GNSS ambiguity resolution and attitude determination by leveraging relative baseline and frequency information

Attitude determination is an important application of Global Navigation Satellite Systems (GNSS). However, before GNSS attitude determination can be achieved, the carrier-phase integer ambiguity must be resolved. We handle the attitude determination problem by arranging the GNSS receiving antennas on two non-collinear baselines, which allow us to obtain the 3-D attitude of the moving platform on which they are stationed. Initially, we tackle the ambiguity resolution problem independently over each baseline based on single phase-difference measurements. To this end, we discuss and test two different approaches to carrier-phase ambiguity resolution. We either exploit the receiver antenna configuration or employ multiple carrier frequencies. Namely, we show that for special configurations of collinear antenna triplets, the ambiguity resolution problem can be handled using a simple algebraic formula. A similar approach is developed for a baseline with only two antennas in which we utilize a pair of GNSS carrier frequencies that satisfy a specific condition. The initial solution to the algebraic formula yields only coarse vectors indicating the pointing direction of the baselines and coarse unwrapped phase-difference measurements. Therefore, we develop and apply refining procedures to improve the initial results. Using the obtained coarse phase differences, we formulate the attitude determination problem as a least-squares problem with dual baseline length constraints and an inter-baseline angle constraint. This is a non-convex optimization problem to which we propose an efficient solution. This solution, combined with each of the two ambiguity resolution approaches, results in two different methods for attitude determination. The proposed methods are extensively tested using simulations covering a broad range of scenarios. The results demonstrate high success rates of ambiguity resolution and high attitude accuracy. Moreover, the proposed methods perform reasonably well even in scenarios with a small number of visible satellites.