A Study Of Estimation Of Time And Frequency Difference Of Arrival For Cyclostationary Signals In Stable Impulsive Noise

Time-difference-of-arrival (TDOA) and differential Doppler shift, or frequency-difference-of-arrival (FDOA) estimation are central topics of signal processing for decades due to their applications to the problem of locating a signal source in communication, radar, and sonar systems, and to military reconnaissance and many walks of life. The TDOA/FDOA offered by distributed sensors gives the information for source location and motion detection. Many of the most widely used emitter location methods rely on the accurate and robust estimation of the TDOA and FDOA. There are many conventional methods for estimating TDOA and/or FDOA. But these methods are unable to produce accurate TDOA and FDOA estimates, when multiple emitters are located spatially close to each other. By exploiting the cyclostationarity property of the signal of interest, the signal-selective methods can obtain substantial tolerance to interference and Gaussian noise, which do not exhibit the same cyclostationarity as the signal of interest. Most of the conventional signal-selective TDOA and FDOA methods based on the second-order cyclostationarity assume that the noise present is additive Gaussian noise. However, the assumption of Gaussian is often unrealistic. Studies and experimental measurements have shown that a broad increasingly important class of noise such as under water acoustic noise, atmospheric noise, multiuser interference, and radar clutters are non-Gaussian processes. It has been shown that a class of α-stable distribution (0<α≤2) is more appropriate for modeling impulsive noise than Gaussian distribution. Since the stable distribution does not have finite second-or higher order moments (1≤α<2), or even first-order moment (α<1) due to the heavy tails, the performance of the existing signal-selective TDOA and/or FDOA estimation methods will degrade severely. From the viewpoint of real world applications, we are interested in developing algorithms accounting for interfering signals, and Gaussian and non-Gaussian impulsive noise.In this dissertation, new signal-selective TDOA and FDOA estimation methods in the presence of interfering signals and α-stable impulsive noise are developed. The main contributions achieved are briefly described as follows:Firstly, the exploitation of fractional lower-order cyclostationarity property of signals and the fractional lower-order cyclic correlation matched filtering method in the presence of interference and α-stable impulsive noise are addressed. Two types of representations pth-order cyclostationarity and fractional lower-order cyclostationarity for revealing the cyclostationarity property of signals are proposed. The new two types of fractional lower-order cyclic statistics have the advantages of the fractional lower order statistics (FLOS) and the cyclic statistics. The relationships between pth-order cyclostalionarity, fractional lower-order cyclostationarity, and second-order cyclostationarity are demonstrated. To overcome the degradation problem of the conventional cyclic correlation matched filter (CCMF), a new fractional lower-order cyclic correlation matched filtering method based on the max-output signal-to-noise ratio criterion is derived. The fractional lower-order cyclic correlation matched filter performs better than conventional CCMF in detecting and estimating of cyclostationary signals in α-stable impulsive noise environments.Secondly, the problem of estimation of TDOA for cyclostationary signals in the presence of interfering signals and α-stable impulsive noise is studied. We summarize the existing signal selective algorithms of the TDOA, and propose the concepts of the cyclic weighting spectral correlation function and the cyclic weighting correlation function. Then, the signal selective TDOA estimation algorithms are classified, and the relationships among them are analyzed and demonstrated. By using the theory of α-stable distributions and the cyclostationary property, two new classes of signal selective TDOA estimation algorithms robust against impulsive noise are developed, including the pth-order cyclic TDOA estimation algorithm and the fractional lower-order cyclic TDOA estimation algorithm. It is shown (hat these new methods are tolerant to interference and robust in both Gaussian and non-Gaussian α-stable impulsive noise environments. To improve the performance of the fractional lower order cyclic TDOA estimation methods further, a modified improved robust TDOA estimation algorithm called robust generalized spectral coherence alignment (RGSPECCOA) is proposed. The improved performance is demonstrated through detailed theoretical analysis and simulations.Thirdly, the problem of joint estimation of TDOA and Doppler shift (or FDOA) in the presence of a-stable impulsive noise is introduced. Although the FLOS-based algorithms can be robust against impulsive noise, it has been demonstrated that they are unable to generate separate unbiased TDOA/FDOA estimates when multiple signals are spectrally overlapped. In order to overcome the limitations of the conventional cyclic cross ambiguity function (CCA), the pth-order cyclic cross ambiguity function (PCCA), and the FLOS-based algorithms, a novel method for joint time delay and Doppler shift estimation based on the fractional lower-order cyclic cross ambiguity function (FCCA) is proposed. To make better use of cyclostationarity features, a multi-cycle TDOA/FDOA estimation methods based on FCCA and multi-cycle frequencies is introduced. Furthermore, in order to improve the performance of the single-cycle algorithm, we analyze the FCCA based on the different fractional lower-order cyclic correlation functions. A new algorithm is derived as a generalization of the FCCA between the fractional lower-order cyclic autocorrelation and the fractional lower-order cyclic cross-correlation of signals, which is referred to as robust generalized fractional lower-order cyclic cross ambiguity (GFCCA). The new algorithm overcomes the shortcomings shared by the single-cycle TDOA/FDOA estimation methods.