Optical navigation: comparison of the extended Kalman filter and the unscented Kalman filter

Small satellites are becoming increasingly appealing as technology advances and shrinks in both size and cost. The development time for a small satellite is also much less compared to a large satellite. For small satellites to be successful, the navigation systems must be accurate and very often they must be autonomous. For lunar navigation, contact with a ground station is not always available and the system needs to be robust.

The extended Kalman filter is a nonlinear estimator that has been used on-board spacecraft for decades. The filter requires linear approximations of the state and measurement models. In the past few years, the unscented Kalman filter has become popular and has been shown to reduce estimation errors. Additionally, the Jacobian matrices do not need to be derived in the unscented Kalman filter implementation. The intent of this research is to explore the capabilities of the extended Kalman filter and the unscented Kalman filter for use as a navigation algorithm on small satellites.

The filters are applied to a satellite orbiting the Moon equipped with an inertial measurement unit, a sun sensor, a star camera, and a GPS-like sensor. The position, velocity, and attitude of the spacecraft are estimated along with sensor biases for the IMU accelerometer, IMU gyroscope, sun sensor and star camera. The estimation errors are compared for the extended Kalman filter and the unscented Kalman filter for the position, velocity and attitude.

The analysis confirms that both navigation algorithms provided accurate position, velocity and attitude. The IMU gyroscope bias was observable for both filters while only the IMU accelerometer bias was observable with the extended Kalman filter. The sun sensor biases and the star camera biases were unobservable. In general, the unscented Kalman filter performed better than the extended Kalman filter in providing position, velocity, and attitude estimates but requires more computation time.