本論文針對鎳氫電池（Nickel-Metal Hydride， NiMH）於動態負載條件下之荷電狀態（State of Charge， SOC）估測問題進行研究。由於NiMH電池具有開路電壓（Open Circuit Voltage， OCV）平坦區特性與明顯之充放電磁滯效應（Hysteresis），使傳統SOC估測方法於動態操作環境下容易產生估測誤差累積與收斂能力下降等問題。因此，本研究提出一套結合磁滯補償、自適應量測雜訊調整功能之三維擴展式卡爾曼濾波器（Three-Dimensional Extended Kalman Filter， 3D-EKF）估測架構。在研究方法方面，本研究以一階RC等效電路模型及七階多項式OCV-SOC關係模型為基礎，建立包含SOC、極化電壓與磁滯電壓之三維狀態空間模型。相較於傳統二維擴展式卡爾曼濾波器（2D-EKF），本研究進一步導入動態磁滯補償模型，以描述充放電切換過程中之電壓路徑差異；同時提出基於OCV斜率特性之自適應量測雜訊協方差（Adaptive Measurement Noise Covariance， ( )）調整機制，使演算法能於電壓平坦區降低量測雜訊干擾，提高估測穩定性。此外，本研究結合SOC估測結果與60秒移動平均電流濾波，建立剩餘運行時間（Time-to-Cutoff， TTC）與剩餘能量（Remaining Energy， ( )）之估測機制，並設計結合時間門檻與預測電壓門檻之雙重防護策略。在系統實現方面，本研究建構由實體電池、動態負載、ESP32/ADS1115資料擷取及PC端MATLAB線上估測所組成之實體電池線上估測平台，以ESP32微控制器搭配16位元ADS1115類比數位轉換器進行即時電壓與電流量測，並透過UDP通訊將量測資料傳輸至MATLAB平台執行3D-EKF估測運算。為驗證所提出方法之有效性，本研究設計純電阻負載、馬達動態負載及頻繁充放電切換等三組實驗情境，每組納入五次正式實驗，共十五筆資料，並刻意設定約50個百分點之初始SOC偏差，以驗證閉迴路估測器之初始狀態修正能力。所有RMSE均以量測起始10分鐘後之資料計算。在庫倫效率設定為0.95之模擬測試中，CC、2D-A及3D-A之RMSE分別為7.25%、3.55%及2.80%。三組代表性Run 1中，Case I之CC、2D-F、2D-A、3D-F及3D-A RMSE分別為3.02%、4.66%、4.67%、3.01%及3.00%；Case II分別為2.86%、2.22%、1.39%、1.80%及2.16%；Case III分別為7.36%、4.94%、4.37%、4.73%及4.02%。五次實驗平均RMSE方面，Case I分別為3.84%、4.93%、4.99%、3.15%及3.11%；Case II分別為3.17%、1.84%、1.67%、2.62%及2.82%；Case III分別為5.82%、2.95%、2.79%、3.03%及2.74%。結果顯示，Case I與Case III以3D-A具有較低之跨實驗平均RMSE，Case II則以2D-A最低，說明磁滯狀態與自適應量測權重之效益會隨SOC工作區域、負載軌跡及資料條件而改變。所有EKF之五次平均prior-NIS均低於自由度1之95%卡方門檻3.841，顯示目前Q與R設定較為保守。此外，本研究亦使用指定之Case II資料進行TTC與雙重截止保護驗證；預測端電壓條件與5分鐘TTC條件分別於約114分鐘及約120分鐘首次成立。;This thesis investigates the state-of-charge (SOC) estimation of nickel-metal hydride (NiMH) batteries under dynamic loading conditions. The flat region of the open-circuit-voltage–SOC (OCV–SOC) relationship reduces the voltage sensitivity to SOC， while charge–discharge hysteresis introduces a path-dependent voltage difference. These characteristics may reduce the correction capability of a conventional two-dimensional extended Kalman filter (2D-EKF). To address these issues， a three-dimensional extended Kalman filter (3D-EKF) incorporating a hysteresis-voltage state and an adaptive measurement-noise covariance mechanism is developed. The proposed estimator is based on a first-order RC equivalent-circuit model and a seventh-order OCV–SOC polynomial identified for the tested battery. The three state variables are polarization voltage， SOC， and hysteresis voltage. The adaptive measurement-noise covariance is determined from the local OCV–SOC slope using a three-region mapping. The covariance is set to its upper value in the flat OCV region， decreases linearly and continuously between the two slope thresholds， and returns exactly to the baseline value in the steep region. This mechanism reduces the influence of low-information voltage residuals without artificially increasing the observability of SOC. An experimental platform consisting of a NiMH battery， dynamic loads， an ESP32 microcontroller， ADS1115 analog-to-digital converters， UDP communication， and a MATLAB-based estimator was constructed. The evaluation included a simulation with fixed Gaussian-noise sequences and three experimental cases involving a resistive load， a motor load with a single charge–discharge transition， and a motor load with frequent operating-mode transitions. The EKF estimators were initialized at 50% SOC， whereas the reference SOC was initialized at 100%. All root-mean-square errors (RMSEs) were calculated using data collected after the first 10 minutes. With a coulombic-efficiency setting of 0.95， the simulation RMSEs of coulomb counting， 2D-A， and 3D-A were 7.25%， 3.55%， and 2.80%， respectively. Fifteen formal experimental runs were evaluated， with five runs for each of Cases I， II， and III. After excluding the first 10 min， the five-run mean RMSEs for CC， 2D-F， 2D-A， 3D-F， and 3D-A were 3.84%， 4.93%， 4.99%， 3.15%， and 3.11% in Case I; 3.17%， 1.84%， 1.67%， 2.62%， and 2.82% in Case II; and 5.82%， 2.95%， 2.79%， 3.03%， and 2.74% in Case III， respectively. Thus， 3D-A achieved the lowest cross-run mean RMSE in Cases I and III， whereas 2D-A performed best in Case II. The mean one-step-prior NIS values of all EKF variants remained below the 95% chi-square threshold of 3.841 for one degree of freedom， indicating conservative covariance settings. The designated Case II dataset was also used to demonstrate time-to-cutoff， remaining-energy， and dual-threshold protection functions. The one-step-prior voltage condition and the 5-min TTC condition were first triggered at 114.017 min and 120.778 min， respectively.
