Hardware Trojan (HT) has emerged as an impending security threat to hardware systems. However, conventional functional tests fail to detect HT since Trojans are triggered by rare events. Most of the existing side-channel based HT detection techniques just simply compare and analyze circuit's parameters and offer no signal calibration or error correction properties, so they suffer from the challenge and interference of large process variations (PV) and noises in modern nanotechnology which can completely mask Trojan's contribution to the circuit. This paper presents a novel HT detection method based on subspace technique which can detect tiny HT characteristics under large PV and noises. First, we formulate the HT detection problem as a weak signal detection problem, and then we model it as a feature extraction model. After that, we propose a novel subspace HT detection technique based on time domain constrained estimator. It is proved that we can distinguish the weak HT from variations and noises through particular subspace projections and reconstructed clean signal analysis. The reconstructed clean signal of the proposed algorithm can also be used for accurate parameter estimation of circuits, e.g. power estimation. The proposed technique is a general method for related HT detection schemes to eliminate noises and PV. Both simulations on benchmarks and hardware implementation validations on FPGA boards show the effectiveness and high sensitivity of the new HT detection technique.