This paper proposes a numerical-integration perspective on the Gaussian filters. A Gaussian filter is approximation of the Bayesian inference with the Gaussian posterior probability density assumption being valid. There exists a variation of Gaussian filters in the literature that derived themselves from very different backgrounds. From the numerical-integration viewpoint, various versions of Gaussian filters are only distinctive from each other in their specific treatments of approximating the multiple statistical integrations. A common base is provided for the first time to analyze and compare Gaussian filters with respect to accuracy, efficiency and stability factor. This study is expected to facilitate the selection of appropriate Gaussian filters in practice and to help design more efficient filters by employing better numerical integration methods

The in-flight alignment is a critical stage for airborne inertial navigation system/Global Positioning System (INS/GPS) applications. The alignment task is usually carried out by the Kalman filtering technique that necessitates a good initial attitude to obtain a satisfying performance. Due to the airborne dynamics, the in-flight alignment is much more difficult than the alignment on the ground. An optimization-based coarse alignment approach that uses GPS position/velocity as input, founded on the newly-derived velocity/position integration formulae is proposed. Simulation and flight test results show that, with the GPS lever arm well handled, it is potentially able to yield the initial heading up to 1 deg accuracy in 10 s. It can serve as a nice coarse in-flight alignment without any prior attitude information for the subsequent fine Kalman alignment. The approach can also be applied to other applications that require aligning the INS on the run.

The design of strapdown inertial navigation system (INS) algorithms based on dual quaternions is addressed. Dual quaternion is a most concise and efficient mathematical tool to represent rotation and translation simultaneously, i.e., the general displacement of a rigid body. The principle of strapdown inertial navigation is represented using the tool of dual quaternion. It is shown that the principle can be expressed by three continuous kinematic equations in dual quaternion. These equations take the same form as the attitude quaternion rate equation. Subsequently, one new numerical integration algorithm is structured to solve the three kinematic equations, utilizing the traditional two-speed approach originally developed in attitude integration. The duality between the coning and sculling corrections, raised in the recent literature, can be essentially explained by splitting the new algorithm into the corresponding rotational and translational parts. The superiority of the new algorithm over conventional ones in accuracy is analytically derived. A variety of simulations are carried out to support the analytic results. The numerical results agree well with the analyses. The new algorithm turns out to be a better choice than any conventional algorithm for high-precision navigation systems and high-maneuver applications. Several guidelines in choosing a suitable navigation algorithm are also provided.

In this paper, we propose a novel visual-inertial odometry (VIO) approach that adopts structural regularity in man-made environments. Instead of using Manhattan world assumption, we use Atlanta world model to describe such regularity. An Atlanta world is a world that contains multiple local Manhattan worlds with different heading directions. Each local Manhattan world is detected on the fly, and their headings are gradually refined by the state estimator when new observations are received. With full exploration of structural lines that aligned with each local Manhattan worlds, our VIO method becomes more accurate and robust, as well as more flexible to different kinds of complex man-made environments. Through benchmark tests and real-world tests, the results show that the proposed approach outperforms existing visual-inertial systems in large-scale man-made environments.

Observability is an important aspect of the state-estimation problem in the integration of the inertial navigation system (INS) and the Global Positioning System (GPS) as it determines the existence and nature of solutions. In most previous research, conservative observability concepts, e.g., local observability and linear observability, have extensively been used to locally characterize the estimability properties. In this paper, a novel approach that directly starts from the basic observability definition is used to investigate the global observability of the nonlinear INS/GPS system with consideration of the lever arm uncertainty. A sufficient condition for the global observability of the system is presented. Covariance simulations with an extended Kalman filter (EKF) and a field test are performed to confirm the theoretical results. The global observability analysis approach is not only straightforward and comprehensive but also provides us with new insights that were unreachable by conventional methods.