Implementation of Kalman Filter in Low-Power, Low-Cost Microcontrollers

Abstract

The Kalman filter, introduced by R. E. Kalman in 1960, is a recursive algorithm that optimally estimates the state of a linear system, effectively removing Gaussian noise. Over time, it has evolved to be applicable to nonlinear systems, leading to the development of the Extended Kalman Filter (EKF), Ensemble Kalman Filter (EnKF), and Unscented Kalman Filter (UKF). Today, the Kalman filter is widely used across various fields due to its high memory efficiency and real-time processing capabilities. Despite its advantages, the Kalman filter's reliance on matrix operations results in high computational demands, making it challenging to implement in low-power, low-cost systems. This paper focuses on optimizing the Kalman filter's computations to enable real-time sensor data processing in low-power, low-cost microcontrollers. The mathematical modeling of the Kalman filter is outlined, along with its implementation and simulation validation using Python. The Kalman filter model is represented in six steps, performing prediction and update processes. The computational load for each step is calculated and summarized. By recognizing that certain model parameters do not change over time, the Kalman gain can be updated independently of sensor input, significantly reducing the overall computational load during real-time sensor data processing. A test board was designed using microcontrollers and temperature/humidity sensors to apply the Kalman filter to an actual sensor system. The test board compared a medium-spec 32-bit MCU with FPU and a low-spec 8-bit MCU. The experimental environment included a temperature and humidity chamber to verify the implementation. Filtering performance was compared using Gaussian, moving average, and FIR filters. In conclusion, the optimized implementation of the Kalman filter is effective for real-time data processing and performance improvement, making it suitable for various applications. Future work may address floating-point limitations and explore fixed-point implementations for wider applicability. Additionally, further research can be directed towards the implementation and optimization of nonlinear Kalman filters such as the Extended Kalman Filter (EKF), Ensemble Kalman Filter (EnKF), and Unscented Kalman Filter (UKF), to enhance performance in more complex systems.