The NUTRIG project is dedicated to the development of advanced radio self-trigger methods for large-scale arrays such as the Giant Radio Array for Neutrino Detection (GRAND). The developed techniques are based on features of the radio emission of air showers to perform an efficient online rejection of background. We first describe a first-level trigger (FLT) template-matching method that uses the shape of transient radio pulses measured at the detection-unit level to target those induced by air showers. We present trigger efficiencies and throughput tests of the template-matching FLT in controlled laboratory conditions. Next, we describe the second-level trigger (SLT), which utilizes the measured FLT times and corresponding voltage amplitudes to construct a trigger at the array level. We present offline performances of the SLT, which performs a coarse reconstruction of timing, direction, and polarization of the air shower.