Duality of Optimal Strapdown Sculling and Coning Compensation Algorithms

Abstract

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.

Equivalency Between Strapdown Inertial Navigation Coning and Sculling Integrals/Algorithms

“…From the preceding de nitions for ® l , À l , ® l ¡ 1 , À l ¡ 1 , 1® l , and 1À l [.® l £ À l / ¡ .® l ¡ 1 £ À l ¡ 1 /] is derived in Ref. 6 [Eqs. (7) and (21) with the Table 1, algorithm 2 coef cients] and is identical to Eq.…”

“…In Ref. 6 Ignagni derives a class of optimized sculling algorithms for the composite sculling/velocity rotation compensation integral and demonstrates a duality between the derived class of sculling algorithms and a previously derived class of coning algorithms. In addition, Ref.…”

Two New Classes of Strapdown Navigation Algorithms

“…(6)] for the reason that the algorithms for the position increments [Eq. The algorithms for the constant-signal models are presented as well.…”

Optimal two-iteration sculling compensation mathematical framework for SINS velocity updating

“…Savage [16] provided a rigorous comprehensive approach to the design of the principal software velocity and position algorithms Manuscript utilized in modern-day SINS. Ignagni [17] and Roscoe [18] developed generic equivalency and duality between strapdown inertial navigation coning and sculling integrals and algorithms respectively. The duality employs the previously coning algorithm to be converted to the sculling algorithm using the approximate mathematical formula.…”