26 May 1995 Determination of 3D angular rates using two-axis measurements
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This paper describes a new observer design method that allows for estimating the angular rates along a vehicle's three principal axes. This method uses measurements from a single two-axis angular rate sensor (gyro) and determines the rates for the third axis by using a nonlinear observer. Unlike conventional approaches where the equations governing vehicle motion (Euler's equations) are linearized and then an observer is constructed based on the linear model, this method does not require linearization of the system. Instead, a pseudo-linear representation is used. The pseudo-linear model is obtained by systematically decomposing a nonlinear system into linear and nonlinear terms. The nonlinear components are then redefined as an auxiliary set of state variables and/or inputs. This leads to an augmented linear system representation that is mathematically equivalent to the original nonlinear system. This method allows standard linear observer design techniques to be applied, and it develops observers that are capable of estimating the third-axis angular rates using measurements corresponding to the other two axes. The method's effectiveness is illustrated with an example. The case studied is the complete attitude rate determination and control of a spinning spacecraft. Computer simulation results show that the new approach provides excellent three-axis attitude control, yet requires angular rate sensors for only two axes.
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Marcelo C. Algrain, Marcelo C. Algrain, } "Determination of 3D angular rates using two-axis measurements", Proc. SPIE 2468, Acquisition, Tracking, and Pointing IX, (26 May 1995); doi: 10.1117/12.210436; https://doi.org/10.1117/12.210436


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