Yuanxin Wu — Page 3

arXiv2012

Velocity/Position Integration Formula (II): Application to Inertial Navigation Computation

Inertial navigation applications are usually referenced to a rotating frame. Consideration of the navigation reference frame rotation in the inertial navigation algorithm design is an important but so far less seriously treated issue, especially for ultra-high-speed flying aircraft or the future ultra-precision navigation system of several meters per hour. This paper proposes a rigorous approach to tackle the issue of navigation frame rotation in velocity/position computation by use of the newly-devised velocity/position integration formulae in the Part I companion paper. The two integration formulae set a well-founded cornerstone for the velocity/position algorithms design that makes the comprehension of the inertial navigation computation principle more accessible to practitioners, and different approximations to the integrals involved will give birth to various velocity/position update algorithms. Two-sample velocity and position algorithms are derived to exemplify the design process. In the context of level-flight airplane examples, the derived algorithm is analytically and numerically compared to the typical algorithms existing in the literature. The results throw light on the problems in existing algorithms and the potential benefits of the derived algorithm.

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arXiv2011

On Position Translation Vector

The paper derives a new "position translation vector" (PTV) with remarkably simpler rate equation, and proves its connections with Savage's PTV.

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arXiv2011

Observability of Strapdown INS Alignment: A Global Perspective

Alignment of the strapdown inertial navigation system (INS) has strong nonlinearity, even worse when maneuvers, e.g., tumbling techniques, are employed to improve the alignment. There is no general rule to attack the observability of a nonlinear system, so most previous works addressed the observability of the corresponding linearized system by implicitly assuming that the original nonlinear system and the linearized one have identical observability characteristics. Strapdown INS alignment is a nonlinear system that has its own characteristics. Using the inherent properties of strapdown INS, e.g., the attitude evolution on the SO(3) manifold, we start from the basic definition and develop a global and constructive approach to investigate the observability of strapdown INS static and tumbling alignment, highlighting the effects of the attitude maneuver on observability. We prove that strapdown INS alignment, considering the unknown constant sensor biases, will be completely observable if the strapdown INS is rotated successively about two different axes and will be nearly observable for finite known unobservable states (no more than two) if it is rotated about a single axis. Observability from a global perspective provides us with insights into and a clearer picture of the problem, shedding light on previous theoretical results on strapdown INS alignment that were not comprehensive or consistent.. The reporting of inconsistencies calls for a review of all linearization-based observability studies in the vast literature. Extensive simulations with constructed ideal observers and an extended Kalman filter are carried out, and the numerical results accord with the analysis. The conclusions can also assist in designing the optimal tumbling strategy and the appropriate state observer in practice to maximize the alignment performance.

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