Global navigation satellite systems (GNSSs)-aided inertial navigation systems (INSs) are a key instrumentation and measurement (I&M) technology, especially for vehicular applications. A requirement of any integrated INS/GNSS is the initialization of the vehicle’s attitude, which is referred to as alignment. This article addresses the particular problem of low-cost dual-antennae GNSS-aided INS stationary coarse alignment. The investigation initiates with a comprehensive analysis of the errors in the traditional three-axis attitude determination (TRIAD) method, purposely modified to employ non-ortho-normal (NON) observations of the gravity and dual-antennae GNSS baseline vectors. Observability analysis motivates innovative estimation algorithms for some sensor parameters, namely, the down accelerometer bias and the forward/down baseline biases. As a direct consequence, a main contribution of this article is an improved strategy, achieving higher accuracy, for the dual-antennae GNSS-aided INS stationary alignment problem, herein referred to as NON-TRIAD with sensor parameter estimation (NON-TRIAD-SPE). Results from simulated and experimental tests confirm the adequacy and robustness of the proposed method.