Unsupervised KalmanNet for Three Stations TOA Localization

Three-station Time-of-Arrival (TOA) positioning technology holds significant application value in electronic reconnaissance and unmanned aerial vehicle tracking. However, TOA measurements in real-world environments are often affected by non-line-of-sight propagation and synchronization errors, making it challenging to accurately obtain the system's noise statistical characteristics. Traditional Kalman filtering (KF) heavily relies on precise system models and noise parameters; when the pre-set noise covariance mismatches the actual environment, positioning accuracy significantly degrades. To address this issue, this paper proposes a deep Kalman network (KalmanNet)-assisted positioning algorithm based on unsupervised learning.The basic idea is that: encapsulating environmental priors and noise distributions into GRU model parameters, the Kalman Gain could be calculated based on observation variables and dynamically updated state variables. This algorithm adopts a hybrid architecture combining model-driven and data-driven approaches. To avoid performance degradation caused by the inability to collect samples or discrepancies between the training data and the real-world environment, we employ an unsupervised training method. Unlike supervised learning that relies on true state values, this paper designs an unsupervised loss function based on observation innovations, optimizing network parameters through backpropagation. Experimental results demonstrate that, even with only observation data and no true system states, the proposed algorithm can predict target states in real time. Its positioning accuracy outperforms traditional Kalman filtering and exhibits strong robustness across varying noise levels.