Extended Kalman Filters (EKFs) are widely employed for attitude estimation using Magnetic and Inertial Measurement Units (MIMUs) in battery-powered sensing systems. In such applications, energy availability influences system operation, yet battery state information is commonly treated by external supervisory mechanisms rather than being integrated into the estimation process. This work presents an EKF-based formulation in which the battery State of Charge (SOC) is explicitly included as a state variable, allowing joint estimation of attitude and energy state within a single filtering framework. SOC dynamics are modeled using a low-complexity estimator based on terminal voltage and current measurements, while attitude estimation is performed using a Simplified Extended Kalman Filter (SEKF) tailored for embedded MIMU-based applications. The proposed approach was evaluated through numerical simulations under constant and time-varying load profiles representative of low-power electronic devices. The results indicate that the inclusion of SOC estimation does not affect the attitude estimation performance of the original SEKF, while SOC estimation errors remain below 8% for the evaluated load conditions with power consumption of approximately 0.1 W, consistent with wearable and small autonomous electronic platforms. By incorporating energy state estimation directly into the filtering structure, rather than treating it as an external supervisory task, the proposed formulation offers a unified estimation approach suitable for embedded MIMU-based systems with limited computational and energy resources.
Silva et al. (Wed,) studied this question.