1 MOTIVATION: CLOCKS AND NAVIGATION

1. Optical Clocks in Future Global Navigation Satellites U. Hugentobler (1), M. Plattner (2), D. Voithenleitner (1), M. Heinze (1), V. Klein (2) and S. Bedrich (2) (1)Technische Universität München, Arcisstrasse 21, 80333 Munich, Germany, Email: urs.hugentobler@bv.tum.de (2)Kayser-Threde GmbH, Wolfratshauser Strasse 48, 81379 Munich, Germany, Email: markus.plattner@kayser-threde.com 1 MOTIVATION: CLOCKS AND NAVIGATION 4STABLE CLOCKS FOR PRECISE ORBIT DETERMINATION Highly stable clocks such as optical frequency generators can support precise orbit determination. In order to investigate the potential, e.g., for the system operator, simulations were performed involving a Galileo constellation of 27 satellites tracked by eight or by five globally distributed stations (s. Fig. 4,5). A different a priori radiation pressure model and more sophisticated troposphere modelling was applied to simulate the observations than for the later analysis. Pseudorange and carrier phase observations were simulated for E1 and E5a with measurement noise of 20cm and 2 mm (1 sigma) respectively. The primary payload of a navigation satellite is its clock. Navigation and positioning performance depends on high precision time measurements and on the quality of the frequency generator. In order to reach the highest accuracy for positions, all involved clocks (satellite and receiver) need to be synchronised for each measurement epoch. Today, only relative positions are obtained at cm-level and to retrieve absolute positions known coordinates for reference sites are needed. Satellite clocks that are stable enough in order to synchronize them at the level of a few picoseconds for hours or days would fundamentally change this picture. Optical clock technology would allow such accuracy and long term frequency stability. With further progress of clock technology a future GNSS system could be equipped with such optical clocks, thus installing clocks of utmost stability in space. A large variety of applications can be envisaged: Such a scenario would enable the absolute positioning at highest accuracy in real time without requiring ad- ditional servicing installations. This would be very helpful e.g. for a tsunami warning system with remote sensors. Similarly precise orbit determination will profit from the increased stability of the observation system (s. 4). If no or only few satellite clock parameters need to be estimated in the orbit determination process, an improvement of the radial orbit error can be expected. The advantages of highly stable satellite clocks can only be materialized if error sources, e.g., in propagation delays or satellite orbits are controlled at a precision similar to the clock stability. Furthermore, relativistic clock corrections have to be modelled at a higher level of accuracy than today. In order to investigate the effects of such a scenario with optical clocks, the project ‚OCTAGON‘ (Optical Clock Technologies and their Applications for Globally Optimized Navigation) was initiated by the partners TU Munich – Research Institution of Satellite Geodesy and Kayser-Threde GmbH. The used software is the Bernese GNSS Software, V5.0. Fig. 4,5: Depth-of-Coverage for the simulated eight stations network (left) and for a five stations network (right), adopting an elevation mask of 10°: Number of stations seen from any satellite location. Realistic clock performances were used for rubidium frequency standards, hydrogen masers, and optical clocks to simulate clock offset time series for satellites and ground stations. In a first run the ionosphere-free linear combination of the simulated observations were used to estimate orbit parameters, differential code biases for receivers and spacecraft as well as epoch-wise receiver and satellite clocks corrections. 2OPTICAL CLOCKS Contrary to microwave clocks, where an atomic transition in the microwave range is excited, optical clocks are based on an atomic transitions in the optical range. Using optical frequencies as clock oscillator can yield higher accuracy since the ticks of the clock have much shorter timing intervals. A typical block diagram of an optical atomic clock is shown in Fig 1. Optical clock technology in principle can be divided into two main implementations: single ion or optical lattice clocks. Single ion clocks use a magneto-electrical trap like a Paul trap in order to confine a charged atom locally. Optical lattice clocks require an additional laser for generating an optical lattice wherein a bunch of neutral atoms is trapped. Although single ion clocks benefit from their simpler and more mature setup, lattice clocks potentially will yield a higher stability. This is due to the fact that in a lattice clock a high amount of atoms is used and thereby a high signal to noise ratio is achieved by averaging. An ultra stable clock laser is used to probe the transition of the ion or neutral atoms. Laser excitation of the reference atom is measured by a photo detector. A feedback electronic automatically tunes the laser frequency in order to maximize the excitation probability. The laser frequency is then “down-converted” to radio frequency signals with an optical frequency comb. Within the OCTAGON project we are estimating the achievable performance benefits for navigation satellites with different optical clocks. These results will then be compared to the technical effort which is necessary to space qualify the different optical clock technologies. Fig. 6,7: Modified Allan deviations for different types of simulated space or ground clocks (left) and the corresponding time series of clock corrections (right). The optical clock characteristics adopted in the simulation corresponds to the Optical EGE. The estimated clock corrections in Fig. 8 (top) show a periodic variation with an amplitude of about 0.5 ns and a period corresponding to the orbital period. Evidently, radial orbit errors are absorbed by the space clock parameters. In fact, the red curve in Fig. 8 (bottom) shows the radial displacement of the orbit with respect to the true orbit. The green curve in the same figure shows the radial orbit errors obtained when in a second run all clock values were fixed on their nominal values and optical clocks are used. Obviously the radial orbit error that is caused by uncertainty in estimation of orbit parameters is no longer present. Fig. 9 (top) shows the epoch-wise clock corrections for different types of space clocks. A once-per-revolution signal indicating absorption of radial orbit errors can be found for optical clocks and for passive space hydrogen masers. A degradation of the orbit has to be expected for rubidium frequency standards (blue curve). The radial orbit errors for the 27 simulated satellites for the 5-stations-solution are shown in Fig. 9 (bottom). Radial orbit errors reach several meters when clock values are estimated epoch-wise (red curves) and are well below 1 m if nominal clock values are kept fixed and optical clocks are used. Fig. 1: Block diagram of an optical clock. The main components are clock laser, atom or ion trap and feedback electronic for closed loop control of the laser frequency. The frequency comb is used for transforming optical to microwave frequencies. 3 SIMULATION OF TIME SERIES Electromagnetic signals are represented by power-law noise processes. The ‚Discrete Simulation of Power Law Noises‘ [Kasdin N.J, Walter T. 1992] presents an algorithm for simulating different atomic clock signals. This is done based on the spectral density of a noise process in the frequency domain which is transformed to the time domain. The result is a time series (s. Fig. 2) of defined length, sampling interval, noise type and scaling. Noise types are characterized by the linear slopes of the frequency stability of the clock oscillator (s. Fig. 3) and the scaling at the beginning of the averaging time of the Allan deviation. Usually, the stability of a specific type of atomic clock is governed by two or three noise processes. The signals simulated for this paper are shown in Fig. 6,7. The optical clock frequency responses are adopted from the project ‚Einstein Gravity Explorer (EGE)‘ [Schiller et al., 2009] which defines expected and desired future optical frequency stability figures for scientific space applications. Fig. 9: Epoch wise clock corrections for different frequency standards (top) and radial orbit errors (bottom) for 27 satellites for a sparse tracking network and estimating epoch-wise clock corrections (red) or fixing clock corrections on nominal values when optical clocks are used (green curves). Fig. 8: Estimated epoch-wise clock corrections for satellite E01 based on optical clocks (top) and corresponding radial orbit errors (bottom). The green curve (bottom) shows the radial orbit error for nominal readings of the optical clocks introduced as fixed. 5CONCLUSIONS Clocks are the main instruments required for navigation with GNSS satellites. Highly stable and accurate satellite clocks bear a large potential for improvements of user positions in real-time. If clocks are stable enough such that epoch-wise clock synchronisation is no longer required for precise positioning involving carrier phase, precise point positions at cm level becomes possible in real-time using only broadcast information from the GNSS alone, i.e., in single receiver mode. A large variety of applications could profit from such improved space infrastructure, ranging from precise navigation, e.g., for automatic navigation of ships in ports without reference station installations, tsunami warning systems with sensors at remote locations, space applications such as docking manoeuvres, and, last but not least, distribution of atomic time and a high-precision frequency standard from space. The paper demonstrates as an example improvements expected for precise orbit determination based on optical clocks. GNSS operators could profit from a possible reduction of ground infrastructure. Upon the result of our ongoing investigations, it can be decided whether single-ion or optical-lattice clocks shall be used for future GNSS. Components of the different types of optical atomic clocks are thus evaluated for their current technical maturity and potential space qualification. Depending on the technical readiness level of the subsystems of optical clocks concerning their space qualification status and performance requirements for optimized navigation, the best suited optical clock technology for future GNSS can be identified. Fig. 2: Generation of pure power-law noise processes. The results are time series of different noise types like the well-known white phase noise (red). With the combination of different noises, the simulation of typical atomic clock values (as of a Rubidium standard or a future optical standard) is possible. Fig. 3: Modified Allan deviation for the main noise types. The types are distinguished by the linear slopes (m) of the frequency stability, represented by the Allan deviation. Further, the slopes enable the simulation of time series for various atomic clock standards. ACKNOWLEDGEMENT The project ‘OCTAGON’ is supported by the Space Agency of the German Aerospace Center (DLR) with funds from the Federal Ministry of Economics and Technology (BMWi) based on a resolution of the German Bundestag under the code 50 NA 0904. 2nd International Colloquium – Scientific and Fundamental Aspects of the Galileo Programme, 14 – 16 October 2009 in Padova, Italy