Odometry estimation using light detection and ranging (LiDAR) and an inertial measurement unit (IMU), known as LiDAR-inertial odometry (LIO), often suffers from performance degradation in degenerate environments, such as long corridors or single-wall scenarios with narrow field-of-view LiDAR. To address this limitation, we propose ALIVE-LIO, a degeneracy-aware LiDAR-inertial odometry framework that explicitly enhances state estimation in degenerate directions. The key contribution of ALIVE-LIO is the strategic integration of a deep neural network into a classical error-state Kalman filter (ESKF) to compensate for the loss of LiDAR observability. Specifically, ALIVE-LIO employs a neural network to predict the body-frame velocity and selectively fuses this prediction into the ESKF only when degeneracy is detected, providing effective state updates along degenerate directions. This design enables ALIVE-LIO to utilize the probabilistic structure and consistency of the ESKF while benefiting from learning-based motion estimation. The proposed method was evaluated on publicly available datasets exhibiting degeneracy, as well as on our own collected data. Experimental results demonstrate that ALIVE-LIO substantially reduces pose drift in degenerate environments, yielding the top-ranked result in 22 out of 32 sequences. Our code is available at https://github.com/cocel-postech/alive-lio.

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