Many applications require the detection of unknown nonlinear frequency modulated (FM) signals in noise. In this paper, a nonlinear FM signal in one time interval is approximated by linear FM (LFM) segments in successive subintervals. Each LFM segment is parameterized by a 2-dimensional (2D) state vector and its evolution from a subinterval to the next one is modeled as a dynamic system of unknown statistics with linear state transition equations and nonlinear measurement equations. A forward–backward cost-reference particle filter (FB-CRPF) is proposed to estimate the state sequence. From the estimated state sequence, the generalized likelihood ratio test (GLRT) statistic and the total variation (TV) statistic are computed for signal detection. In the 2D feature plane of the GLRT versus TV, the decision region of the null hypothesis at a given false alarm rate is determined by the 2D convexhull learning algorithm from noise-only training samples. Two kinds of simulated signals are used to test the proposed detector and results show that the proposed detector attains better performance than the two existing detectors. 
Detection of nonlinear FM signals via forward–backward cost-reference particle filter