CNPE-KalmanNet: Learning-Aided Kalman Filter With Complex Number Position Encoding

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Abstract
KalmanNet demonstrates potential for nonlinear state estimation, but it directly concatenates heterogeneous components with disparate semantics into a composite vector. This approach ignores capturing semantic component correlations, limiting the network's ability to utilize this information when computing the Kalman gain. To address this, we propose CNPE-KalmanNet, a novel learning-aided Kalman filter that models semantic component correlations by integrating element-wise rotary encoding with multilayer perceptrons in the complex domain. CNPE serves as a plug-and-play module compatible with two baseline KalmanNet architectures. Experiments on the Michigan NCLT dataset demonstrate that CNPE-KalmanNet significantly improves estimation accuracy. Compared to the existing KalmanNet, our method reduces the RMSE by 20%-25% in state estimation tasks and by 15%-20% in sensor fusion tasks.

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