Ranging Processing and Clock Synchronization
LISA will use pseudo-random noise (PRN) code methods to obtain a measure of the absolute distance between the spacecraft.
In LISA, we measure variations in the distance between the spacecraft with picometer precision. Yet, the absolute distance between the spacecraft is not a natural signal in a laser interferometer such as LISA. However, the absolute distance between the spacecraft needs to be known to meter precision, otherwise time-delay interferometry would not sufficiently suppress laser frequency noise. Therefore, a pseudo-random noise (PRN) code generated according to the local clock is imprinted onto the laser beams in form of a weak phase modulation. Interference of the received laser beam from the distant spacecraft with the local laser beam involves a comparison of the local PRN-code with the PRN-code received from the distant spacecraft. Please note: the received and local PRN-codes are identical, they just appear shifted because they are generated according to different clocks and at different events, as illustrated in the picture below. Hence, this comparison yields a measurement of what we call the pseudo-range: the time shown by the receiving spacecraft clock at the event of reception minus the time shown by the emitting spacecraft clock at the event of emission. Basically, this pseudo-range is a combination of the distance between the spacecraft and the offset between the two clocks. We call it pseudo-range, because it contains not just the distance (range) but also the clock offset.
In order to synchronize the clocks and to estimate the distance between the spacecraft for TDI, we are developing algorithms to disentangle the pseudo-ranges into ranges and clock offsets. We have built a Kalman-like filter that achieves the inter-spacecraft clock synchronization to nanosecond level and the estimation of the inter-spacecraft distances to meter precision by processing the pseudo-ranges together with tracking data from the ESA ground stations.
In the future, we aim to refine the underlying noise models of the Kalman filter and to study alternative Kalman filter designs in order to improve our clock synchronization and ranging performance. Furthermore, we will work on further increasing the ranging precision by combining time delay interferometric ranging with PRN-ranging
