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With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions, its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications. This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics. Then the theoretical convergence behavior of the complex Gaussian kernel least mean square (LMS) algorithm is studied by using the fixed dictionary strategy. The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algorithms using non-circular complex data. The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error (MSE) performance among of complex kernel LMS (KLMS) methods according to the specified kernel bandwidth and the length of dictionary. [ABSTRACT FROM AUTHOR]

Although a various of existing techniques are able to improve the performance of detection of the weak interesting signal, how to adaptively and efficiently attenuate the intricate noises especially in the case of no available reference noise signal is still the bottleneck to be overcome. According to the characteristics of sonar arrays, a multi-channel differencing method is presented to provide the prerequisite reference noise. However, the ingredient of obtained reference noise is too complicated to be used to effectively reduce the interference noise only using the classical linear cancellation methods. Hence, a novel adaptive noise cancellation method based on the multi-kernel normalized leastmean- square algorithm consisting of weighted linear and Gaussian kernel functions is proposed, which allows to simultaneously consider the cancellation of linear and nonlinear components in the reference noise. The simulation results demonstrate that the output signal-to-noise ratio (SNR) of the novel multi-kernel adaptive filtering method outperforms the conventional linear normalized least-mean-square method and the mono-kernel normalized leastmean- square method using the realistic noise data measured in the lake experiment. [ABSTRACT FROM AUTHOR]

An efficient hybrid time reversal (TR) imaging method based on signal subspace and noise subspace is proposed for electromagnetic superresolution detecting and imaging. First, the locations of targets are estimated by the transmitting-mode decomposition of the TR operator (DORT) method employing the signal subspace. Then, the TR multiple signal classification (TR-MUSIC) method employing the noise subspace is used in the estimated target area to get the superresolution imaging of targets. Two examples with homogeneous and inhomogeneous background mediums are considered, respectively. The results show that the proposed hybrid method has advantages in CPU time and memory cost because of the combination of rough and fine imaging. [ABSTRACT FROM AUTHOR]

A novel Krein space approach to robust H∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then a Krein space approach is used to tackle the robust. H∞ filtering problem. To this end, a new Krein space formal system is designed according to the original sum quadratic constraint (SQC) without introducing any nonzero factors into it and, consequently, the estimate recursion is obtained through the filter gain in Krein space. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]