Approach to Recovering Maneuver Accuracy in Classical Coning Algorithms

Abstract

Nomenclature C s = coefficient of compressed coning correction algorithm c k r = combination, k elements selected from a set of r elements without regard to the order of selection f 3 ; f 4 ; : : : = coefficients in the derivatives of δφ unc t m = computer interval index, as subscript indicates parameter value at computer cycle m N = total number of samples used in the coning calculation n = number of samples in current iteration time interval o = an equivalent infinitesimal to ( ) r = order of derivatives s = index of coefficients for compressed coning algorithm T k = sampling time interval t = time α, α = integral of ω over t m−1 ; t time interval and its magnitude β = normalized coning frequency Δα N1−i , Δα N1−j = gyro data samples spaced backward in time from time t δϕ c t = coning integral over the time interval from t m−1 to t δφ cmp t = compressed coning correction algorithm δφ cmpf t = compressed frequency-series coning algorithm δφ unc t = uncompressed coning correction algorithm δφ uncE t = uncompressed Explicit coning algorithm δφ uncE3 t; δφ uncE4 t; : : := uncompressed Explicit coning algorithms taking three, four, and five samples of gyro data per update δφ uncf t = uncompressed frequency-seriesbased coning algorithm δφ uncf3 t; δφ uncf4 t; : : := uncompressed frequency-series coning correction algorithms taking three, four, and five samples of gyro data per update ς ij = coefficients of uncompressed frequency-series coning algorithms _ ΦΩ, _ Φ Eval Ω = coning rate amplitude Ω = coning frequency ω = angular rate vector _ ω, ω, ω first-, second-, third-, fourth-, fifth-, and sixth-order derivatives of ω × = skew symmetric cross-product matrix form of vector ( ) that indicates × ×

High-order attitude compensation in coning and rotation coexisting environment

“…Miller's and Ignagni's results were achieved by using Taylor series expansions in powers of coning frequency [2][3][4]. Such frequency series-based methods were discussed in [5,6,8]. Savage [7] presented an approach that was called the explicit frequency shaping for the coning algorithm design, with coefficients designed by using least-squares error minimization rather than the frequency series expansion to achieve optimal coning performance.…”

“…In the case of a small rotation angle, the triple-cross-product term is ignored due to its limited influence. As a result, various algorithms have been designed and optimized to improve the accuracy of the coning correction term [1][2][3][4][5][6][7][8]. Miller [2] introduced the concept of optimizing the coning compensation algorithms in a pure coning environment.…”

“…In 2013, an approach was proposed for the analysis of the coning algorithms under highly dynamic environments, which include pure coning and maneuvering environments [8]. In this approach, the eighth-order Taylor series about time was calculated for the continuous coning integral as the base of error analysis and optimization for coning algorithms.…”

A Real-Time Structure of Attitude Algorithm for High Dynamic Bodies

“…Moreover, the larger the amount of subsamples is, the smaller the drifting error is. Several drifting errors for different algorithms of conventional structure are provided in Table 1 [12,19,20].…”

“…These algorithms calculate several angular increments at a higher frequency and then compress them as one value in a relative lower frequency. Considering the maneuver situation of flight vehicles, the performance of coning correction of attitude algorithms under pure coning environment is examined to verify the validity [12,13]. A cone algorithm uses a cone frame and cone attitude to describe the coning movement of high dynamic bodies and restrains the coning error by environment disturbance [14].…”