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Visual Odometry (VO) is a method to estimate self-motion of a mobile robot using visual sensors. Unlike odometry based on integrating differential measurements that can accumulate errors, such as inertial sensors or wheel encoders, visual odometry is not compromised by drift. However, image-based VO is computationally demanding, limiting its application in use cases with low-latency, -memory, and -energy requirements. Neuromorphic hardware offers low-power solutions to many vision and AI problems, but designing such solutions is complicated and often has to be assembled from scratch. Here we propose to use Vector Symbolic Architecture (VSA) as an abstraction layer to design algorithms compatible with neuromorphic hardware. Building from a VSA model for scene analysis, described in our companion paper, we present a modular neuromorphic algorithm that achieves state-of-the-art performance on two-dimensional VO tasks. Specifically, the proposed algorithm stores and updates a working memory of the presented visual environment. Based on this working memory, a resonator network estimates the changing location and orientation of the camera. We experimentally validate the neuromorphic VSA-based approach to VO with two benchmarks: one based on an event camera dataset and the other in a dynamic scene with a robotic task.