Constrained Wrapped Least Squares: A Tool for High-Accuracy GNSS Attitude Determination

Abstract

Attitude determination is a popular application of Global Navigation Satellite Systems (GNSS). Many methods have been developed to solve the attitude determination problem with different performance offerings. We develop a constrained wrapped least-squares (C-WLS) method for highaccuracy attitude determination. This approach is built on an optimization model that leverages prior information related to the antenna array and the integer nature of the carrier-phase ambiguities in an innovative way. The proposed approach adopts an efficient search strategy to estimate the vehicle's attitude parameters using ambiguous carrier-phase observations directly, without requiring prior carrier-phase ambiguity fixing. The performance of the proposed method is evaluated via simulations and experimentally utilizing data collected using multiple GNSS receivers. The simulation and experimental results demonstrate excellent performance, with the proposed method outperforming the ambiguity function method, the constrained LAMBDA and multivariate constrained LAMBDA methods, three prominent attitude determination algorithms.

Instantaneous GNSS Ambiguity Resolution and Attitude Determination via Riemannian Manifold Optimization

“…The performance of the MC-LAMBDA approach relies on the quality of their (initial) float solution, that is, the least-squares estimations with the integer constraint of ambiguities ignored. Under satellite-deprived environments such as urban canyons, searching the integers requires a huge computational load due to the poor float solutions initially obtained through unconstrained leastsquares (LS) estimation [36].…”

“…RieMOCAD-LF, (38), only partially employs the orthonormality constraint, which can be used as a lowcomplexity option in many practical applications. To fully incorporate this constraint, one needs to achieve the tight-form solution of RieMOCAD (RieMOCAD-TF), i.e., minimizing (36). Section IV-B.2 presents the details to solve the optimization problem (36).…”

“…To fully incorporate this constraint, one needs to achieve the tight-form solution of RieMOCAD (RieMOCAD-TF), i.e., minimizing (36). Section IV-B.2 presents the details to solve the optimization problem (36). Note that (36) provides only one possible tight-form solution of the OC-AM, and ( 16) is another alternative.…”

“…Section IV-B.2 presents the details to solve the optimization problem (36). Note that (36) provides only one possible tight-form solution of the OC-AM, and ( 16) is another alternative. In this contribution, (36) is applied rather than (16) to accelerate the process of the integer ambiguity resolution.…”

Dual-antenna GPS-based UAV Attitude Determination Method and Accuracy Analysis

“…Over the years, various experts have studied the multi-antenna attitude solution methods, the most common ones being the direct method as well as the least squares method. [7][8][9]. Moreover, the quantity and configuration of antennas and the longness of baselines can impact the attitude solution accuracy.…”