Papers by Denis Laurichesse
Computers & Security, 1991
is being used more and more in security mechanisms such as encipherment schemes, authentication, ... more is being used more and more in security mechanisms such as encipherment schemes, authentication, digital signatures etc. In this paper some modular exponentiation algorithms with an original optimization method are described. These algorithms have been used to implement a software version of the RSA asymmetric cipher on several general-purpose machines. The performance is 50% faster than the best-known algorithms on the same machines. In many applications that need relatively slow decipherment throughput, software-implemented algorithms are therefore an acceptable alternative to specialized hardware.
A method to solve the GPS zero-difference measurement equations with integer ambiguities has been... more A method to solve the GPS zero-difference measurement equations with integer ambiguities has been recently introduced at CNES. When the method is applied to data from a global network of GPS receivers it provides a consistent set of satellite orbits and clocks, which have an ‘integer' property: phase residuals for any receiver computed using these orbits and clocks easily reveal integer ambiguities. The presentation focuses on the application of this novel approach to the computation of real-time orbits and clocks for the GPS constellation, and the benefit of using these products for real-time Precise Point Positioning (PPP) with integer ambiguity fixing of user receivers. In this method, real-time corrections to extrapolated IGS IGU orbits are estimated at the same time as all other relevant parameters by a Kalman filter which processes measurements from a world-wide stations network. The filter performs zero-difference ambiguity fixing in real-time. Two results are presented; the first with one month of raw data taken from the IGS, the second with raw data taken from the Internet in real-time using the NTRIP protocol. Relative to IGS final orbits, the 3-D precision of the real-time orbits is about 3 cm RMS. When these constellation orbits and clocks are used to perform real-time PPP for receivers outside of the reference network, the horizontal precision obtained using zero-difference integer ambiguity fixing is close to 1 cm RMS. This is about one order of magnitude better than standard solutions, which rely upon floating ambiguity fixing, close to the precision of RTK. We present several ‘site survey' type real-time experiments conducted at CNES that confirm these results. Advantages and drawbacks of this new integer-PPP method with respect to RTK are outlined. These topics include mainly the time to convergence, the baselines size and the associated precision. Some specific applications of this new method, especially those that cannot be obtained using a standard RTK method are proposed. Finally, ongoing and future work conducted at CNES on real-time applications is outlined. This work concerns mainly the development of a real-time integer PPP demonstrator. The goal and architecture of this demonstrator is presented, as well as the current development state and some preliminary results.
Modern Numerical Weather Prediction (NWP) models make use of the GNSS derived Zenith Total Delay ... more Modern Numerical Weather Prediction (NWP) models make use of the GNSS derived Zenith Total Delay (ZTD) or Integrated Water Vapour (IWV) estimates to enhance the quality of their forecasts. Usually, the ZTD is assimilated into the NWP models on hourly intervals but with the advancement of NWP models towards higher update rates, it has become necessary to estimate the ZTD on sub-hourly intervals. In turn, this imposes requirements related to the timeliness and accuracy of the ZTD estimates and has lead to a development of various strategies to process GNSS observations to obtain ZTD with different latencies and accuracies. Using present GNSS products and tools, ZTD can be estimated in real-time (RT), near real-time (NRT) and post-processing (PP) modes. The aim of this study is to provide an overview and accuracy assessment of various RT, NRT, and PP IWV estimation systems and comparing their achieved accuracy with the user requirements for GNSS meteorology. The NRT and PP systems are based on the Bernese GNSS Software v5.2 using a double-difference network and Precise Point Positioning (PPP) strategy, and the RT systems are based on BKG Ntrip Client 2.7 and PPP-Wizard both using PPP. One of the RT systems allows integer ambiguity resolution with PPP and therefore the effect of fixing integer ambiguities on ZTD estimates will also be presented.
AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 2006
ABSTRACT An in-flight demonstration of Autonomous Orbit Control (AOC) will be carried out in 2004... more ABSTRACT An in-flight demonstration of Autonomous Orbit Control (AOC) will be carried out in 2004/2005 on the French micro-satellite DEMETER. The experiment aims at computing and performing station keeping maneuvers on board and autonomously. It is based on a TOPSTAR 3000 GPS receiver including the "DIOGENE" orbital navigator. In order to limit the impacts on the satellite platform, the maneuver computation software is installed in the GPS receiver, whereas the effective velocity and attitude maneuvering commands are generated by a dedicated piece of software installed in the payload management unit. This paper will first introduce the experiment and its context. Some simulation results will be shown in order to illustrate the expected long-term station keeping performance. Finally, newly obtained in-flight results of the navigation performance and of the maneuver computation software behavior will be presented.
A method for solving GPS problems using zero difference integer ambiguities has been recently dev... more A method for solving GPS problems using zero difference integer ambiguities has been recently developed at CNES. This ambiguity resolution involves two steps : - first the zero-difference widelane ambiguities are solved for using GPS satellite biases. This solution can be performed independently on each receiver (no network solution is needed). The satellite biases are estimated using a small reference network of three or four stations, and are sufficiently stable to be defined by daily values. - second, the ionosphere free phase observables corrected with these identified widelane ambiguities are constructed. The complete problem is now reduced to a single frequency problem, with no first order ionosphere effects and a remaining ambiguity to solve, corresponding to a wavelength of 10.7 cm. This characteristic has important applications for time transfer, as it is now possible to estimate the clock differences between two stations without any frequency error. Also the computed clocks solutions are defined modulo this wavelength of 10.7 cm, and this allows the construction of very long clocks solutions using overlapping daily solutions for example ('integer phase clocks'). Some results will be shown for a baseline of ~500 km. Also, using these observations on a global network, it is now possible to define GPS satellite clocks which are consistent enough to produce integer ambiguities in the residuals computed for an isolated receiver. This means that integer ambiguity solutions are possible using all the satellite in view of the receiver, and not only the satellites which are in common view with a reference station. This is very interesting when there is no close reference station in order to construct a standard double difference solution. Results will be shown for static and kinematic positioning.
The continuous evolution of Global Navigation Satellite Systems (GNSS) meteorology has lead to an... more The continuous evolution of Global Navigation Satellite Systems (GNSS) meteorology has lead to an increased use of associated observations for operational meteorology worldwide. In order to enhance short-term weather forecasts meteorological institutions use modern low-latency Numerical Weather Prediction (NWP) models which assimilate GNSS-derived Zenith Total Delay (ZTD) estimates. For such NWP models a number of GNSS processing strategies allow the provision of these ZTDs with the required accuracy (up to a few millimetres) and latency (hourly). However, meteorological now-casting applications, e.g. for storm tracking, require higher update rates for the ZTDs of 10 or even 5 min, which can be achieved, but only at a loss in accuracy. Using the IGS Real-Time Service orbit and clock products together with an appropriate GNSS software, it is possible to estimate the ZTDs in real-time. Available software packages either use GNSS processing strategies based on differenced or un-differe...
Navigation, 2009
... 56, N° 2, Summer 2009 Integer ambiguity resolution on undifferenced GPS phase measurements an... more ... 56, N° 2, Summer 2009 Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP and satellite precise orbit determination ... (zenith delays are mapped to all elevations using the Stanag function). Typically, using state-of-the art correction ...
A method to solve the GPS zero-difference measurement equations with integer ambiguities has been... more A method to solve the GPS zero-difference measurement equations with integer ambiguities has been recently introduced at CNES. When the method is applied to data from a global network of GPS receivers it provides a consistent set of satellite orbits and clocks, which have an `integer' property: phase residuals for any receiver computed using these orbits and clocks easily reveal integer ambiguities. The presentation focuses on the application of this novel approach to the computation of real-time orbits and clocks for the GPS constellation, and the benefit of using these products for real-time Precise Point Positioning (PPP) with integer ambiguity fixing of user receivers. In this method, real-time corrections to extrapolated IGS IGU orbits are estimated at the same time as all other relevant parameters by a Kalman filter which processes measurements from a world-wide stations network. The filter performs zero-difference ambiguity fixing in real-time. Two results are presented;...
GPS Solutions, 2013
ABSTRACT Recent research has demonstrated that the undifferenced integer ambiguities can be recov... more ABSTRACT Recent research has demonstrated that the undifferenced integer ambiguities can be recovered using products from a network solution. The standard dual-frequency PPP integer ambiguity resolution consists of two aspects: Hatch-Melbourne-Wübbena wide-lane (WL) and ionosphere-free narrow-lane (NL) integer ambiguity resolution. A major issue affecting the performance of dual-frequency PPP applications is the time it takes to fix these two types of integer ambiguities, especially if the WL integer ambiguity resolution suffers from the noisy pseudorange measurements and strong multipath effects. With modernized Global Navigation Satellite Systems, triple-frequency measurements will be available to global users and an extra WL (EWL) model with very long wavelength can be formulated. Then, the easily resolved EWL integer ambiguities can be used to construct linear combinations to accelerate the PPP WL integer ambiguity resolution. Therefore, we propose a new reliable procedure for the modeling and quality control of triple-frequency PPP WL and NL integer ambiguity resolution. First, we analyze a WL integer ambiguity resolution model based on triple-frequency measurements. Then, an optimal pseudorange linear combination which is ionosphere-free and has minimum measurement noise is developed and used as constraint in the WL and the NL integer ambiguity resolution. Based on simulations, we have investigated the inefficiency of dual-frequency WL integer ambiguity resolution and the performance of EWL integer ambiguity resolution. Using almanacs of GPS, Galileo and BeiDou, the performances of the proposed triple-frequency WL and NL models have been evaluated in terms of success rate. Comparing with dual-frequency PPP, numerical results indicate that the proposed triple-frequency models can outperform the dual-frequency PPP WL and NL integer ambiguity resolution. With 1 s sampling rate, generally, only several minutes of data are required for reliable triple-frequency PPP WL and NL integer ambiguity resolution. Under benign observation situations and good geometries, the integer ambiguity can be reliably resolved even within 10 s.
The continuous evolution of global navigation satellite systems (GNSS) meteorology has led to an ... more The continuous evolution of global navigation satellite systems (GNSS) meteorology has led to an increased use of associated observations for operational modern low-latency numerical weather prediction (NWP) models, which assimilate GNSS-derived zenith total delay (ZTD) estimates. The development of NWP models with faster assimilation cycles, e.g., 1-h assimilation cycle in the rapid update cycle NWP model, has increased the interest of the meteorological community toward sub-hour ZTD estimates. The suitability of real-time ZTD estimates obtained from three different precise point positioning software packages has been assessed by comparing them with the state-of-the-art IGS final troposphere product as well as collocated radiosonde (RS) observations. The ZTD estimates obtained by BNC2.7 show a mean bias of 0.21 cm, and those obtained by the G-Nut/Tefnut software library show a mean bias of 1.09 cm to the IGS final tro-posphere product. In comparison with the RS-based ZTD, the BNC2.7 solutions show mean biases between 1 and 2 cm, whereas the G-Nut/Tefnut solutions show mean biases between 2 and 3 cm with the RS-based ZTD, and the ambiguity float and ambiguity fixed solutions obtained by PPP-Wizard have mean biases between 6 and 7 cm with the references. The large biases in the time series from PPP-Wizard are due to the fact that this software has been developed for kinematic applications and hence does not apply receiver antenna eccentricity and phase center offset (PCO) corrections on the observations. Application of the eccentricity and PCO corrections to the a priori coordinates has resulted in a 66 % reduction of bias in the PPP-Wizard solutions. The biases are found to be stable over the whole period of the comparison, which are criteria (rather than the magnitude of the bias) for the suitability of ZTD estimates for use in NWP nowcasting. A millimeter-level impact on the ZTD estimates has also been observed in relation to ambiguity resolution. As a result of a comparison with the established user requirements for NWP nowcasting, it was found that both the G-Nut/Tefnut solutions and one of the BNC2.7 solutions meet the threshold requirements, whereas one of the BNC2.7 solution and both the PPP-Wizard solutions currently exceed this threshold.
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Papers by Denis Laurichesse