Multi-platform Integrated Positioning and Attitude Determination using GNSS (2013)

There is trend in spacecraft engineering toward distributed systems where a number of smaller spacecraft work as a larger satellite. However, in order to make the small satellites work together as a single large platform, the precise relative positions (baseline) and orientations (attitude) of the elements of the formation have to be estimated. Global Navigation Satellite System (GNSS, the general term for systems as GPS and Galileo) receivers can be utilized to provide baseline estimates with centimeter to millimeter level accuracy. These precise GNSS applications utilize the carrier phase observations, which are inherently ambiguous. While precise relative positioning using GNSS for surveying has been around for some time, precise relative navigation for moving applications on land, on water, in the air and even in space is still under development. The methods developed in this thesis can be applied for all these applications as no model for the user dynamics is applied (the methods are independent of the user motion). A functional model was developed, in which the difference between the topocentric distance at the GNSS system time and at the GNSS receiver time is taken into account. For users with high dynamics and/or large clock offsets, not taking this affect into account can cause time-varying offsets in the baseline estimate. The Doppler observation was reviewed and analysed for different types of applications. In most GNSS receivers, as the Doppler observation is generated from carrier phase observations, these observations are highly correlated with carrier-phase observations. For relative positioning applications, it was shown that inclusion of the Doppler observations in the model is only desirable 1. if the GNSS receivers have large clock offsets. Especially in a dynamic environment, the standard Double Difference model will result in an offset in the baseline estimation. 2. for applications were the relative position between two platforms is actively controlled, the relative velocity is generally required as input for the control loop. The Doppler observation will not improve the float solution of the relative positioning problem and therefore will not improve ambiguity resolution. The drawback of using the Doppler for relative velocity estimation is that the effect from the relative motion and the clock drift cannot be separated. If the relative velocity can be obtained offline, taking the time derivative of the baseline estimate can provide a more accurate relative velocity estimation. A single and multi-epoch data processing strategy was introduced that exploits the capability of the current GPS system, however, the tests are focused on its stand-alone, unaided, single-frequency, single-epoch performance, as this is the most challenging case for ambiguity resolution. A stronger model (larger number of observations, lower observation noise) will improve the performance of the developed approach in terms of the probability of correctly fixing the ambiguities. Multiple GNSS antennas mounted on one platform may be used to determine the attitude of the platform as well. In terms of accuracy not much room for improvement is expected in GNSS attitude determination, as the theoretical limit has been reached by the available techniques. However, for ambiguity resolution still a number of open challenges remain. Ideally, one would like to have an ambiguity resolution method with a high probability of correctly fixing the ambiguities even when a limited number of observations is available (weak models) which could work instantaneously, eliminating the need for a dynamics model, and is computational efficient. The method applied in this thesis is based on a constrained extension of the popular LAMBDA method, known as the Multivariate Constrained (MC-) LAMBDA method. The MC-LAMBDA method is a nontrivial modification of the standard LAMBDA method. In contrast to existing methods that make use of the known baseline length, the MCLAMBDA method does full justice to the given information by fully integrating the nonlinear baseline constraint into the ambiguity objective function. As a result, the a priori information receives a proper weighting in the ambiguity objective function, thus leading to higher success rates. The method was tested, using simulated as well as actual GPS data. The simulations cover a large number of different measurement scenarios, where the impact of measurement precision and receiver-GNSS satellite geometry was analysed. GNSS-based precise relative positioning between spacecraft normally requires dual frequency observations, whereas attitude determination of the spacecraft can be performed precisely using only single frequency observations. In this contribution, the possibility was investigated to use multi-antenna data in an integrated approach, not only for attitude determination, but also to improve the relative positioning between spacecraft. The rigorous inclusion of the known geometry of the antennas at the platform into the ambiguity objective function shows  dramatic improvements in the ambiguity resolution success rates for the baselines at and between the spacecraft.  improved precision of the baseline estimation for the baseline between the platforms. The theoretical improvement achievable for the baseline between the platforms as a function of the number of antennas on each platform was shown, both for ambiguity resolution and accuracy of the baseline solution. The obtained mathematical relationship was verified by software based, hardware-in-the-loop simulations and field experiments. The improved instantaneous ambiguity resolution will result in an even stronger reduction in time to fix (TTF). An additional benefit of the method is an improved robustness against multipath.