Parallel iteration of two-step Runge-Kutta methods

In this paper, we introduce the Parallel iteration of two-step Runge-Kutta methods for solving non-stiff initial-value problems for systems of first-order differential equations (ODEs): y′(t) = f(t, y(t)), for use on parallel computers. Starting with an s−stage implicit two-step Runge-Kutta (TSRK) method of order p, we apply the highly parallel predictor-corrector iteration process in P (EC)mE mode. In this way, we obtain an explicit two-step Runge-Kutta method that has order p for all m, and that requires s(m+1) right-hand side evaluations per step of which each s evaluation can be computed parallelly. By a number of numerical experiments, we show the superiority of the parallel predictor-corrector methods proposed in this paper over both sequential and parallel methods available in the literature.

PBR Clutter Suppression Algorithm Based on Dilation Morphology of Non-Uniform Grid

Many new challenges are faced by the PBR (passive bi-static radar) employing non-cooperative radar illuminators. After the CFAR (constant false alarm) processor, the appearance of the amount of false alarm clutter points impacts the following tracing performance. To enhance the PBR tracing performance, we consider to reduce these clutter points before target tracing as soon as possible. In this paper, we propose a PBR clutter suppression algorithm based on dilation morphology of non-uniform grid. Firstly, we construct the non-uniform polar grid based on the acquisition geometry of PBR. Then, with the help of the grid platform, we separate the false alarm clutter points based on the dilation morphology. To efficiently operate the algorithm, we build up its parallel iteration scheme. To verify the performance of the proposed algorithm, we utilize both simulated data and field data to do the experiment. Experimental results show that the algorithm can effectively suppress most of the clutter points. Besides, we respectively combine the proposed suppression algorithm with two typical tracking algorithms to test the performance. Experimental results reveal that the compound tracing algorithm outperforms the traditional one. It can enhance the PBR tracing performance, reduce the occurrence probability of false tracks and meanwhile save time.

Prior Rough Estimation and Trigonometric Decomposition Method for Frequency Estimation of Sine Wave Distorted by Noise

Frequency estimation of sine wave distorted by noise plays an important role in modern power systems. The widely used windowed interpolation fast Fourier transform (WIFFT) can only reduce, but not completely remove, the estimation errors at the cost of an increment in the computation burden of frequency estimation. This paper proposes a frequency estimator by using the prior rough frequency estimation and trigonometric decomposition under white Gaussian noises. Firstly, a prior rough frequency is estimated by the three spectral lines WIFFT based on the Hanning window. Then, a parallel iteration of trigonometric decomposition is applied for the accurate frequency estimation. The gradient-descent method is used in the parallel iteration procedure, which can effectively restrain the interferences from harmonics and noise. Simulation and experiments results show that the proposed method can achieve accurate frequency estimation within one cycle.