Robust Convergence Performance Research Articles

Combination of Land-Based and Satellite-Based OTH Geolocations Using Differentiable Exact Penalty Method

In civil or military applications, a transmitter on Earth may utilize different means of communications. A typical example is the naval craft, which often radiates very high frequency signals received by a satellite system and high frequency signals received by land-based observers. This article concentrates on the combination of land-based and satellite-based over-the-horizon (OTH) geolocations. A quadratic constrained weighted least-squares optimization model for the combined geolocation is established and a differentiable exact penalty solution is developed to locate the OTH transmitter in an iterative manner, which is shown to have robust convergence performance. Theoretical analysis is presented, which involves the Cramér–Rao bound for combined geolocation under the constraint of ellipsoidal Earth model and the closed-form expression of mean square error for the proposed method. Numerical examples are provided to validate our theoretical analysis and illustrate that the proposed method outperforms other geolocation methods in a wide range of scenarios.

Fast Blind Equalization Using Bounded Non-Linear Function With Non-Gaussian Noise

Blind equalization is widely utilized to eliminate inter-symbol interference in communication system. It is still a challenge to support blind equalization method within non-Gaussian noise environments. Aiming at improving its convergence speed and robustness performance, in this letter, a novel fast blind equalization method is proposed by using bounded nonlinear function (BNF) and quasi-Newton method. Firstly, BNF-based cost function is proposed to effectively eliminate non-Gaussian noise and realize equalization. Next, quasi-Newton method is developed as the iteration method, which can accelerate the convergence speed. Moreover, theoretical analysis is provided to illustrate that the proposed algorithm has a robust convergence performance. Simulation results show that the proposed method enables evident performance improvement in terms of convergence speed and robustness with non-Gaussian noise.

Delayless Block Individual-Weighting-Factors Sign Subband Adaptive Filters With an Improved Band-Dependent Variable Step-Size

Delayless individual-weighting-factors sign subband adaptive filter (IWF-SSAF) algorithms with a band-dependent variable step-size (BDVSS) were recently introduced to achieve a robust convergence performance against the impulsive interference and to avoid an undesirable signal path delay in subband systems. In this paper, we develop a block implementation of the delayless IWF-SSAF algorithm designed for an active impulsive noise control (AINC) system. With the block-processing approach, the proposed delayless block IWF-SSAF algorithm can be implemented more efficiently than the original delayless algorithm regardless of number of subbands, which is verified through the computational analysis. Furthermore, an improved BDVSS version (I-BDVSS) is also proposed by using the multiple auxiliary past gradients, which are given for each band by the block-processing. Finally, the simulation results illustrate that the proposed delayless block IWF-SSAF algorithm with the I-BDVSS, even requiring less computational burden, can achieve a better convergence performance than the original delayless algorithm with the BDVSS under severe impulsive noise control environment.

Interferometric spherical surface testing with unknown phase shifts.

A general method is presented for spherical surface testing with unknown phase shifts based on a physical model of the interferometer cavity, which describes the phase shifts taking into account the rigid cavity motions and the radial imaging distortion of the interferometer. The captured interferograms are processed frame by frame with the regularized frequency-stabilizing method, so as to get the phase shifts between the frames. These phase shift data are subsequently fitted, and the initial estimations for the wavefront, direct current and interference contrast terms are calculated by the least-squares method. Specially, a simple way is proposed to find reasonable initial guess for numerical aperture (NA) of the test beam (when NA is unknown), so as to ensure the effectiveness of the above phase shift fitting procedure. Then, the wavefront result is further refined in an iterative way, by fitting the sequence of interferograms to the physical model of the interferometer cavity with the linear regression technique. Finally, the wavefront result related to the actual surface profile is retrieved after removing the aberrations due to the surface misalignment and the imaging distortion. Both simulations and experiments with the ZYGO interferometer have been carried out to validate the proposed method, with experimental accuracies better than 0.004λ RMS achieved. The proposed method provides a feasible way to spherical surface testing without the use of any phase-shifting devices, while retaining good accuracy and robust convergence performance.

An efficient conjugate gradient method and application to dynamic force reconstruction

In this paper, we propose and create an efficient conjugate gradient method (MCG) based on a new operator, prove its stability and convergence and apply it to the multi-source dynamic loads identification of practical engineering structure. Numerical simulations of two engineering examples demonstrate that the present method has high efficiency and very robust convergence performance, and reduces the number of iterations. In addition, the proposed method can provide more efficient and numerically stable approximation of the true loads, compared with the Landweber iteration method. The results validate the stability and the effectiveness of the present method and coincide with the results of the theoretical analysis.

Normalized p-Norm Blind Equalization Algorithm with Adaptive Momentum under Impulsive Noise Environment

Hereby a normalized p-norm blind equalization algorithm with adaptive momentum was proposed. Normalized p-norm LMS-CMA can obtain robust convergence performance under impulsive noise environment, however, the convergence rate is slow. To further improve the performance of the normalized p-norm LMS-CMA, adaptive momentum according to the instantaneous error is designed. If the instantaneous error based on CMA criterion and DD criterion has the same sign, the momentum factor remains unchanged. Otherwise, the momentum factor is set to 0. The simulation results show that, the proposed algorithm has faster convergence rate than the normalized p-norm blind equalization algorithm, furthermore, it has robust convergence performance under impulsive noise environment.

A new reliability analysis method for uncertain structures with random and interval variables

In this paper, a new reliability analysis method is developed for uncertain structures with mixed uncertainty. In our problem, the uncertain parameters with sufficient information are treated by random distributions, while some ones with limited information can only be given variation intervals. A complex nesting optimization will be involved when using the existing methods to compute such a hybrid reliability, which will lead to extremely low efficiency or instable convergence performance. In this paper, an equivalent model is firstly created for the hybrid reliability, which is a conventional reliability analysis problem with only random variables. Thus only through computing the reliability of the equivalent model the original hybrid reliability can be easily evaluated. Based on the above equivalent model, an algorithm with high efficiency and robust convergence performance is then constructed for computation of the above hybrid reliability with both random and interval variables. Two numerical examples are provided to demonstrate the effectiveness of the present method.

Natural gradient multichannel blind deconvolution and speech separation using causal FIR filters

Natural gradient adaptation is an especially convenient method for adapting the coefficients of a linear system in inverse filtering tasks such as convolutive blind source separation and multichannel blind deconvolution. When developing practical implementations of such methods, however, it is not clear how best to window the signals and truncate the filter impulse responses within the filtered gradient updates. We show how inadequate use of truncation of the filter impulse responses and signal windowing within a well-known natural gradient algorithm for multichannel blind deconvolution and source separation can introduce a bias into its steady-state solution. We then provide modifications of this algorithm that effectively mitigate these effects for estimating causal FIR solutions to single- and multichannel equalization and source separation tasks. The new multichannel blind deconvolution algorithm requires approximately 6.5 multiply/adds per adaptive filter coefficient, making its computational complexity about 63% greater than the originally-proposed version. Numerical experiments verify the robust convergence performance of the new method both in multichannel blind deconvolution tasks for i.i.d. sources and in convolutive BSS tasks for real-world acoustic sources, even for extremely-short separation filters.