Performance evaluation of a central difference Kalman filter applied to attitude determination

The attitude determination system is an important subsystem for most satellite missions. Attitude estimation is often performed using Kalman filters. In particular, for nanosatellites or CubeSats missions, a compromise between precision in the results and low computational load must be achieved, due to design constraints, such as reduced size and cost. In this work, it is proposed to evaluate the performance in attitude determination of a central difference Kalman filter, and compared to an extended Kalman filter. The application of the Kalman filter in non-linear problems requires the calculation of partial derivatives matrices (Jacobian matrices) of the dynamics or measurements, originating the extended version of the filter. In some cases, this calculation may be analytically impossible, complex, or even very computationally expensive. The central difference filter formulation uses a polynomial interpolation to avoid computing these Jacobian matrices. The same set of simulated data was applied to both extended and central difference filters, and the results were compared to the true values given by the simulation. The data were simulated considering a CubeSat 3U equipped with gyroscopes, magnetometers, and sun sensor, and the attitude was parametrized by quaternions. The values estimated by the filters are attitude quaternions and gyroscope deviations (bias). Performance was analyzed in terms of quaternion and gyroscope bias errors, and computational load. Finally, the analysis shows the comparative advantages and disadvantages of the central difference filter to the extended Kalman filter and the unscented Kalman filter.