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This paper presents a generic motion model to capture mobile robots' dynamicbehaviors (translation and rotation). The model is based on statistical modelsdriven by white random processes and is formulated into a full state estimationalgorithm based on the error-state extended Kalman filtering framework (ESEKF).Major benefits of this method are its versatility, being applicable todifferent robotic systems without accurately modeling the robots' specificdynamics, and ability to estimate the robot's (angular) acceleration, jerk, orhigher-order dynamic states with low delay. Mathematical analysis withnumerical simulations are presented to show the properties of the statisticalmodel-based estimation framework and to reveal its connection to existinglow-pass filters. Furthermore, a new paradigm is developed for robotsobservability analysis by developing Lie derivatives and associated partialdifferentiation directly on manifolds. It is shown that this new paradigm ismuch simpler and more natural than existing methods based on quaternionparameterizations. It is also scalable to high dimensional systems. A novel\textbf{\textit{thin}} set concept is introduced to characterize theunobservable subset of the system states, providing the theoretical foundationto observability analysis of robotic systems operating on manifolds and in highdimension. Finally, extensive experiments including full state estimation andextrinsic calibration (both POS-IMU and IMU-IMU) on a quadrotor UAV, a handheldplatform and a ground vehicle are conducted. Comparisons with existing methodsshow that the proposed method can effectively estimate all extrinsicparameters, the robot's translation/angular acceleration and other statevariables (e.g., position, velocity, attitude) of high accuracy and low delay.

Robots State Estimation and Observability Analysis Based on Statistical Motion Models