We use different ab initio methods to compute the three-dimensional potential energy surface (3D-PES) of the ground state of N2H+. This includes the standard coupled cluster, the complete active space self-consistent field, the internally contacted multi reference configuration interaction, and the newly developed CCSD(T)-F12 methods. For the description of H and N atoms, several basis sets are tested. Then, we incorporate the 3D-PES analytical representations into variational calculations of the rovibrational spectrum of N2H+((X) over tilde (1)Sigma(+)) up to 7200 cm(-1) above the zero point vibrational energy. Our data show that the CCSD(T)-F12/aug-cc-pVTZ approach represents a compromise for good description of the PES and computation cost. This technique is recommended for full dimensional PES generation of atmospheric and astrophysical relevant polyatomic systems. We applied this method to derive the rovibrational spectra of N2H+((X) over tilde (1)Sigma(+)) and of N2H++((X) over tilde (2)Sigma(+)). Finally, we discuss the existence of the N2H++((X) over tilde (2)Sigma(+)) in Titan's atmosphere.