Power minimisation approach is an effective interference suppression algorithm for satellite navigation systems. It forms automatically deep nulls in the direction-of-arrival (DOA) of interferences without prior information about the DOAs of satellite signals and interferences. However, it cannot provide flat gains for other directions. Thus, the desired satellite signals may be partly suppressed when they locate in the shallow nulls. By combining eigenvalue thresholding method and l1-norm constraint, a new interference suppression algorithm is proposed for satellite navigation systems that would provide approximately flat gains in all directions except that of interferences. However, the l1-norm constraint leads to a non-smooth optimisation problem which cannot be solved by the conventional gradient-based algorithm. After that, by utilising the proximal operator, an iterative algorithm is proposed. The simulations demonstrate the effectiveness of the proposed algorithm.

We consider estimating time delays and amplitudes (real-or complex-valued) from the superposition of very closely spaced signals with known shapes. The well—known high resolution MODE (Method Of Direction Estimation) algorithm, which was originally proposed for angle estimation in array processing, is modified and used with our efficient time delay estimation method WRELAX (Weighted Fourier transformand RELAXation based) algorithm to deal with this problem. The proposed method is referred to as MODE-WRELAX. MODE-WRELAX provides better accuracy than MODE and higher resolution than WRELAX. Moreove it can be used for both complex-and real-valued signals (including those with highly oscillatory correlation functions). Numerical results show that the MODE-WRELAX estimates can approach the corresponding Cram6r-Rao bound. Efficient implementation of the algorithm is also discussed.

We present a conceptually simple and computationally efficient algorithm, which is referred to as WRELAX, for the well-known time delay estimation problem. The method is a relaxation-based minimizer of a complicated nonlinear least squares criterion. WRELAX can be applied to detecting and classifying roadway subsurface anomalies by using an ultra-wideband ground-penetrating radar. Numerical and experimental examples are provided to demonstrate the performance of the new algorithm.

We present an efficient algorithm for high resolution time delay estimation in colored Gausslan nalse with multiple looks. By using a relaxation-based optimization approach and exploiting the Toeplitz property of the noise eovaliauee matrix, the enhaneed new algorithm can achieve the corresponding Cramer-Rao bounds (CRBs) with a very small number of lndependent looks.

In sonar and many other applications, time-delay estimation is an important problem. When bandpass probe signals are used, the correlation function between the received and the known transmitted signals oscillates near the carrier frequency of the transmitted signal. In this case, many existing time-delay estimation algorithms perform poorly due to converging to local optimum points. In this paper, two efficient algorithms, Hybrid-WRELAX and EXIP-WRELAX, are proposed to deal with the above problem. They are relaxation-based global minimizers of a highly oscillatory nonlinear least-squares cost function. Both algorithms are shown to achieve the Cram´er–Rao bound and require only a sequence of weighted Fourier transforms.