Attitude Determination and Calibration using a Recursive Maximum Likelihood-Based Adaptive Kalman Filter

Kalman filter technniques are widely used in the areas of attitude and orbit determination, prediction and calibration. These techniques work well if the system dynamics are well-defined. Problems arise, however, when the system parameters are unknown ahead of time or changing over time. This paper discusses an adaptive Kalman filter design that utilizes recursive maximum likelihood parameter identification. At the center of this design is the Kalman filter itself, which has the responsibility for attitude determination. At the same time, however, the identification algorithm is continually identifying the system parameters. The approach is applicable to nonlinear as well as linear systems. This adaptive Kalman filter design has much potential for real-time implementation, especially considering the fast clock speeds, cache memory and internal RAM available today. The recursive maximum likelihood (RML) identification algorithm is discussed in detail, with special attention directed towards its unique matrix formulation. Next, the procedure for using the algorithm is described along with comments on how this algorithm interacts with the Kalman filter. Finally, a spacecraft attitude determination/calibration example is provided. In the development of the dynamics for this example, the angular velocity of one of the axis is assumed to be constant. In the simulation, however, this velocity varies slowly. The RML identifier is used to continually identify this changing velocity. This AKF-RML method may be used to identify multiple parameters such as sensor biases or external torques. *Hughes Aircraft Company, Aurora, Colorado tMechanica! and Aerospace Department, North Carolina State University