# Composite clock

Both on-board the navigation satellites and within the monitoring stations atomic clocks realize the time of the system. The accuracy of such atomic clocks differs by their types. E.g. the time deviation of a typical satellite clock (LINK1) is statistically around a few nanoseconds after 1 day, which results multiplied by the speed of light in a length error of meters. Therefore it is required to measure the time offsets of the atomic clocks to the system time and to provide the capability to correct them.

Composite clock states such a method and computes the offset of the atomic clocks to the system time whose time offset is understandable as a weighted average out of the time offsets of the atomic clocks. A different principle is called master clock. A particular atomic clock defines the time of the system and the time offset of the remaining ones is determined. The composite clock has got two important advantages against the master clock. By using an average the statistical properties of the system time improves. E.g. assuming identical weights of N clocks the statistical properties scale by a factor of . A second advantage concerns its robustness. The system time is not dependent on a single clock, which means, that the loss of a clock is compensated by the remaining ones. This is not the case if the master clock fails which results in a immediate loss of the system time having no counter procedures available.

 Figure1: Detection of step (case 2) results in shorter initial time compared to case 1

Different algorithms are available to establish a composite clock. For instance, GPS (LINK2)  operates a Kalman filter. The offsets of the atomic clocks are modelled by a three state stochastical process which is the solution of a linear stochastically differential equation with White Gaussian noise. The Kalman filter processes the measurements of the atomic clocks and calculates estimates of the atomic clocks.

Key aspects are the investigation of operational properties of composite clocks and new algorithms to calculate them. Figure 1 exemplary shows the impact of a frequeny step of size 1E-11 on the Kalman filter estimation of a clock signal with ID 3. Case 1 represents the result without any modification. The Kalman filter requires an initial time of around one day after the step and does not deliver accurate estimates. Case 2 modifies the algorithm by two steps. At first, a detector algorithm is available which recognizes the frequency step and secondly, an adaption of the covariance is triggered. The modifications result in a distinctly shorter initial time and there are right estimates available.

Contact
 Matthias SüßGerman Aerospace CenterInstitute of Communications and Navigation, Navigation Tel: +49 8153 28-3178 Fax: +49 8153 28-2328E-Mail: matthias.suess@dlr.de