Adaptive extended Kalman filter and point ahead angle prediction in the detection of gravitational waves in space

In the detection of gravitational waves in space, during the science phase of the mission, the point ahead angle mechanism (PAAM) serves to steer a laser beam to compensate for the angle generated by the relative motion of the two spacecrafts (SCs) during the approximately 10 seconds of flight time a laser beam will take from one SC to reach a distant SC of three million kilometers away. The common practice for pointing stability control of a laser beam is to first do a coarse tracking by the PAAM to steer a laser beam to compensate for the relative motion between two SCs and to be followed by a fine pointing stability control. In the present work, by exploiting the near-circular orbit structure of an individual SC in the triangular constellation, the feasibility of inserting an adaptive extended Kalman filter (AEKF) into the PAAM control loop is investigated. By adopting a colored measurement noise model that closely resembles the prospective on an orbit situation, numerical simulation suggests that the dynamic range of the PAAM may be reduced to the level of nanoradians using the prediction of the pointing head angle by the AEKF. This will cut down on the tilt-to-length (TTL) coupling noise and the position noise budget allocated to the PAAM. This in turn reduces the dynamic range of the fine pointing control and leaves room to improve its accuracy, thereby offering the prospect of reduction of the position noise budget allocated to the laser pointing instability as a whole.