TCAR and MCAR Options with Galileo and GPS

The big number of available Galileo and GPS-IIF signals and frequencies available at the end of this decade makes the use of three-carrier ambiguity resolution (TCAR) or multiple carrier ambiguity resolution (MCAR) approaches interesting. However, not all possibilities perform equally. Due to the different wavelengths that are involved different success rates for a correct fixing of any type of wide-lane ambiguity can be given. All relevant different options of signal combinations have been analysed systematically with respect to their success rates and are presented in the paper. The current Galileo baseline signal structures and the modernized GPS-IIF signal structures have been investigated. The important point in selecting a well performing signal and frequency combination for TCAR is that in the cascading steps, the noise of the measurement of one step is low with respect to the virtual wavelength of the next steps ambiguity. Having this in mind and having available a certain number of frequencies, this leads to the MCAR approach, where the TCAR steps can be sequentially ordered according to their virtual wavelength to maximise the success rate for correct ambiguity fixing. In literature, the term "gap-bridging" concept is used for the steps of TCAR, where the gap between code pseudorange and finally the base carrier phase measurement accuracy is bridged. Analogously, the MCAR approach presented here makes use of a concept that can be called "fine-gap-bridging" concept. By making use of all available signals the risk for a wrong fixing in any of the steps is minimised. Furthermore, comparisons to the state-of-the-art ambiguity resolution approaches sometimes called real-time kinematic (RTK) have been made. With more than two frequencies available both approaches yield very good results. However, one major difference between both approaches is that in the TCAR (or MCAR) case no geometry information is exploited. This leads to the severe disadvantage that there might be wrong ambiguity fixings. As these wrong fixes can even happen in the early steps of TCAR or MCAR, huge range errors result. If this is the case, then the remaining steps generate a random lower-level range error as a result. Of course, there are several possibilities to perform post-TCAR plausibility checks, but there is no guarantee that could lead to a strong statement about integrity. This paper reviews the TCAR approach, lists all assumptions that have been made and presents the results of the TCAR/MCAR analyses that have been made. Comparisons to RTK approaches are also discussed. Finally, recommendations based on these results are given. The main results can be summarised as follows: 1. The code accuracy of Galileo AltBOC (15,120) on E5ab does allow for a (very) safe correct fixing of any superwidelane ambiguity. 2. The signal combinations that do not make use of the E5ab code range for the first step, have a high success rate for the remaining two fixing steps (widelane and base frequency ambiguity fixes). 3. The combination with E5ab, E6-E5ab, L1E5ab, E5ab seems to be the best under the used assumptions. 4. Compared to GPS TCAR, in Galileo there are combinations with higher success rates, based on the relationships of the available signal frequencies. 5. Using MCAR, the risk of wrong ambiguity fixings is below the 10 level under the assumptions that have been made here. CARRIER-PHASE TECHNIQUES To achieve very high position accuracies (position errors less than about 1 m) the satellite navigation system user needs to exploit not only code pseudoranges but also – and more importantly the carrier phase measurements. However, the carrier phase measurements are ambiguous with respect to the integer number of cycles from satellite to receiver. There are several well-known approaches for making use of these high-precision but ambiguous measurements. In the following the methods for RTK (float and fixed) as well as the TCAR/MCAR methods are considered in detail. Before, however, a clear definition of what is understood under these acronyms is given: • Float RTK: A standard kinematic DGPS solution including carrier-phase measurements. The unknown integer ambiguities are part of the filter state and will be estimated within the positioning (Kalman) filter. They will be used as float values and are not fixed to integers. • Fixed RTK: This approach is the same as in the float RTK case. But, when enough information in the positioning filter is available (variances in the ambiguity states are low or other statistical tests are positive), the ambiguities are fixed to integer values. In the further processing only the fixed values of the ambiguities are used for positioning. The fixing of the ambiguities is done via state-of-the-art algorithms like Euler/Landau search (Euler and Landau, 1992) and possibly a presearch decorrelation (e.g. LAMBDA transformation, see Teunissen at al., 1995). It is important to note here, that the ambiguity fixing is performed simultaneously on all ambiguity states based on the covariance matrix of the positioning filter including geometrical information. • TCAR: This is a quite new approach proposed by Harris (1997) and Forssell et al. (1997). It makes use of at least three different carrier-frequencies and is able to fix the ambiguities directly, without using the information of the positioning filter. This means that no ambiguity search is necessary with this type of approach. • MCAR: This is a generalised approach of TCAR using more than three carrier frequencies. Considering the availability of more frequencies, the approach will be more robust (more integer) than TCAR alone. Again, no ambiguity search is needed here. Generally, when talking of these high-accurate position solutions, differencing techniques have to be applied. So, in all the following analyses it is assumed that there are a differential reference station and its measurements available. Only brief deliberations are given for each case, when there is no reference station available at all. Of course, usage of a differential reference station requires the transmission of the reference station data to the user, which needs some time. In the following this latency is not considered. The obtainable accuracy will appropriately be reduced dependent on the relation between this latency, the user dynamics, data rate and positioning filter design. However, this is a general effect that is independent on which of the above approaches is taken. All carrier-phase approaches have with respect to the standard (code-only) DGPS the following quality features in common: # Advantage / Disadvantage Eval. Mitigation 1 Dramatic accuracy improvement (Carrier-phase +++ None necessary accuracies obtained) 2 Continuity reduced (After a signal outage, the ambiguities have to be resolved again) None 3 Availability reduction (Carrier-phase measurements must be available for all used frequencies) Possible, when more than three frequencies are available 4 No integrity (But long-term plausibility checks possible) --None known to date Table 1: Carrier-phase quality features In the following the individual approaches are generically analysed in detail.