systems, input primarily comes from the sensing devices, rather than data files. Unfortunately, today's simulators focus on either instruction-set or hardware execution without assisting designers with the sensing data itself, which should be of main concern to the designer. The problem is exacerbated by the trend towards digital sensors, which not only perform analog-to-digital conversion (ADC) on-chip but also digital signal processing on the data, none of which is supported by today's simulators.
To address this problem, we propose a data-centric functional simulator for a new design tool for embedded systems. The simulator simulates the communication interface and the commands supported by the digital sensor so that it can operate on the data before sending it to the controller. Most importantly, the data can be collected from an actual sensor in advance or synthesized based on the laws of physics, plus additional modeling for noise injection and environmental modeling.
This thesis represents the first step toward the goal of such a simulator by a case study of a digital inertial measurement unit (IMU). Our simulator allows designers to ask many what-if questions, including different sampling rates, resolutions, dynamic ranges, triggering conditions, noise conditions, and many more, all in a fully reproducible way. This simulator is expected to be an important tool for the optimization of many IoT devices.

Contents ......................................................i
Acknowledgments ...............................................vi
1 Introduction ................................................1
1.1 Motivation ..............................................1
1.2 Contributions ...........................................3
1.3 Thesis Organization .....................................3
2 Related Work ................................................4
2.1 Functional Models .......................................4
2.1.1 Electro-Mechanical Models ...........................4
2.1.2 Mathematical Model ..................................5
2.1.3 System Model ........................................6
2.2 Stochastic Models .......................................7
2.2.1 System Noise in Allan Method ........................7
2.2.2 Environmental Factors ...............................7
2.3 Simulation Software .....................................8
2.3.1 System Simulators ...................................8
2.3.2 Additional tools for simulation .....................9
3 Configurations in Digital Sensors ...........................10
3.1 Analog Front-End ........................................10
3.1.1 Analog-to-Digital Converter .........................10
3.1.2 Sampling Frequency ..................................11
3.1.3 Threshold ...........................................11
3.1.4 Duration ............................................12
3.1.5 Full Scale (FS) .....................................12
3.1.6 Re-orientation ......................................13
3.2 Digital Signal Processing ...............................13
3.3 Data Buffering ..........................................14
3.4 Digital Interface .......................................16
3.4.1 I2C .................................................17
3.4.2 SPI .................................................18
3.4.3 Interrupt Request (IRQ) .............................20
3.5 Register Map ............................................21
3.6 Sensor Noise ............................................21
3.6.1 Bias Stability ......................................22
3.6.2 Angular Random Walk and Velocity Random Walk ........22
4 IMU Simulator ...............................................23
4.1 System Overview .........................................23
4.1.1 Discrete Event Simulation ...........................24
4.1.2 IMU Simulator .......................................24
4.1.3 Test Bench ..........................................25
4.2 IMU Simulator ...........................................25
4.2.1 Analog Front-End (AFE) ..............................25
4.2.2 Digital Signal Processing (DSP) .....................27
4.2.3 Data Buffering ......................................33
4.2.4 Digital Interface ...................................33
5 Implementations and Case Study ..............................38
5.1 Simulator Prerequisites .................................38
5.1.1 Parameters for Initialization .......................38
5.1.2 Input Data ..........................................39
5.2 Simulator Implementations ...............................39
5.3 Test Bench Controller ...................................40
6 Evaluation ..................................................42
6.1 Discussion ..............................................42
6.1.1 Time Shift ..........................................42
6.1.2 Data Loss ...........................................43
6.2 Comparison ..............................................43
6.2.1 Signal Generator ....................................44
6.2.2 Component Replacement ...............................44
6.2.3 Data Reproduction ...................................45
7 Conclusions and Future Work .................................46
7.1 Conclusions .............................................46
7.2 Future Work .............................................47
Appendix A Python Code for Simulator ..........................51

[1] D. Teegarden, G. Lorenz, and R. Neuf. How to model and simulate microgyroscope systems. IEEE Spectrum, 35(7):66–75, 1998.
[2] S. Megherbi, R. Levy, F. Parrain, H. Mathias, O. Le Traon, D. Janiaud, and J. P. Gilles. Behavioral modelling of vibrating piezoelectric micro-gyro sensor and detection electronics. In 2007 International Conference on Thermal, Mechanical and Multi-Physics Simulation Experiments in Microelectronics and Micro-Systems. EuroSime 2007, pages 1–4, 2007.
[3] Cicci David. Mathematical modeling of inertial measurement units, 08 2006.
[4] G. Baldo Carvalho, S. Theil, and H. Koiti Kuga. IMU: Generic model development approach. In Simposio Brasileiro de Engenharia Inercial. Available online: http://www2. dem. inpe. br/hkk/2007/vsbein019-Gustavo. pdf (accessed on 27 February 2015), 2007.
[5] M.E. Parés, J.J. Rosales, and I. Colomina. Yet another IMU simulator: Validation and applications. Proceedings of the Eurocow, Castelldefels, Spain, 30, 2008.
[6] El-Sheimy Naser, Hou Haiying, and Niu Xiaoji. Analysis and modeling of inertial sensors using Allan Variance. IEEE Transactions on Instrumentation and Measurement, 57(1):140–149, 2008.
[7] Barreda Pupo and Leslie. Characterization of errors and noises in MEMS inertial sensors using allan variance method. Master’s thesis, Universitat Politècnica de Catalunya, 2016.
[8] Zhao Yueming, Horemuz Milan, and Sjöberg Lars E. Stochastic modelling and analysis of IMU sensor errors. Archiwum Fotogrametrii, Kartografii i Teledetekcji, 22:437–449, 2011.
[9] Jay A. Farrell, Felipe Oliveira e Silva, Farzana Rahman, and Jan Wendel. IMU error modeling for state estimation and sensor calibration: A tutorial. 2021.
[10] M. E. Parés, J. A. Navarro, and I. Colomina. On the generation of realistic simulated inertial measurements. In 2015 DGON Inertial Sensors and Systems Symposium (ISS), pages 1–15, 2015. doi: 10.1109/InertialSensors.2015.7314268.
[11] Yigiter Yuksel, Naser El-Sheimy, and Aboelmagd Noureldin. Error modeling and characterization of environmental effects for low cost inertial MEMS units. In IEEE/ION Position, Location and Navigation Symposium, pages 598–612, 2010. doi: 10.1109/PLANS.2010.5507180.
[12] Matlab. https://www.mathworks.com/products/matlab.html.
[13] IMU simulation model in simulink. https://www.mathworks.com/products/simulink.html.
[14] Lukáš Palkovič, Jozef Rodina, L’uboš Chovanec, and Peter Hubinsky. Integration of inertial ` measuring unit platform into MATLAB simulink. IFAC Proceedings Volumes, 45(11):200–205, 2012.
[15] Laszlo Kis, Zoltan Prohaszka, and Gergely Regula. Calibration and testing issues of the vision, inertial measurement and control system of an autonomous indoor quadrotor helicopter. Proceedings of the RAAD, 2008.
[16] Cédric Berbra, Sylviane Gentil, and Suzanne Lesecq. Identification of multiple faults in an inertial measurement unit. In ACD 2009-7th European Workshop on Advanced Control and Diagnosis, page 6p, 2009.
[17] Pavol Božek. Control of a robotic arm on the principle of separate decision of an inertial navigation system. In Applied Mechanics and Materials, volume 611, pages 60–66. Trans Tech Publ, 2014.
[18] O.A. Sushchenko and Y.V. Beliavtsev. Modelling of inertial sensors in UAV systems. In 2017 IEEE 4th International Conference Actual Problems of Unmanned Aerial Vehicles Developments (APUAVD), pages 130–133. IEEE, 2017.
[19] Xin Xia, Lu Xiong, Yishi Lu, Letian Gao, and Zhuoping Yu. Vehicle sideslip angle estimation by fusing inertial measurement unit and global navigation satellite system with heading alignment. Mechanical Systems and Signal Processing, 150:107290, 2021.
[20] Open Robotics. Gazebo: Simulate before you build. https://gazebosim.org/home, 2022.
[21] MORSE. Modular OpenRobots Simulation Engine. https://morse-simulator.github.io/, 2022.
[22] A. D. Young, M. J. Ling, and D. K. Arvind. IMUSim: A simulation environment for inertial sensing algorithm design and evaluation. In Proceedings of the 10th ACM/IEEE International Conference on Information Processing in Sensor Networks, pages 199 – 210, Chicago, IL, USA, 2011. IEEE.
[23] Gabriele Ligorio and Angelo Maria Sabatini. A simulation environment for bench marking sensor fusion-based pose estimators. Sensors, 15(12):32031–32044, 2015.
[24] Strasnick Evan, Agrawala Maneesh, and Follmer Sean. Scanalog: Interactive design and debugging of analog circuits with programmable hardware. In UIST ’17: Proceedings of the 30th Annual ACM Symposium on User Interface Software and Technology, page 321–330, New York, NY, USA, 2017. ACM.
[25] Hao Yujiao, Wang Boyu, and Zheng Rong. CROMOSim: A deep learning-based cross-modality inertial measurement simulator. arXiv preprint arXiv:2202.10562, 2022.
[26] MyHDL. http://docs.myhdl.org/en/stable/manual/highlevel.html.