Array-based satellite phase bias sensing: theory and GPS/BeiDou/QZSS results

Single-receiver integer ambiguity resolution (IAR) is a measurement concept that makes use of network-derived non-integer satellite phase biases (SPBs), among other corrections, to recover and resolve the integer ambiguities of the carrier-phase data of a single GNSS receiver. If it is realized, the very precise integer ambiguity-resolved carrier-phase data would then contribute to the estimation of the receiver's position, thus making (near) real-time precise point positioning feasible. Proper definition and determination of the SPBs take a leading part in developing the idea of single-receiver IAR. In this contribution, the concept of array-based between-satellite single-differenced (SD) SPB determination is introduced, which is aimed to reduce the code-dominated precision of the SD-SPB corrections. The underlying model is realized by giving the role of the local reference network to an array of antennas, mounted on rigid platforms that are separated by short distances so that the same ionospheric delay is assumed to be experienced by all the antennas. To that end, a closed-form expression of the array-aided SD-SPB corrections is presented, thereby proposing a simple strategy to compute the SD-SPBs. After resolving double-differenced ambiguities of the array's data, the variance of the SD-SPB corrections is shown to be reduced by a factor equal to the number of antennas. This improvement in precision is also affirmed by numerical results of the three GNSSs GPS, BeiDou and QZSS. Experimental results demonstrate that the integer-recovered ambiguities converge to integers faster, upon increasing the number of antennas aiding the SD-SPB corrections