Signal Detection Method Based On Compressive Sensing Theory Research

Compressed sensing theory has developed to the mature stage, gains a lot of achievements, and is widely applied in the field and in practical engineering. On one hand, in the applications of image reconstruction, contourlet transform is a new type of the performance of high quality image analysis tool. This paper will study an important application of the contourlet transform in image compression. On the another hand, at present, most of the compressive sensing research focus on how to accurately reconstruct the original signal, but little on directly deal with the "information" of compressive measurement. Aiming at this problem, this thesis launches the research on the accurate signal detection in the smart grid applications.The main work is as follows:Firstly, this paper analyses and studys the compressive sensing theory, and discuss the research status of the compressive sensing theory, compressive measurement theory and dynamic testing signal model. A brief introduction to the three core content of compression perception theory respectively:Signal sparse representation, measurement matrix construction and reconstruction algorithm. The advantages and defects of typical methods are summarized.Secondly, the method of image signal sparse representation is studied further--image compression method based on the transformation. The contourlet transform which advantage in the characteristic of multi-scale, direction and anisotropic is mainly studied. Through the analysis of the correlation of parent-child contourlet coefficient, the hidden markov quadtree model is established, and the image signal compressive sensing reconstruction method which is based on the contourlet domain hidden markov quadtree model (CT-HMQT) isproposed.Finally, the theory of compressive measurement with the characteristic of power is proposed. Aiming at the problem that the dynamic load influences on electric power measurement in the smart meter, firstly adopting the method that m-sequence modulates the steady-state signal to establish pseudo random dynamic test signal model with m-sequence modulation. Statistical properties of the pseudo random dynamic test current signal are analyzed. This dynamic test signal model can satisfy the authenticity and representative of dynamic test signal model. Then the frequency sparity of the signal is proved, and adopting compressive sensing theory and the stable state optimization method to build the compressive measurement matrix. On this basis, a compressive sensing measurement system model for measuring the electric energy of pseudo random dynamic test signal is established. On this basis, aiming at the pseudo random dynamic test signal, a compressive sensing measurement method for the electric energy of pseudo random dynamic test signal with m-sequence modulation is proposed. Finally for length of 255 bits,511 bits, and 1023 bits single cycle and multi-cycle of m-sequence dynamic testing signals, the simulation analysis the theoretical relative errors of compressive sensing measurement method, the errors are superior to 1×10-12. Compressive sensing measurement method in the paper is able to measure the signal electric power accurately, and the problem that measuring the dynamic test signal electric power accurately is solved.