Recurrent Neural Networks on Drifting Time-of-Flight Measurements

Kalman filters (KFs) are popular methods to estimate position information from a set of time-of-flight (ToF) values in radio frequency (RF)-based locating systems. Such filters are proven to be optimal under zero-mean Gaussian error distributions. In presence of multipath propagation ToF measurement errors drift due to small-scale motion. This results in changing phases of the multipath components (MPCs) which cause a drift on the ToF measurements. Thus, on a short-term scale the ToF measurements have a non-constant bias that changes while moving. KFs cannot distinguish between the drifting measurement errors and the true motion of the tracked object. Hence, very rigid motion models have to be used for the KF which commonly causes the filters to diverge. Therefore, the KF cannot resolve the short-term errors of consecutive measurements and the long-term motion of the tracked object. This paper presents a data-driven approach that uses training sequences to derive a near-optimal position estimator. A Long Short-Term Memory (LSTM) Recurrent Neural Network (RNN) learns to interpret drifting errors in ToF measurements of a tracked dynamic object directly from raw ToF data. Our evaluation shows that our approach outperforms state-of-the-art KFs on both synthetically generated and real-world dynamic motion trajectories that include drifting ToF measurement errors.