Coning Algorithm Design by Explicit Frequency Shaping

Abstract

A new optimum approach is presented for strapdown coning algorithm design based on Explicit matching of desired response to expected coning input magnitude as a function of coning frequency. Unlike previous time or frequency Taylor series expansion techniques, the new method achieves optimization through minimum least-squares estimation over a user selected design frequency range. The error being minimized is the square of the weighted algorithm error, the weighting factor being user specified coning amplitude over frequency. This methodology allows the coning algorithm coefficients to be independently designed for each coning axis to achieve optimal balanced performance over the frequency range of expected coning inputs. Performance of the new algorithm design technique is evaluated by comparison with previous time and frequency-series approaches, in discrete and stochastic coning environments, and over a time based extreme dynamic maneuvering profile. A generalized method is presented for translating system performance requirements into expected coning amplitude versus frequency profiles for calculating Explicit algorithm coefficients, and for evaluating coning algorithm accuracy. The paper includes derivations of generalized formulas for calculating algorithm coefficients for previous time and frequency-series design approaches.