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In this paper, the global navigation satellite system (GNSS) precise point positioning (PPP) concept is generalized to array-aided PPP (A-PPP). A-PPP is a measurement concept that uses GNSS data, from multiple antennas in an array of known geometry, to realize improved GNSS parameter estimation (position, attitude, time and atmospheric delays). The concept is formulated such that it applies to each current and future multifrequency GNSS, stand-alone or in combination. A-PPP is made possible through solving a novel orthonormality-constrained multivariate (mixed) integer least-squares problem. It is shown that the integer matrix constraint is necessary to obtain a precise instantaneous attitude- and position solution, whereas the inclusion of the orthonormality constraint in the integer ambiguity objective function is essential to achieve high instantaneous probabilities of correct integer estimation. Different A-PPP applications are discussed, with their performances illustrated by means of empirical GPS results.