Discrete-time nonlinear observer design for reproducing angular rates along the third-axis of a spinning spacecraft using only two-axis measurements

This paper describes a new observer design method that allows us to estimate the angular rates along a vehicle's three principal axes. The method uses measurements from a single two-axis angular rate sensor (gyro) and determines the rates along the third axis by using a discrete-time 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 the 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 us to use standard linear observer design techniques, and develop observers that are capable of estimating the third-axis angular rates using measurements corresponding to the other two axes. The effectiveness of this approach is illustrated with an example. The case studied is the 3-axis attitude rate determination and control of a spinning spacecraft. Computer simulation results show that this new approach provides excellent three-axis attitude control, yet requires angular rate sensors for only two axes.