The affine constrained GNSS attitude model and its multivariate integer least-squares solution

Abstract

A new global navigation satellite system (GNSS) carrier-phase attitude model and its solution are introduced in this contribution. This affine-constrained GNSS attitude model has the advantage that it avoids the computational complexity of the orthonormality-constrained GNSS attitude model, while it still has a significantly improved ambiguity resolution performance over its unconstrained counterpart. The functional and stochastic model is formulated in multivariate form, for one-, two-and three-dimensional antenna arrays, tracking GNSS signals on an arbitrary number of frequencies with two or more antennas. The stochastic model includes the capability to capture variations in the antennaquality within the array. The multivariate integer leastsquares solution of the model parameters is given and the model's ambiguity success-rate is analysed by means of the ambiguity dilution of precision (ADOP). A general closedform expression for the affine-constrained ADOP is derived, thus providing an easy-to-use and insightful rule-of-thumb for the ambiguity resolution capabilities of the affine constrained GNSS attitude model.

Geometrically constrained kinematic global navigation satellite systems positioning: Implementation and performance

“…However, owing to the nonlinear nature of the given constraints, the search algorithm would be inherently complex. Therefore, a method, referred to as the affine constraint attitude model, has been proposed by Teunissen (2011), which is based on the assumption that the reference frame baseline matrix is related to the body frame baseline matrix by an affine transformation rather than a simple rotation.…”

Attitude Determination Algorithms through Accelerometers, GNSS Sensors, and Gravity Vector Estimator

“…Example publications describing such actual real-world GNSSattitude determination results can be found in [3][4][5][6]. The underlying theory and advanced algorithms for much of the above-referred integer-ambiguity-resolved carrier-phase GNSS attitude determination methods can be found in [7][8][9]. Multi-GNSS developments of integrating GNSS systems for attitude determination are stated in [10,11].…”

Precise and Fast GNSS Signal Direction of Arrival Estimation

“…An alternative rigorous solution for the multivariate case called AC-LAMBDA (affine constrained LAMBDA) was proposed by Teunissen (2011). This approach discards the nonlinear constraints but rigorously includes the remaining linear affine constraints to the search space.…”

“…Intensive computations can be avoided as the search space remains ellipsoidal and the original LAMBDA search can be applied. However, it only works in the multivariate case when the constraints can be split into affine and nonlinear constraints (Teunissen, 2011).…”

“…These approaches still aim for integer minimizing the standard ambiguity objective function, and in a reduced search space (Teunissen, 2011). Therefore, they provide computational efficiency.…”