Based on the results obtained in this research, some recommendations for improvements and/or further advancements on the proposed schemes are given below.
4.2 Recommendations and outlook 55
• An improvement of the quantitative characterization of robustness of the proposed schemes could be carried out in further long-term analyses with various distributed spacecraft missions.
• The proposed scheme for float ambiguity estimation is, in principle, extensible to include more complex approaches for ionospheric delay modeling/estimation. One strategy could consist in pre-computing values for each estimation epoch using sophisticated models such as NeQuick (Di Giovani and Radicella, 1990; Nava et al., 2008). Then, such values could be fed into the scheme as a priori information. However, a major challenge in this approach would be a proper statistical characterization of such pre-computed values that is required by the estimation scheme.
• More methods for selection of reference GNSS satellites for the formation of processing batches could be used. Currently, only two have been implemented and they have been used in a complementary way. A comparative study of the advantages and weaknesses of various possible methods may help for the analysis of more mission scenarios.
• One of the factors that affect the performance of the proposed method for float ambiguity estimation is the presence of short passes. These may result either from true carrier phase cycle-slips or from loss of individual observations from the receiver (i.e. without actual tracking interruption). Within the proposed scheme, simple algorithms were implemented to attempt a correction of miss-detected pass-breaks. These algorithms exhibited an acceptable performance in tests with data from PRISMA and Swarm. However, a more robust and complete scheme for cycle-slip and/or pass-break correction that can be applied for more general mission scenarios could be implemented.
• With the availability of more signals from multi-GNSS spaceborne receivers, the proposed scheme can be adapted to process such new signals. In particular, a dual-frequency dual-constellation scheme could be one of the most suitable approaches to follow. In this case, the number of ambiguities to fix in each batch would not increase dramatically so as to have a major impact on the computational performance. Additionally, using signals from two constellations already provides major benefits for differential ionospheric delay estimation and consequently an improved ambiguity fixing performance could be expected.
• The integer ambiguity validation scheme makes use of the fixed-failure rate ratio test approach (see §A.3.2) in order to determine the threshold µRT IA in Eq. (A.6). Such value is obtained by using generic look-up tables (Verhagen and Li, 2012). Although such approach exhibits an acceptable perfomance (see tests in §A.3.2), further analyses could be focused on the computation of look-up tables that consider more specific scenarios.
Corresponding tests could be performed to compare both approaches. In addition, different integer aperture estimators could be implemented in substitution or as a complement to the ratio test integer aperture estimator (see e.g. Wang and Verhagen (2015); Wang et al.
(2014)).
• Future theoretical improvements in the field of integer aperture estimators could be leveraged to enhance the proposed ambiguity validation scheme. A desirable scenario would be to reduce the number of free-thresholds (i.e. to be selected by hand) and substitute them by more formal methods.
56 Lessons learned and outlook
• The implemented scheme for partial ambiguity resolution is based on the analysis of iterative solutions from the ILS estimator. More efficient methods could be implemented, based on recent research on the field (see e.g. Nardo et al. (2016) and Brack (2015)).
• A further improvement on the strategy for mixed-cycle ambiguity resolution could be carried in the stage of cycle type determination. In principle, the problem can be framed in the signal detection theory (Kay, 1998), which may allow the implementation of more formal methods.
• The batch relative orbit determination system estimates a reference trajectory in a POD scheme. However, it would be possible to enhance this strategy by adjusting both the absolute reference and relative orbits to differential GNSS observations. In this case, it is expected that the precision of the reference trajectory can be improved due to the use of fixed ambiguities. For the case of an EKF-based scheme, such an approach has been implemented by van Barneveld (2012).
• An evaluation of the impact on the precision of maneuver estimates if (relative) empirical accelerations are estimated during maneuvering periods could be carried out. A similar approach has been recently proposed by Ju et al. (2017), but a more complete analysis of this strategy in multi-mission tests (with different maneuvering execution rates and duration) is yet to be performed.
Addendum
Methodology for integer ambiguity resolution
The integer ambiguity resolution strategy introduced in Publication 1 has been roughly de-scribed as a two-steps method consisting in dedicated schemes for float and integer ambiguities estimation. In a first stage, float ambiguities are estimated using an a priori-constrained LSQ method. Integer ambiguities are later resolved by using a scheme consisting of ILS and integer aperture estimators with additional semi-empirical and empirical ambiguity validation tests.
Although the overall flow of the algorithms has been described in Publication 1, some details regarding specific design decisions can be detailed in order to better analyze their impact on the final results. This addendum provides a more in-depth description of the implemented algorithms in the introduced methodology for integer ambiguity resolution. The details provided in the present addendum may be useful as starting point for further developments of the pro-posed scheme. Similarly, the additional obtained results may have some relevance for prospect alternative proposals and/or improvements to the research presented in this dissertation.