Various algorithms are examined for integrating the noncommutivity rate equation that is the basis for the coning correction applied in strapdown inertial reference systems. A concept for improving the computational accuracy and efficiency of strapdown coning correction algorithms is described and applied to the development of six new algorithms, each possessing optimal accuracy characteristics and leading to minimum computational throughput requirements. The accuracies of the six new algorithms are compared to those associated with four previously known algorithms in both pure coning and benign angular rate environments. It is shown that, for all algorithms, the error incurred in a benign environment is negligibly small, even for very severe maneuvers, and that algorithm optimization based strictly on a consideration of its accuracy characteristics in a pure coning environment is justified. An algorithm simplification concept employed that is similarly based solely on the properties of the algorithm in a pure coning environment is also shown to be justified.

Efficient Class of Optimized Coning Compensation Algorithms

Three improved algorithms for strapdown attitude computation utilizing accumulated gyro increments from the previous and current update are developed and evaluated analytically under classical coning motion. The error criterion of Miller is derived directly from the rotation vector concept. The accuracy of updating rotation vector estimation can be improved at least two orders of magnitude as compared with those of conventional algorithms. The proposed algorithm is equivalent to increasing the number of gyro samples used in the conventional method and it requires less computer loading. >

https://ir.nctu.edu.tw:443/bitstream/11536/3470/1/A1992JC43100017.pdf

Improved strapdown coning algorithms

With the development of high-accuracy inertial navigation system inertial sensors, such as ring laser gyroscopes and atomic spin gyroscopes, it is increasingly important to improve the strapdown inertial navigation algorithms to match such high-accuracy inertial sensors. For example, the existing inertial navigation algorithms have not taken into account the triple-cross-product term of noncommutativity error. However, theoretical analysis demonstrates that the ignored triple-cross-product term is nonignorable under coning motion with constant angular rate precession environments. In this paper, a new high-accuracy rotation vector algorithm is proposed for strapdown inertial navigation. The Taylor series about time is used for error analysis and optimization of the new algorithm. General maneuvers and coning motion with constant angular rate precession environments are considered in establishing the coefficient equations in the proposed algorithm. Error drift equations are given after the error compensation. Normalized quaternion under coning motion with constant angular rate precession environments and Savage’s severe integrated angular-rate profiles are used to numerically verify the new algorithm. The results indicate that the new high-order attitude updating algorithm can improve inertial navigation accuracy.

High-order attitude compensation in coning and rotation coexisting environment

This paper addresses the design of optimal algorithms for the sculling compensation applied in strapdown inertial systems A class of optimized algorithms for the sculling compensation is derived and evaluated for three dynamic environments: a pure sculling environment, a benign environment, and a generalized vibrational environment The resultant class of optimized sculling algorithms is shown to manifest an interesting duality property when compared with a class of optimized coning compensation algorithms previously derived, in both algorithm structure and the algorithm errors incurred in the three dynamic environments considered

Duality of Optimal Strapdown Sculling and Coning Compensation Algorithms

As shown in Fig. 6, for 3⁄4 D 0:3 and low damping (3model 1, but this will cause the second amplitude A2 to be negativeand we were interested in positive amplitude shapers [see Eq. (2)]. This suggests that, when uncertaintiesare very large (and 3model is small), the best designs or more appropriate designs are those obtained by taking convex combinations of ZVDD and 2-hump EI shapers.

Formalized Approach to Obtaining Optimal Coefficients for Coning Algorithms

In this paper, we have expanded an application of the rotation vector concept to develop an efficient attitude algorithm for a strapdown system under a coning base motion. The proposed algorithm takes four samples of gyroscope data per update. A rotation vector error analysis for a coning motion has been employed to come up with an optimum four-sample algorithm. Also presented is an efficient way to implement the algorithm in a real-time environment. The algorithm is formulated in a recursive form using two time-rate executions and using only integer arithmetic. To compare the performance of the proposed algorithm with an already existing threesample algorithm, a simulation has been performed by varying coning motion frequency and update rate. Results Show that the four-sample algorithm outperforms the three-sample algorithm in case of high-frequency coning motion. The use of the four-sample algorithm is economical since it requires less computing time for an equal accuracy.

Jang G. Lee

Papers

Extension of strapdown attitude algorithm for high-frequency base motion