Tracking and modeling unknown rigid objects in the environment play a crucial role in autonomous unmanned systems and virtual-real interactive applications. However, many existing Simultaneous Localization, Mapping and Moving Object Tracking (SLAMMOT) methods focus solely on estimating specific object poses and lack estimation of object scales and are unable to effectively track unknown objects. In this paper, we propose a novel SLAM backend that unifies ego-motion tracking, rigid object motion tracking, and modeling within a joint optimization framework. In the perception part, we designed a pixel-level asynchronous object tracker (AOT) based on the Segment Anything Model (SAM) and DeAOT, enabling the tracker to effectively track target unknown objects guided by various predefined tasks and prompts. In the modeling part, we present a novel object-centric quadric parameterization to unify both static and dynamic object initialization and optimization. Subsequently, in the part of object state estimation, we propose a tightly coupled optimization model for object pose and scale estimation, incorporating hybrids constraints into a novel dual sliding window optimization framework for joint estimation. To our knowledge, we are the first to tightly couple object pose tracking with light-weight modeling of dynamic and static objects using quadric. We conduct qualitative and quantitative experiments on simulation datasets and real-world datasets, demonstrating the state-of-the-art robustness and accuracy in motion estimation and modeling. Our system showcases the potential application of object perception in complex dynamic scenes.

We introduce Cayley transform ellipsoid fitting (CTEF), an algorithm that uses the Cayley transform to fit ellipsoids to noisy data in any dimension. Unlike many ellipsoid fitting methods, CTEF is ellipsoid specific, meaning it always returns elliptic solutions, and can fit arbitrary ellipsoids. It also significantly outperforms other fitting methods when data are not uniformly distributed over the surface of an ellipsoid. Inspired by growing calls for interpretable and reproducible methods in machine learning, we apply CTEF to dimension reduction, data visualization, and clustering in the context of cell cycle and circadian rhythm data and several classical toy examples. Since CTEF captures global curvature, it extracts nonlinear features in data that other machine learning methods fail to identify. For example, on the clustering examples CTEF outperforms 10 popular algorithms.