A Neural Error-State Kalman Network for Foot-Mounted Inertial Navigation Systems

Inertial Measurement Units (IMUs) are widely used in Indoor Location-Based Systems (ILBS) for self-localization without relying on external data. However, traditional methods that rely on accelerometers and gyroscopes are prone to biases, leading to cumulative positioning errors over time. While existing deep learning-based models offer high accuracy, they are often large and computationally intensive, posing challenges for mobile devices. To address the above issues, we propose the Error State Kalman Network (ES-KalmanNet), a low-cost, lightweight approach that combines the advantages of Kalman filtering with deep learning. ES-KalmanNet not only uses a Kalman filter to update the neural network parameters but also integrates Error-State models to structure the network. Additionally, we present a lightweight zero-velocity detection method that uses diverse gait features to extract zero-velocity information, which is then used as pseudo-measurements for ES-KalmanNet. This method can adaptively adjust thresholds according to different motion states, thus reducing sensor error and making zero-velocity measurement more accurate and reliable. Experimental results demonstrate that the proposed zero-velocity detection method can accurately identify zero-velocity intervals in walking, running, and complex gait scenarios. Moreover, compared with the traditional ESKF based method, ES-Kalmannet significantly improves positioning accuracy and robustness in long-distance experiments of nearly 120m (Based on the same zero velocity detection results), while reducing position cumulative error (ATE) and relative error (RTE) per meter by about 90%. This method is ideal for practical applications in mobile and foot-mounted inertial navigation systems, since it has low computational requirements and superior performance.