Velocity/Position Integration Formula (I): Application to In-flight Coarse Alignment (1207.1550v1)

Abstract: The in-flight alignment is a critical stage for airborne INS/GPS applications. The alignment task is usually carried out by the Kalman filtering technique that necessitates a good initial attitude to obtain satisfying performance. Due to the airborne dynamics, the in-flight alignment is much difficult than alignment on the ground. This paper proposes an optimization-based coarse alignment approach using GPS position/velocity as input, founded on the newly-derived velocity/position integration formulae. 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 one degree accuracy in ten seconds. 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 paper proposes a novel optimization method using velocity/position integration formulae to achieve rapid, reliable in-flight coarse alignment for airborne INS/GPS.
• Validation through simulation and flight tests demonstrated the method's rapid convergence and high accuracy, with IFA-VIF achieving heading within one degree in ten seconds.
• This approach enhances reliable in-flight alignment for aviation applications and shows potential for use with lower-grade sensors, expanding its applicability.

An Expert Analysis of "Velocity/Position Integration Formula (I): Application to In-flight Coarse Alignment"

The paper authored by Yuanxin Wu and Xianfei Pan presents a novel optimization-based approach to in-flight coarse alignment for airborne INS/GPS systems. The proposed method leverages newly-developed velocity and position integration formulae to achieve rapid, reliable initial attitude determination without prior attitude information. This capability is critical for improving the alignment performance of Strapdown Inertial Navigation Systems (SINS) used in dynamic airborne environments where traditional approaches fail due to increased difficulty compared to static conditions.

Methodological Framework

The alignment process in inertial navigation systems typically involves two stages: coarse and fine alignment. The coarse alignment stage crucially provides an initial estimate of the system's attitude, which is subsequently refined using Kalman filtering in the fine alignment stage. The authors of this paper address the challenges inherent in coarse alignment for in-flight scenarios by deriving and implementing velocity/position integration formulae. These formulae mathematically relate the collected GPS velocity and position data to the SINS body frame's attitude matrix, thereby circumventing the need for velocity rate data and enhancing robustness against sensor noise.

Detailed Examination of Integration Formulas

The paper introduces two distinct integration formulas: the velocity integration formula and the position integration formula. These formulas are derived from the navigation rate equations and are employed in recursive discrete algorithms designed for in-flight alignment. The velocity integration formula integrates GPS velocity data, while the position integration formula enhances this by also considering GPS-derived position data.

The rigorous derivation of these formulas provides a robust mathematical foundation for addressing in-flight alignment challenges. Notably, the optimization-based approach adopted by the authors involves expressing the initial attitude matrix in terms of unit attitude quaternions. This method effectively transforms the alignment problem into a continuous attitude determination problem, which is theoretically robust and computationally feasible.

Simulation and Empirical Validation

The authors have validated their approach through a series of simulations alongside real-world flight tests. In simulations involving large motions, the proposed algorithms demonstrated significant accuracy. For instance, the simulation results indicated that the In-flight Algorithm derived from the Velocity Integration Formula (IFA-VIF) achieves rapid convergence, bringing alignment angle errors to minimal levels within the initial 300 seconds of motion.

Further validation is provided through flight tests conducted aboard a Cessna 208 aircraft. These tests were designed to emulate operational conditions and included large maneuvers to test the robustness of the alignment algorithms. The data show that the IFA-VIF yields more accurate attitude estimations than the In-flight Algorithm derived from the Position Integration Formula (IFA-PIF) when quirks such as GPS lever arm effect are considered. IFA-VIF consistently demonstrated accuracy within one degree for heading alignment in as little as ten seconds, significantly outperforming existing methods.

Practical Implications and Future Directions

The proposed methodology and its successful validation have notable implications for both theoretical and practical aspects of inertial navigation systems. The use of velocity/position integration formulas enhances the potential for reliable in-flight alignment, which is critical for various military and civilian aviation applications where rapid, accurate navigation data is indispensable.

The authors suggest that future work should focus on further refining these algorithms to address sensor biases and to accommodate lower-grade sensors, potentially expanding the applicability of this approach to consumer-level devices. This expansion could broaden the scope of potential use cases in navigation and increase the resilience of SINS operations in various dynamic conditions.

Through a detailed mathematical exploration and empirical validation, this paper contributes a substantial advancement in the optimization-based alignment methods for airborne INS/GPS systems, offering a systematic way to enhance accuracy and efficiency in dynamic navigation environments.