This paper presents a unified formal framework for integrated circuits (IC) Trojan detection that can simultaneously employ multiple noninvasive measurement types. Hardware Trojans refer to modifications, alterations, or insertions to the original IC for adversarial purposes. The new framework formally defines the IC Trojan detection for each measurement type as an optimization problem and discusses the complexity. A formulation of the problem that is applicable to a large class of Trojan detection problems and is submodular is devised. Based on the objective function properties, an efficient Trojan detection method with strong approximation and optimality guarantees is introduced. Signal processing methods for calibrating the impact of inter-chip and intra-chip correlations are presented. We propose a number of methods for combining the detections of the different measurement types. Experimental evaluations on benchmark designs reveal the low-overhead and effectiveness of the new Trojan detection framework and provides a comparison of different detection combining methods.