Integrate-and-Differentiate Approach to Nonlinear System Identification

In this paper, we consider a problem of parametric identification of a piece-wise linear mechanical system described by ordinary differential equations. We reconstruct the phase space of the investigated system from accelerometer data and perform parameter identification using iteratively reweighted least squares. Two key features of our study are as follows. First, we use a differentiated governing equation containing acceleration and velocity as the main independent variables instead of the conventional governing equation in velocity and position. Second, we modify the iteratively reweighted least squares method by including an auxiliary reclassification step into it. The application of this method allows us to improve the identification accuracy through the elimination of classification errors needed for parameter estimation of piece-wise linear differential equations. Simulation of the Duffing-like chaotic mechanical system and experimental study of an aluminum beam with asymmetric joint show that the proposed approach is more accurate than state-of-the-art solutions.

Optimization of sparse randomly spaced linear antenna array using hybrid iteratively reweighted least squares

Uniformly Spaced Antenna Array (USAA) with large radiating elements is characterized with complex feed network as well as high sidelobes level (SLL) leading to interference and power wastage. To solve these problems, research works have been carried out using different methodologies, to synthesize sparse Randomly Spaced An- tenna Array (RSAA) to reconstruct the desired radiation pattern using fewer radiating elements and suppressed SLL. In this paper, a deterministic Iteratively Reweighted Least Squares (IRLS) algorithm based on the concept of compressed sensing was used to achieve better sparsity through thinning. The SLL was also suppressed using Convex Technique (CT). The performance of the synthesized array was evaluated in terms of sparsity and SLL. Simulation results showed that it has a higher sparsity of 12 elements with SLL of -39.44dB which are 14.29% and 28.72% improvements, respectively compared to previous research work with 14 elements and SLL of -30.64dB.

Poisson noisy image restoration via overlapping group sparse and nonconvex second-order total variation priors

The restoration of the Poisson noisy images is an essential task in many imaging applications due to the uncertainty of the number of discrete particles incident on the image sensor. In this paper, we consider utilizing a hybrid regularizer for Poisson noisy image restoration. The proposed regularizer, which combines the overlapping group sparse (OGS) total variation with the high-order nonconvex total variation, can alleviate the staircase artifacts while preserving the original sharp edges. We use the framework of the alternating direction method of multipliers to design an efficient minimization algorithm for the proposed model. Since the objective function is the sum of the non-quadratic log-likelihood and nonconvex nondifferentiable regularizer, we propose to solve the intractable subproblems by the majorization-minimization (MM) method and the iteratively reweighted least squares (IRLS) algorithm, respectively. Numerical experiments show the efficiency of the proposed method for Poissonian image restoration including denoising and deblurring.