Neural networks are seeing rapid adoption in purely inertial odometry, where accelerometer and gyroscope measurements from commodity inertial measurement units (IMU) are used to regress displacements and associated uncertainties. They can learn informative displacement priors, which can be directly fused with the raw data with off-the-shelf non-linear filters. Nevertheless, these networks do not consider the physical roto-reflective symmetries inherent in IMU data, leading to the need to memorize the same priors for every possible motion direction, which hinders generalization. In this work, we characterize these symmetries and show that the IMU data and the resulting displacement and covariance transform equivariantly, when rotated around the gravity vector and reflected with respect to arbitrary planes parallel to gravity. We design a neural network that respects these symmetries by design through equivariant processing in three steps: First, it estimates an equivariant gravity-aligned frame from equivariant vectors and invariant scalars derived from IMU data, leveraging expressive linear and non-linear layers tailored to commute with the underlying symmetry transformation. We then map the IMU data into this frame, thereby achieving an invariant canonicalization that can be directly used with off-the-shelf inertial odometry networks. Finally, we map these network outputs back into the original frame, thereby obtaining equivariant covariances and displacements. We demonstrate the generality of our framework by applying it to the filter-based approach based on TLIO, and the end-to-end RONIN architecture, and show better performance on the TLIO, Aria, RIDI and OxIOD datasets than existing methods.

翻译：神经网络在纯惯性里程计领域正迅速普及，其中利用商用惯性测量单元（IMU）的加速度计和陀螺仪测量数据来回归位移及其相关不确定性。这些网络能够学习信息丰富的位移先验，并可直接通过现成的非线性滤波器与原始数据融合。然而，这些网络未考虑IMU数据中固有的物理旋转反射对称性，导致需要为每个可能的运动方向记忆相同的先验，从而阻碍了泛化能力。本研究系统刻画了这些对称性，并证明当IMU数据绕重力矢量旋转及相对于任意平行于重力的平面进行反射时，其产生的位移与协方差具有等变性。我们设计了一种通过等变处理在结构上遵循这些对称性的神经网络，其包含三个步骤：首先，网络从IMU数据导出的等变向量与不变标量中估计等变的重力对齐坐标系，该过程利用了为与底层对称变换可交换而专门设计的表达性线性和非线性层。随后将IMU数据映射至该坐标系，从而实现不变的正则化处理，使其可直接与现有惯性里程计网络兼容。最后，将这些网络输出映射回原始坐标系，从而获得等变的协方差与位移。我们通过将本框架应用于基于TLIO的滤波器方法及端到端的RONIN架构，验证了其普适性，并在TLIO、Aria、RIDI和OxIOD数据集上展现出优于现有方法的性能。