Abstract: This paper studies the parameter estimation problems of feedback nonlinear systems. Combining the multi-innovation identification theory with the negative gradient search, we derive a multi-innovation gradient-based iterative algorithm. In order to reduce the computational burden and further improve the parameter estimation accuracy, a decomposition multi-innovation gradient-based iterative algorithm is proposed by using the decomposition technique. The key is to transform an original system into two subsystems and to estimate the parameters of each subsystem, respectively. A simulation example is provided to demonstrate the effectiveness of the proposed algorithms.

Abstract: This paper focuses on the parameter estimation issues of multivariate equation‐error autoregressive moving average systems. By applying the gradient search and the multi‐innovation theory, we derive a multi‐innovation gradient based iterative (MI‐GI) algorithm. In order to improve the computational efficiency and the parameter estimation accuracy, a filtering and decomposition based gradient iterative (F‐D‐GI) algorithm is presented by using the data filtering technique and the decomposition technique. The key is to choose an appropriate filter to filter the input‐output data and to transform an original system into several subsystems. Compared with the MI‐GI algorithm, the F‐D‐GI algorithm can generate more accurate parameter estimates. Finally, an illustrative example is provided to indicate the effectiveness of the proposed algorithms.

Abstract: This paper investigates the identification problem of an output‐error nonlinear system with saturation and dead‐zone nonlinearity. Introducing a switching function and by means of the auxiliary model identification idea, an auxiliary model hierarchical least squares‐based iterative algorithm is proposed for estimating the parameters of the nonlinear system. Based on the hierarchical identification model, an auxiliary model hierarchical gradient‐based iterative algorithm is presented for the nonlinear system by utilizing the gradient search. In order to take full advantage of the system data, an auxiliary model hierarchical multi‐innovation gradient‐based iterative algorithm is derived for the nonlinear system according to the multi‐innovation identification theory. Finally, the numerical simulation results illustrate the effectiveness of the proposed algorithms.

Abstract: We consider an unmanned aerial vehicle (UAV) assisting data collection from multiple sensor nodes (SNs). We provide a completion time minimization design via jointly deciding the UAV trajectory and the SN assignment scheme. In particular, we first characterize the fundamental features of the joint optimal solution to the formulated problem. On the one hand, the optimal UAV trajectory is proved following a successive-hover-fly (SHF) structure. Namely, in an optimal solution, the UAV successively visits multiple hovering points and performs hovering with designated duration, while the maximum speed is achieved during the whole flying period between each two hovering points. On the other hand, the optimal SN assignment is characterized to follow a segment-based scheme. Based on the two characterizations, we are motivated to implement SHF structure with turning points in trajectory design and reasonably assume each segment in SHF structure having constant SN assignment. Afterwards, we relax the binary constraints for SN assignments and establish a convex approximation for the reformulated problem, which enables an iterative algorithm. A suboptimal joint solution is obtained via iteratively optimizing the completion time. A realization strategy is also provided for the relaxed solution while assuring the completion of data collection tasks. Finally, the proposed solution is validated and evaluated through numerical results. Both a low complexity and an accurate task completion guarantee of our proposed solution are observed in comparison with the benchmarks.

Abstract: We address the problem of joint source localization and association (JSLA) under a multipath propagation environment for sensor arrays. Taking into account inaccurate prior information in practical applications, we propose a JSLA algorithm based on the iterative implementation of the minimum mean-square error (MMSE) framework with semi-unitary and sparsity constraints and the subspace technique. The proposed algorithm exploits benefits of both spatial signals' sparse characteristic and coherence structure when localizing unknown sources in a mixed interference environment. In contrast with previous works, the proposed algorithm can associate the incident paths to each source from the complex propagation environment with improved association performance even under low signal-to-noise ratio conditions. Neither additional decorrelation preprocessing nor prior information pertaining to the multipath propagation is required. Both simulations and real data experiments demonstrate the effectiveness and robustness of the proposed algorithm.

Abstract: Using angle-of-arrival (AOA) measurements from several sensors to locate a target in 3-D space is one of the commonly used wireless localization techniques. A challenge of this technique is that the weighted least-squares (WLS) needed for it tend to incur the threshold effect when the noise level is high or when the localization geometry is poor, because its implementation requires the inversion of a matrix whose condition number will be large under such conditions. This paper presents an iterative method that does not require any matrix operation and is proved to be convergent with any initial value. Additionally, it outperforms the WLS-based methods as validated by comprehensive simulation results.

Abstract: The quality of point clouds is often limited by noise introduced during their capture process. Consequently, a fundamental 3D vision task is the removal of noise, known as point cloud filtering or denoising. State-of-the-art learning based methods focus on training neural networks to infer filtered displacements and directly shift noisy points onto the underlying clean surfaces. In high noise conditions, they iterate the filtering process. However, this iterative filtering is only done at test time and is less effective at ensuring points converge quickly onto the clean surfaces. We propose IterativePFN (iterative point cloud filtering network), which consists of multiple IterationModules that model the true iterative filtering process internally, within a single network. We train our IterativePFn network using a novel loss function that utilizes an adaptive ground truth target at each iteration to capture the relationship between intermediate filtering results during training. This ensures that the filtered results converge faster to the clean surfaces. Our method is able to obtain better performance compared to state-of-the-art methods. The source code can be found at: https://github.com/ddsediri/IterativePFN

Abstract: Abstract We investigate Newton’s method as a root finder for complex polynomials of arbitrary degrees. While polynomial root finding continues to be one of the fundamental tasks of computing, with essential use in all areas of theoretical mathematics, numerics, computer graphics and physics, known methods may have excellent theoretical complexity but cannot be used in practice, or are practically efficient but lack a successful theory behind them. We provide precise and strong upper bounds for the theoretical complexity of Newton’s method and show that it is near-optimal with respect to the known set of starting points that find all roots. This theoretical result is complemented by a recent implementation of Newton’s method that finds all roots of various polynomials of degree more than a billion, significantly faster than our upper bounds on the complexity indicate, and often much faster than established fast root finders. Newton’s method thus stands out as a method that has strong merits both from the theoretical and from the practical point of view. Our study is based on the known explicit set of universal starting points, for each degree d , that are guaranteed to find all roots of polynomials of degree d (appropriately normalized). We show that this set contains d points that converge very quickly to the d roots: the expected total number of Newton iterations required to find all d roots with precision ɛ is O(d3 log3d+d log | log ε|) , which can be further improved to O(d2 log4d+d log | log ε|) . The key argument shows that many root finding orbits are ‘ R -central’ in the sense that they stay forever in a disk of radius R , and each iteration ‘uses up’ an explicit amount An,k(ℓ) of area within this disk.

Abstract: The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.

Abstract: Abstract The consumption of solving large-scale linear equations is one of the most critical issues in numerical computation. An innovative method is introduced in this study to solve linear equations based on deep neural networks. To achieve a high accuracy, we employ the residual network architecture and the correction iteration inspired by the classic iteration methods. By solving the one-dimensional Burgers equation and the two-dimensional heat-conduction equation, the precision and effectiveness of the proposed method have been proven. Numerical results indicate that this DNN-based technique is capable of obtaining an error of less than 10 –7 . Moreover, its computation time is less sensitive to the problem size than that of classic iterative methods. Consequently, the proposed method possesses a significant efficiency advantage for large-scale problems.

Abstract: Constant modulus (CM) waveform design with good auto- and cross- correlation properties is the key issue in the multiple-input multiple-output (MEMO) radar systems. The problem is non-convex and NP-hard, due to the CM constraint and the nonconvex objective function. Most existing methods solve this problem by relaxation (relaxing CM costrint or the objective function) or directly designing phase, which degrade the performance or need huge computational cost. To address these issues, an unsupervised double Iterative Optimization Network (ION) method is proposed, by using the strong non-linear mapping ability of the deep learning network. The outer iteration updates the input waveform, and the inner iteration optimizes the waveform through the residual network. Compared with the existing methods, the proposed method has lower sidelobe in both the weighted maximum autocorrelation sidelobe (WMAS) and the weighted maximum crosscorrelation sidelobe (WMCS) with less computational cost.

Abstract: In this work, we consider the self-calibration problem of joint calibration and direction-of-arrival (DOA) estimation using acoustic sensor arrays. Unlike many previous iterative approaches, we propose solvers that can be readily used for both linear and non-linear arrays for jointly estimating the sensor gain, phase errors, and the source DOAs. We derive these algorithms for both the conventional element-space and covariance data models. We focus on sparse and regular arrays formed using scalar sensors as well as vector sensors. The developed algorithms are obtained by transforming the underlying non-linear calibration model into a linear model, and subsequently by using convex relaxation techniques to estimate the unknown parameters. We also derive identifiability conditions for the existence of a unique solution to the self-calibration problem. To demonstrate the effectiveness of the developed techniques, numerical experiments, and comparisons to the state-of-the-art methods are provided. Finally, the results from an experiment that was performed in an anechoic chamber using an acoustic vector sensor array are presented to demonstrate the usefulness of the proposed self-calibration techniques.

Abstract: This work aims at a new semi-analytical method called the variational iteration transform method for investigating fractional-order Emden–Fowler equations. The Shehu transformation and the iterative method are applied to achieve the solution of the given problems. The proposed method has the edge over other techniques as it does not required extra calculations. Some numerical problems are used to test the validity of the suggested method. The solution obtained has demonstrated that the proposed technique has a higher level of accuracy. The proposed method is capable of tackling various nonlinear fractional-order problems due to its simple implementation.

Abstract: In this article, we propose the neural Born iterative method (NeuralBIM) for solving 2-D inverse scattering problems (ISPs) by drawing on the scheme of the physics-informed supervised residual learning (PhiSRL) to emulate the computing process of the traditional Born iterative method (TBIM). NeuralBIM uses independent convolutional neural networks (CNNs) to learn the alternate update rules of two different candidate solutions regarding the residuals. Two different schemes are presented in this article, including the supervised and unsupervised learning schemes. With the dataset generated by the method of moments (MoM), supervised NeuralBIM is trained with the knowledge of the total fields and contrasts. Unsupervised NeuralBIM is guided by the physics-embedded objective function founding on the governing equations of ISPs, which results in no requirement of the total fields and contrasts for training. Numerical and experimental results further validate the efficacy of NeuralBIM.

Abstract: The control approaches generally resort to the tools from the mathematics, but whether and how the mathematics can benefit from the control approaches is unclear. This article aims to bring the “control design” idea into the mathematics by providing an observer-based iterative method that focuses on solving linear algebraic equations (LAEs). An inherent relationship is revealed between the problem-solving of LAEs and the design of observer-based control systems, with which the iterative method for solving LAEs is exploited based on the design of the basic state observers. It is shown that all (least squares) solutions for any (un)solvable LAEs can be determined exponentially fast or monotonically with the different selections of initial conditions. Moreover, the general solution subspace and particular (least squares) solutions of LAEs are related closely with the unobservable subspace and observable states of their associated observer systems, respectively. Through incorporating the design idea of the deadbeat control, the solving of LAEs can be realized within only finite iterations. In particular, our proposed iterative method can be leveraged to develop a new observer-based design algorithm for traditional two-dimensional iterative learning control to realize the perfect tracking tasks.

Abstract: In this paper, we present a new variational Born iterative method (VBIM) for real-time microwave imaging (MWI) applications. The S-parameter volume integral equation and waveport vector Green's function are implemented to utilize the measured signal of the MWI system. Meanwhile, the real and imaginary separation (RIS) approach is used at each iterative step to simultaneously reconstruct the dielectric permittivity and conductivity of unknown objects. Compared with the Born iterative method and distorted Born iterative method, VBIM requires less computational time to reach the convergence threshold. The graphics processing unit based acceleration technique is implemented for real-time imaging. To demonstrate the efficiency and accuracy of this VBIM-RIS method, synthetic analysis of a complex multi-layer spherical phantom is first conducted. Then, the algorithm is tested with measured data using our new MWI system prototype. Finally, a synthetic brain-tumor phantom model under a thermal therapy procedure is monitored to exemplify the real-time imaging with about 5 seconds per reconstruction frame.

Abstract: Solving linear systems, often accomplished by iterative algorithms, is a ubiquitous task in science and engineering. To accommodate the dynamic range and precision requirements, these iterative solvers are carried out on floating-point processing units, which are not efficient in handling large-scale matrix multiplications and inversions. Low-precision, fixed-point digital or analog processors consume only a fraction of the energy per operation than their floating-point counterparts, yet their current usages exclude iterative solvers due to the cumulative computational errors arising from fixed-point arithmetic. In this work, we show that for a simple iterative algorithm, such as Richardson iteration, using a fixed-point processor can provide the same convergence rate and achieve solutions beyond its native precision when combined with residual iteration. These results indicate that power-efficient computing platforms consisting of analog computing devices can be used to solve a broad range of problems without compromising the speed or precision.

Abstract: This letter investigates a full-duplex (FD) non-orthogonal multiple access (NOMA) enabled multiuser transmission with backscatter communication (FD-MTBC), where a multiuser downlink NOMA network is served by an FD source while backscatter devices transmit their information to the source simultaneously. Considering the constraints for successive interference cancellation (SIC) and the desired target uplink sum rate, we formulate an optimization problem to maximize the downlink sum rate. Further, we propose an iterative algorithm that jointly optimizes the power allocation coefficient and reflection coefficient to maximize the downlink sum rate. The effectiveness of the proposed algorithm is demonstrated using simulation results.

Abstract: In this work, a data-driven indirect iterative learning control (DD-iILC) is presented for a repetitive nonlinear system by taking a proportional-integral-derivative (PID) feedback control in the inner loop. A linear parametric iterative tuning algorithm for the set-point is developed from an ideal nonlinear learning function that exists in theory by utilizing an iterative dynamic linearization (IDL) technique. Then, an adaptive iterative updating strategy of the parameter in the linear parametric set-point iterative tuning law is presented by optimizing an objective function for the controlled system. Since the system considered is nonlinear and nonaffine with no available model information, the IDL technique is also used along with a strategy similar to the parameter adaptive iterative learning law. Finally, the entire DD-iILC scheme is completed by incorporating the local PID controller. The convergence is proved by applying contraction mapping and mathematical induction. The theoretical results are verified by simulations on a numerical example and a permanent magnet linear motor example.

Abstract: This paper addresses the problem of direction of arrival (DOA) estimation only relying on the sign bits of the array signal. A new optimization model is formulated to realize the simultaneous estimation of one-bit DOAs and source number. Specifically, the proposed model jointly optimizes the DOA vector and row sparse signal matrix under an improved maximum posteriori probability criterion. The resulting problem is quite challenging due to the non-convexity of DOA vector and the integral form in the model. By utilizing the framework of block successive upper-bound minimization, an off-grid iterative reweighted algorithm is devised to transform the original problem into a series of tractable subproblems. Numerical results are presented to confirm the superiority of our method.

Abstract: Accurate positioning and state estimation of surface vessels are prerequisites to achieving autonomous navigation. Recently, the rapid development of 3D LiDARs has promoted the autonomy of both land and aerial vehicles, which has aroused the interest of researchers in the maritime community accordingly. In this paper, the state estimation schemes based on 3D LiDAR scan matching are explored in depth. Firstly, the iterative closest point (ICP) and normal distribution transformation (NDT) algorithms and their variants are introduced in detail. Besides, ten representative registration algorithms are selected from the variants for comparative analysis. Two types of experiments are designed by utilizing the field test data of an ASV equipped with a 3D LiDAR. Both the accuracy and real-time performance of the selected algorithms are systemically analyzed based on the experimental results. It follows that ICP and Levenberg–Marquardt iterative closest point (LMICP) methods perform well on single-frame experiments, while the voxelized generalized iterative closest point (FastVGICP) and multi-threaded optimization generalized iterative closest point (FastGICP) methods have the best performance on continuous-frame experiments. However, all methods have lower accuracy during fast turning. Consequently, the limitations of current methods are discussed in detail, which provides insights for future exploration of accurate state estimation based on 3D LiDAR for ASVs.

Abstract: Aimed at infinite horizon optimal control problems of discrete time-varying nonlinear systems, in this paper, a new iterative adaptive dynamic programming algorithm, which is the discrete-time time-varying policy iteration (DTTV) algorithm, is developed. The iterative control law is designed to update the iterative value function which approximates the index function of optimal performance. The admissibility of the iterative control law is analyzed. The results show that the iterative value function is non-increasingly convergent to the Bellman-equation optimal solution. To implement the algorithm, neural networks are employed and a new implementation structure is established, which avoids solving the generalized Bellman equation in each iteration. Finally, the optimal control laws for torsional pendulum and inverted pendulum systems are obtained by using the DTTV policy iteration algorithm, where the mass and pendulum bar length are permitted to be time-varying parameters. The effectiveness of the developed method is illustrated by numerical results and comparisons.

Abstract: ABSTRACT A test-based model-free adaptive iterative learning control algorithm (TB-MFAILC) with strong robustness is proposed in this paper. The algorithm improves the situation where existing model-free adaptive iterative learning control algorithms fail to converge or converge relatively slowly in noisy environments. Also, this work demonstrates the convergence and robustness of the proposed algorithm in different environments. Subsequently, the effectiveness of the proposed algorithm is illustrated by numerical comparison simulations with the existing model-free adaptive iterative learning control algorithm and the PD-based adaptive switching learning control algorithm in noisy environments. Finally, the advantages of the proposed algorithm are further illustrated through the analysis of relevant parameters.

Abstract: Abstract In order to improve the real-time performance of the aero-engine Component-Level Model (CLM) while ensuring accuracy, a method for the Calculation of Thermodynamic Parameters of Working Fluids (CTPWF) based on a Neural Network and Newton Raphson (NN-NR) is proposed. In this method, the enthalpy or entropy under different fuel-air ratio and humidity conditions is mapped to temperature by a neural network, and the mapping output is used as the initial solution of Newton Raphson (NR) iteration. Then, a high-precision solution can be obtained through a few iterations, which avoids the shortcoming that the traditional method uses a fixed initial solution that leads to too many iterative steps. This effectively reduces the number of iterative steps and improves the calculation efficiency. This method is applied to the aero-thermodynamic calculation of each component of an engine CLM, which improves the accuracy and real-time performance of the CLM. The simulation results show that, compared to the traditional method, the proposed method improves the accuracy of the CTPWF and can reduces the single aero-thermodynamic calculation time by 25 % when humidity is not considered and by 47 % when humidity is considered. This effectively improves the real-time performance of the CLM.