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In this paper we have proposed a novel robust method of estimation of the unknown parameters of a fundamental frequency and its harmonics model. Although the least squares estimators (LSEs) or the periodogram type estimators are the most efficient estimators, it is well known that they are not robust. In presence of outliers the LSEs are known to be not efficient. In presence of outliers, robust estimators like least absolute deviation estimators (LADEs) or Huber's M-estimators (HMEs) may be used. But implementation of the LADEs or HMEs are quite challenging, particularly if the number of component is large. Finding initial guesses in the higher dimensions is always a non-trivial issue. Moreover, theoretical properties of the robust estimators can be established under stronger assumptions than what are needed for the LSEs. In this paper we have proposed novel weighted least squares estimators (WLSEs) which are more robust compared to the LSEs or periodogram estimators in presence of outliers. The proposed WLSEs can be implemented very conveniently in practice. It involves in solving only one non-linear equation. We have established the theoretical properties of the proposed WLSEs. Extensive simulations suggest that in presence of outliers, the WLSEs behave better than the LSEs, periodogram estimators, LADEs and HMEs. The performance of the WLSEs depend on the weight function, and we have discussed how to choose the weight function. We have analyzed one synthetic data set to show how the proposed method can be used in practice. [ABSTRACT FROM AUTHOR]

The controlled autoregressive autoregressive moving average (CARARMA) models are of popularity to describe the evolution characteristics of dynamical systems. To overcome the identification obstacle resulting from colored noises, this paper studies the identification of the CARARMA models by forming an intermediate correlated noise model. In order to realize the real-time prediction function of the models, the on-line identification scheme is developed by constructing the dynamical objective functions based on the real-time sampled observations. Firstly, a rolling optimization cost function is built based on the observation at a single sampling instant to catch the modal information at a single time point and a generalized extended stochastic gradient (GESG) algorithm is proposed through the stochastic gradient optimization. Secondly, a rolling window cost function is built in accordance with the dynamical batch observations within data window by extending the proposed GESG algorithm and the multi-innovation generalized extended stochastic gradient algorithm is derived. Thirdly, from the perspective of theoretical analysis, the convergence proof of the proposed algorithm is provided based on the stochastic martingale convergence theory. Finally, the simulation analysis and comparison studies are provided to show the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

High-accuracy positioning plays an important role in future 5G-Advanced cellular networks. However, it is quite challenging to utilize 5G signals to estimate positioning parameters accurately under multipath environments. To establish a high-precision real-time location system (RTLS), which is suitable for indoor scenarios, advanced parameter estimation techniques with low computational complexity should be developed. This paper proposes a modified subspace-based time-of-arrival (TOA) estimation algorithm for 5G signals with ultra-high accuracy and reduced complexity under multipath environments. A novel smoothing scheme termed as grouped subcarrier smoothing (GSS) is proposed to reduce the dimension of the covariance matrix involved in typical subspace-based methods. Then, the computational complexity of the corresponding eigenspace calculation is reduced. The TOA estimation performance is enhanced by constructing multiple snapshots of the estimated channel frequency response vector in the frequency domain. Finally, the super-resolution TOA estimate can be obtained using only one orthogonal frequency division multiplexing (OFDM) symbol. Simulation results show that the proposed method achieves centimeter-level TOA estimation accuracy under multipath channels when the signal-to-noise ratio (SNR) is high. [ABSTRACT FROM AUTHOR]

The synchrosqueezing transform (SST) is an advanced post-processing method to sharpen the time–frequency representation (TFR). However, it still processes the signal in frequency domain. Therefore, it cannot effectively analyze signals whose energy is not well concentrated in frequency domain. The fractional S-transform (FrST) inherits the merits of the short-time fractional Fourier transform and the continuous wavelet transform, processing signals in fractional frequency domain. In this paper, a novel non-stationary signal processing tool, synchrosqueezing fractional S-transform (SSFrST) has been proposed, which combines the advantages of SST and FrST. First, we introduce a novel FrST and derive its fundamental properties. Second, based on the novel FrST, we propose SSFrST and discuss its reconstruction formula and implementation. It can not only improve time–frequency resolution, but also process signals in the time-fractional–frequency plane. Finally, we provide several applications to validate the effectiveness of our methods, including chirp signal parameters estimation, signal separation, filtering and noise separation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of robust estimation of parameters of a 1-dimensional chirp signal model. We propose regression quantile estimators (RQE) for parameter estimation and establish asymptotic theoretical properties of the RQE. We establish that the RQE are strongly consistent estimators and also derive their asymptotic normal distribution. We perform extensive simulation studies and real signal analysis to access the performance of the proposed estimators and also to empirically validate the theoretical asymptotic results. We also present performance of RQE at different signal-to-noise ratio levels. It is observed that the RQE provide robust estimators when the noise distribution is heavy tailed and when outliers are present in the data. It is also observed that the performance of the RQE is much better than the least squares estimators. Real signal analysis provides evidence of practical applicability and usefulness of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper focuses on iterative parameter estimation methods for a nonlinear closed-loop system (i.e., a nonlinear feedback system) with an equation-error model for the open-loop part. By applying negative gradient search, a gradient-based iterative algorithm is constructed. To reduce the computational costs and improve the parameter estimation accuracy, the hierarchical identification principle is employed to derive a hierarchical gradient-based iterative algorithm. A simulation example is provided to test the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, an unambiguous two-dimensional (2D) direction of arrival (DOA) estimation algorithm based on a large-space L-shaped array is proposed. The proposed L-shaped array is composed of two large-space linear arrays. Each linear array consists of two uniform linear arrays with internal element spacing being larger than half wavelength of incident signal. Firstly, an unambiguous modified estimation of signal parameter via rotational invariance techniques (ESPRIT) algorithm is proposed to estimate the elevation angles. Then, using the estimated elevation angles, automatically matched azimuth angles can be estimated. On account of the adjustable element spacing, the proposed array is robust to mutual coupling effect. Moreover, simulation results can prove that the proposed algorithm has higher estimation accuracy than many similar 2D DOA estimation algorithms based on L-shaped array. [ABSTRACT FROM AUTHOR]

The multipath effect error (MEE) is typically not taken into account by the RTKLIB localization method, and this may lead to poor positioning accuracy. This paper proposes an expectation maximization (EM) algorithm for GPS positioning based on Volterra series, and the pseudoranges contaminated by MEE are considered as missing data. Firstly, the Volterra series is introduced to linearize the pseudorange equation. Then, the EM algorithm is used to iteratively update the user location and missing data. Compared with the RTKLIB method, the proposed algorithm has more accurate positioning accuracy. The simulation example shows the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Coherently Distributed (CD) sources are suitable for practical direction-of-arrival (DOA) estimation in massive Multiple-Input Multiple-Output (MIMO) communication systems. However, massive MIMO systems employ a large number of antennas to improve performance, which significantly raises the complexity of conventional DOA estimation algorithms for CD sources. To reduce the complexity, a novel low-complexity CD unitary estimation of signal parameters via the rotational invariance technique (U-ESPRIT) algorithm based on discrete cosine transformation (DCT) beamspace transformation and multistage Wiener filter (BU-ESPRIT) is proposed in this paper. To concentrate the signal energy and make better use of beamspace features, the DCT transformation is used to extract the signal. For the sake of reducing the complexity and achieving accurate angle estimation, U-ESPRIT is performed in beamspace. Moreover, the covariance matrix matching process and eigenvalue decomposition of the covariance matrix are substituted by forward recursion of the multistage Wiener filter to further reduce the complexity of the proposed algorithm. Theoretical analysis indicates the computational superiority of the proposed algorithm over that of some existing algorithms. Simulation results demonstrate that the proposed algorithm can be utilized to efficiently estimate angles of CD sources in massive MIMO systems. [ABSTRACT FROM AUTHOR]

The dictionary grid mismatch problem in sparse processing is an important factor affecting parameter reconstruction. The existing grid correction algorithms are limited by the initial grid division and the accurate estimation of the support set vector. Furthermore, these methods fail if multiple scattering points fall into the same grid interval. In this paper, a constrained inhomogeneous grid optimization sparse processing algorithm is proposed. The proposed method includes two sub-processes, namely initial grid optimization and the support set vector correction. The optimization of the initial grid is to use the idea of the coordinate descent method to iteratively generate an updated grid vector, which is used for the inhomogeneous fission of the grid around the target from coarse to dense. Moreover, under the constraint of dictionary atom maximum correlation, multiple scattering points are separated in different grids, which improves the search accuracy of support set atoms. The correction process of the support set vector is to use the first-order Taylor expansion of the dictionary grid to linearly approximate the real parameters of the target, to achieve adaptive correction of dictionary mismatched atoms. According to the simulation experiment of the frequency agile radar scenario, the proposed algorithm can achieve higher range-Doppler parameter joint estimation accuracy in the multi-scattering point scenario in comparison with the conventional sparse recovery algorithm and grid point correction algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose a parameters estimation method for three-dimensional (3-D) mixed far-field and near-field sources based on nonuniform cross tripole array where location and polarization estimates are considered. By designing several special fourth-order cumulants and making use of the shift-invariant properties in cumulant domain, the 2D-DOA and polarization information at five known tripoles are captured. With the 2D-DOA estimates, a matrix equation is derived to classify the source type and determine the coarse locate estimates. Then, the coarse parameters estimates can be used as references for disambiguating the cyclically ambiguous estimates to obtain the high accuracy estimation of 2D-DOA and range. Compared with the existing methods, The proposed one can separate and locate the mixed sources in 3-D space with the priori knowledge of only five sensors' positions. Moreover, it does not restrict the array sensors to be uniformly placed with inter-element spacing no more than a quarter or one-eighth wavelength, and thus, the array aperture can be extended by extending the inter-sensor spacing. Additionally, requirements for the placement of five known tripoles are analyzed. Numerical results show that the proposed algorithm achieves high parameter estimation accuracy. [ABSTRACT FROM AUTHOR]

This paper considers the identification problem of the linear continuous time-delay systems. By using the multi-frequency responses, a stochastic gradient gradient-based iterative (SG-GI) algorithm is derived. The proposed algorithm can estimate the unknown parameters and the unknown time delays simultaneously. To improve the parameter estimation accuracy of the SG-GI algorithm, a multi-innovation stochastic gradient gradient-based iterative (MISG-GI) algorithm is derived by using the multi-innovation identification theory. In addition, a forgetting factor is introduced to increase the parameter estimation accuracy. The resulting algorithm is called the multi-innovation forgetting gradient gradient-based iterative (MIFG-GI) algorithm. The effectiveness of the proposed strategies is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

The traditional identification algorithms are generally based on the quadratic criterion functions and perform well under the interference of Gaussian noise. However, their performances become worse when non-Gaussian impulsive noise is encountered in practical situations. By introducing the maximum correntropy criterion and utilizing its robustness against outliers, this paper develops a robust recursive algorithm for the linear parameter-varying system with the non-Gaussian noise. The algorithm is not only simple and easy to implement, but also can resist the negative influence of the non-Gaussian noise. Moreover, a maximum correntropy criterion-based robust hierarchical algorithm is presented to increase the calculative efficiency. Three simulation examples are provided to demonstrate the validity of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper focuses on the parameter estimation problem of Hammerstein nonlinear systems with colored noise. By virtue of the covariance matrix adaptation strategy and the auxiliary model identification idea, an auxiliary model-based covariance matrix adaptation (AM-CMA) identification algorithm is presented. Furthermore, for the purpose of improving the optimization efficiency of the AM-CMA algorithm, we introduce the gradient search into the AM-CMA algorithm and propose an auxiliary model-based covariance matrix and gradient search adaptation (AM-CMGA) identification algorithm. The proposed algorithms are efficient and can give satisfactory parameter estimation results. The proposed algorithms are efficient and can give satisfactory parameter estimation results. The simulation examples are provided to demonstrate the effectiveness of our approaches. [ABSTRACT FROM AUTHOR]

This paper intends to apply a new mathematical approach based on Riemann–Liouville fractional–differential operator to the design of fractional-order digital differentiators (FODDs). Under the research area of fractional-order calculus, Grünwald–Letnikov (GL) and Riemann–Liouville (RL) are most widely used fractional–differential operators. The GL-based methods have been extensively investigated by research community to design FODD, but there seems to be an improvement window for designing FIR filters based upon RL fractional–differential operator. Therefore, this paper establishes a generalized framework for the design of RL-based FODD (RL-FODD) and compares its performance with well-established GL-FODD designs, based upon their ability to yield ideal frequency response of FODD. Initially, closed-form analytical expression is formulated for computing FIR filter coefficients of RL-FODD. Then, the design accuracy of proposed filter in the high-frequency region is improved by incorporating non-integer sample delay into the design process. Several design examples are presented to illustrate the comparative analysis between conventional GL-FODD and proposed RL-FODD for varying fractional orders. The proposed method is evaluated, taking into account several amplitude-modulated and harmonic signals corrupted by AWGN and high-frequency chirp noise. Furthermore, the application in parameter estimation of fractional noise process is investigated. Compared with conventional GL-FODD, results of the proposed study validate its superiority and robustness based upon various experimental simulations. [ABSTRACT FROM AUTHOR]

This paper addresses both the problems of identification and state estimation of the class of nonlinear fractional systems. Using the combined state and parameter estimation approach, a new method of estimation serving to estimate simultaneously the unknown parameters, the unknown fractional orders and the inaccessible states, is proposed for the discrete fractional-order Wiener systems. The principle is that the estimation of the states uses the estimates of the parameters and the identification of the parameters utilizes the estimated states. By minimizing the defined criterion, which is non-convex and nonlinear in the parameters, the model parameters are firstly identified using the recursive least squares. Then, the fractional orders are determined with the Levenberg–Marquardt algorithm. Next, the estimates of the parameters and the orders will be used to estimate the immeasurable states based on the extended Luenberger observer. To prove the consistence of the proposed algorithm, a complete convergence analysis is developed. Finally, the effectiveness of the suggested method is illustrated in simulation examples. [ABSTRACT FROM AUTHOR]

This paper presents an effective angular parameter estimation method based on the manifold separation technique (MST) for incoherently distributed sources, named as MST-ID algorithm. In the proposed method, at first, a mathematical model is established through the first-order Taylor expansion of the steering vector, in which the nominal direction of arrival (DOA) can be decoupled from the angular spread. Then, the decoupled steering vector is divided into two sub-steering vectors with equal dimensions, and further the nominal DOA is estimated by the shift invariant structure between the sub-steering vectors. Finally, the MST is used to separate the antenna array structure from the nominal DOA in the array steering vector, such that the signal covariance matrix can be easily obtained according to the antenna array structure and the estimated nominal DOA. On this basis, a spectrum search function is given to estimate the angular spread. Compared with the previous works, the presented method can not only improve the angular parameter estimation accuracy but also be suitable for arbitrary line array structures. Theoretical analysis and simulation results confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Statistical properties of signals play an essential role in designing algorithms for Direction of Arrival (DoA) estimation. Many times, signals are assumed to be circular, and circular moments are used thereof. Practically, non-circular signals exist and provide extra statistical information in terms of pseudo/non-circular moments/cumulants which can be used to improve the performance of any parameter estimation algorithm. This paper uses the 2qth-order non-circular cumulants along with circular cumulants to solve the underdetermined non-Gaussian non-circular system. A generalized method based on higher-order non-circularity has been proposed to design the physical array such that the corresponding virtual array provides the larger degree of freedoms than existing arrays. The weight function, an important metric, to measure the stability of the corresponding virtual array, has also been evaluated analytically. Numerical simulation demonstrates performance gain due to the proposed array structure. [ABSTRACT FROM AUTHOR]

The traditional least squares (LS) and gradient descent (GD) algorithms can estimate the parameters of the regression models. They can be inefficient when the models have complex structures: (1) the unknown parameters in the information vector make the algorithm be impossible to update the parameters; (2) the zigzagging nature of the gradient descent algorithm and the complex structures lead to slow convergence rates; and (3) the step-size and derivative function calculations may be unsolvable for complex nonlinear models. This paper proposes two kinds of algorithms for exponential nonlinear models. The first is the two-stage algorithm, which decomposes the complex model into a linear part and a nonlinear part, where the linear part is estimated using the LS algorithm and the nonlinear part is identified based on the GD algorithm. The second is the particle swarm optimization algorithm which can simultaneously obtain all the parameters. To increase the convergence rates, the Aitken method is also introduced. The simulation results demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper considers a single-input single-output linear dynamic system, whose input and output are corrupted by Gaussian white measurement noises with zero means and unknown variances; the parameter estimation of such a system is a typical errors-in-variables (EIV) system identification problem. This paper proposes the correlation function-based two-step identification methods for the EIV systems. In order to obtain the unbiased parameter estimates of the EIV system, we derive the correlation function equation by using the correlation analysis method and adopt the least squares method and the instrumental variable method to recursively compute the parameter estimates of the model, resulting in the unbiased parameter estimates of the EIV systems. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we present some options to deal with the problem of parameter estimation in continuous-time stochastic systems under white, and coloured noise perturbations using classical methods. Least-squares method (LSM) is one of the most widely used estimation methods, in continuous and discrete time systems, but it presents a bias problem. The instrumental variable method (IV), even though is considered the best option when a noise is present in the system dynamics, cannot completely minimize its effect in continuous time. Here, we propose to combine these algorithms with two auxiliary techniques: the Kalman filter and the equivalent control. These techniques working in parallel with the LSM and IV estimation algorithm will reduce the bias, the noise effect in the estimated parameters, and are very easy to implement. The effectiveness of the proposed methods is illustrated in a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, a two-dimensional direction-of-arrival (DOA) estimation algorithm based on nested acoustic vector-sensor (AVS) array is introduced. The minimum unit interval of the used nested AVS array is integral multiple of half-wavelength of signal. Firstly, four selection matrices are used to recombine four received vectors, by which four special cross-covariance matrices are obtained to form an extended block covariance matrix. Then, a set of parameters on elevation angles are estimated by traditional estimation of signal parameter via rotational invariance technique (ESPRIT) algorithm. Using these parameters, unambiguous elevation angles can be obtained without spectral peak search and added eigenvalue decomposition. At last, using the estimated elevation angles, the azimuth angles can be estimated by array manifold matching algorithm. The proposed algorithm can distinguish more signals than some existing ESPRIT algorithms. Many simulation results can prove the performance of the proposed algorithm in improving the accuracy of DOA estimation. Simulation results also show that the unit interval of optimal nested AVS array should be larger than half-wavelength of received signal. [ABSTRACT FROM AUTHOR]

Entropy has been widely applied in system identification in the last decade. In this paper, a novel stochastic gradient algorithm based on minimum Shannon entropy is proposed. Though needing less computation than the mean square error algorithm, the traditional stochastic gradient algorithm converges relatively slowly. To make the convergence faster, a multi-error method and a forgetting factor are integrated into the algorithm. The scalar error is replaced by a vector error with stacked errors. Further, a simple step size method is proposed and a forgetting factor is adopted to adjust the step size. The proposed algorithm is utilized to estimate the parameters of an ARX model with random impulse noise. Several numerical solutions and case study indicate that the proposed algorithm can obtain more accurate estimates than the traditional gradient algorithm and has a faster convergence speed. [ABSTRACT FROM AUTHOR]

Signal modeling is an important technique in many engineering applications. This paper is concerned about signal modeling problem for the sine multi-frequency signals or periodic signals. In terms of different characteristics between the signal output and the signal parameters, a separable modeling scheme is presented for estimating the signal parameters. In order to seize the real-time information of the signals to be modeled, a sliding measurement window is designed for using the observations dynamically and implementing accurate parameter estimates. Because the amplitude parameters are linear with respect to the signal output and the angular frequency parameters are nonlinear with respect to the signal output, the signal parameters are separated into a linear parameter set and a nonlinear parameter set. Based on these separable parameter sets, a nonlinear optimization problem is converted into a combination of the optimization quadric and the nonlinear optimization. Then, a separable multi-innovation Newton iterative signal modeling method is derived and implemented to estimate sine multi-frequency signals and periodic signals. The simulation results are found to be effective of modeling dynamic signals. For the reason that the proposed method is based on dynamic sliding measurement window, it can be used for online estimation applications. [ABSTRACT FROM AUTHOR]

In this paper, an idea from the quasi-maximum-likelihood (QML) algorithm has been applied to estimation of the direction of arrival (DOA) and parameters of the polynomial phase signals (PPS) impinging on the uniform linear array. The algorithm uses a search over a set of possible DOA values. For considered value, the DOA is compensated and resulted signal parameters are estimated using the original QML approach. In this way, several sets of potential estimates are obtained. Optimal DOA and PPS parameters belong to set that maximizes the proposed cost function. In the proposed approach, parameters are estimated using 2-D search over DOA and window widths used for calculation of the short Fourier transform in the QML that is an important advantage with respect to existing strategies like, for example, the polynomial beamformer requiring multi-dimensional or metaheuristic search strategies. Numerical validation of the proposed approach for both mono- and multi-component signals is provided in the paper. Both far- and near-field scenarios are considered. [ABSTRACT FROM AUTHOR]

In this paper, a new array configuration termed as Spread Orthogonal Loop and Dipole (SOLD) array is presented for estimating direction and polarization parameters of multiple incident signals. In the SOLD array configuration, the spacings of any two adjacent SOLD antennas are set to be mutual primes with respect to a half-wavelength. Moreover, the loop is separated far away from the dipole within a single SOLD antenna. This SOLD array configuration thus imposes a significantly less antenna mutual coupling effect. To demonstrate the practical value of the SOLD array, a joint direction and polarization estimation algorithm is developed subsequently. Simulations are carried out to justify the SOLD array in improving parameter estimation accuracy and in reducing the effect of mutual coupling. [ABSTRACT FROM AUTHOR]

Many classic chirp signal processing algorithms may show significant performance degradation when the signal-to-noise ratio (SNR) is low. To address this problem, this paper proposes a pre-filtering method in time-domain based on deep learning. Different from traditional signal filtering methods, the proposed denoising convolutional neural network (DCNN) is trained to recover the pure signal from the noisy signal as much as possible. Following denoising, we use two classic chirp signal parameter estimation algorithms to estimate the parameters of the DCNN output. The simulation results show that, compared with no DCNN processing, the parameter estimation accuracy is significantly improved. This is mainly due to the powerful pure signal extraction ability of DCNN, which can significantly improve the SNR and the accuracy of signal parameter estimation. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient global gravitational search (GGS) algorithm-assisted Kalman filter (KF) design, called a GGS-KF technique, for accurate estimation of the Volterra-type nonlinear systems. KF is a well-known estimation technique for the dynamic states of the system. The best estimate is achieved if the system dynamics and noise statistical model parameters are available at the beginning. However, to estimate the real-time problems, these parameters are unstipulated or partly known. Due to this limitation, the performance of the KF degrades or sometimes diverges. In this work, two steps have been proposed for unknown system identification while overcoming the difficulty encountered in KF. The first step is to optimise the parameters of the KF using the GGS algorithm by considering a properly balanced fitness function. The second step is to estimate the unknown coefficients of the system by using the basic KF method with the optimally tuned KF parameters obtained from the first step. The proposed GGS-KF technique is tested on five different Volterra systems with various levels of noisy (10 dB, 15 dB and 20 dB) and noise-free input conditions. The simulation results confirm that the GGS-KF-based identification approach results in the most accurate estimations compared to the conventional KF and other reported techniques in terms of parameter estimation error, mean-squared error (MSE), fitness percentage (FIT%), mean-squared deviation (MSD), and cumulative density function (CDF). To validate the practical applicability of the proposed technique, two benchmark systems have also been identified based on the original data sets. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of robust adaptive beamforming (RAB) for a linear array in the presence of gain-phase errors. By setting a few calibrated auxiliary elements on one side of a linear array, we propose a novel gain error and phase error estimation algorithm to calibrate gain-phase errors. According to the proposed estimation algorithm, the unknown gain error and phase error are jointly estimated by calculating the eigenvector corresponding to the minimum eigenvalue of the available transitional matrices. Furthermore, we calibrate the received data and compensate for the nonwhite noise caused by the calibration process. Then, the interference-plus-noise covariance matrix (INCM) is reconstructed based on the calibrated steering vector. By incorporating the reconstructed INCM with the minimum variance distortionless response principle, a novel robust adaptive beamformer for a linear array with gain-phase errors is designed. The proposed beamformer can obviously improve RAB performance in a linear array with gain-phase errors. The robustness and superiority of the designed beamformer are demonstrated in simulations. [ABSTRACT FROM AUTHOR]

Some stochastic gradient (SG) algorithms for Hammerstein systems with piecewise linearity are developed in this paper. Due to the complexity of the nonlinear structure, the key term separation is used to transfer the nonlinear model into a regression model, and then, some SG algorithms are proposed for this model. Since the SG algorithm has slow convergence rate, a forgetting factor SG algorithm and an Aitken SG algorithm are provided. Compared with the forgetting factor SG algorithm, the Aitken SG algorithm has smaller variance of estimation error, which means the Aitken SG algorithm is more effective. Two simulation examples are provided to show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Due to the sparse multipath characteristic of the channel, millimeter wave (mmWave) channel estimation can be treated as a sparse signal recovery problem. By exploiting the channel sparse characteristics with compressive sensing (CS) theory, sparse signal recovery algorithms can be used for channel estimation. Orthogonal matching pursuit (OMP) algorithm is one of the most popular CS reconstruction algorithms. Hence, in this paper, we present OFDM-based mmWave sparse indoor channel estimation using the OMP algorithm. However, the computational effort for OMP remains high, even for problems of moderate size in real-time applications. Hence, a new VLSI architecture for mmWave channel estimation using the OMP algorithm is designed and simulated using Xilinx 15.4 Vivado HLS simulator in this paper. Our empirical results illustrate the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

The problem of DOA and polarization parameter estimation is considered in this paper from a perspective of sparse reconstruction. We present a novel off-grid hierarchical block-sparse Bayesian method for DOA and polarization parameter estimation to improve the estimation accuracy. Firstly, an off-grid model is formulated via the first-order Taylor expansion of the source steering vector. Then, a block-sparse vector is constructed based on sparse Bayesian inference, on which a two-layer hierarchical prior is imposed to promote block sparsity and internal sparsity simultaneously. Finally, the variables and model parameters are updated alternately by adopting the variational Bayesian approximation. In addition, the Cramer–Rao bound for DOA and polarization estimation, the convergence property and the computational complexity analysis of the proposed method are derived. Compared with the existing sparse reconstruction methods and the traditional subspace-based methods, the proposed method can achieve higher estimation accuracy. Simulation results demonstrate the effectiveness and notable performance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper develops a bias correction-based recursive estimation algorithm for dual-rate output-error systems. The system output is subjected to both output noise and sampling noise. Using the polynomial transformation technique, the dual-rate output-error system is converted into an identification model where the sampled data can be directly applied. The noise variances of output noise and sampling noise are estimated by solving a nonlinear equation, which can minimize the estimation errors of noise variances. The simulation examples demonstrate that the proposed algorithm has higher parameter estimation accuracy in contrast to the auxiliary model-based recursive least-squares algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the modeling problem of the multi-frequency signals which contain many different frequency components. Based on the Newton search and the measured data, a Newton recursive parameter estimation algorithm is developed to estimate the amplitude, the angular frequency and the phase of a multi-frequency signal. In order to improve the performance of the identification algorithm, a convergence factor is introduced in the Hessian matrix of the developed Newton recursive method. The numerical examples verify that the proposed algorithm is effective for modeling the multi-frequency sine signals. [ABSTRACT FROM AUTHOR]

The Wiener nonlinear system is composed of a linear dynamic subsystem in series with a static nonlinear subsystem. This type of system is widely found in the petroleum, chemistry, thermal and other process industries. It is of great significance to obtain the parameter estimates of the Wiener systems. This paper studies the identification problem of the Wiener time delay nonlinear system. Based on the gradient search principle, a stochastic gradient identification algorithm and a gradient-based iterative identification algorithm are derived. Furthermore, a linearly decreasing weight particle swarm iterative identification algorithm is also proposed for the discussed Wiener time delay systems. Finally, a numerical example and two application cases are given for validating the feasibility of the three identification methods. The results demonstrate that the three algorithms can identify the unknown parameters of the Wiener model effectively. Moreover, the linearly decreasing weight particle swarm iterative identification algorithm behaves much better than the stochastic gradient and the gradient-based iterative algorithms in accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

Long-time coherent integration can remarkably improve the detection and motion parameter estimation ability of radar for maneuvering targets. Unfortunately, the linear range migration, quadratic range migration (QRM), and Doppler frequency migration (DFM) within the coherent processing interval seriously degrade the target detection and parameter estimation performance. In this regard, a novel coherent integration approach based on frequency autocorrelation function (FAF) and Lv's distribution (LVD), i.e., FAF–LVD, is proposed in this paper. The QRM is firstly removed by the second-order keystone transform. Then, the FAF with a variable delay is introduced to remove the DFM, followed by the scaled Fourier transform to achieve coherent integration. Finally, the acceleration and velocity are estimated simultaneously by LVD. Analysis demonstrates that FAF–LVD could be efficiently implemented via complex multiplications, the fast Fourier transform (FFT) and inverse FFT. Detailed comparisons with several representative methods indicate that FAF–LVD achieves a better balance among computational complexity, detection ability, and parameter estimation performance. Extensive simulations are presented to validate the effectiveness of FAF–LVD method. [ABSTRACT FROM AUTHOR]

This paper proposes parameter estimation algorithms for Hammerstein nonlinear ARX systems. By making full use of the current and previous input–output data of the system, a weighted multi-innovation stochastic gradient algorithm is presented to improve the convergence rate of identification. The innovation term in the traditional identification algorithms can be treated as a particle in the particle-filtering technique, and the weight of each innovation then can be computed according to their importance. The simulation results indicate that the algorithm can improve the accuracy of parameter estimation. [ABSTRACT FROM AUTHOR]

Model parameter estimation and controller tuning of the nonlinear clarification process are primary issues in the sugar industry. This paper proposes a Lagrangian-based state transition algorithm (LSTA) for controlling the clarification process and identifying the model parameters. First, the standard system identification procedure is used to estimate the model parameters for the clarifier. Then, the LSTA is used to enhance the accuracy of the identified system parameters. Once a suitable model is obtained, the proposed LSTA is used to fine-tune the optimal controller parameters off-line. We choose two types of evolutionary algorithms for comparison to show the efficacy of the proposed design. The results of the simulations indicate that the proposed controller achieves optimum transient and tracking performance in all cases. For fast convergence and the ability to provide the global optimum when estimating the modeling and controller parameters, the LSTA performance was found to be superior to that of the other algorithms. [ABSTRACT FROM AUTHOR]

Direct position determination (DPD) methods are known to outperform classical two-step localization methods under the condition of low signal-to-noise ratios and/or small number of snapshots. Additionally, they can directly exploit the prior knowledge of signal waveforms to achieve higher estimation accuracy. In this paper, we concentrate on the DPD method for locating multiple constant modulus (CM) sources based on a single moving receiving station. Both direction of arrival and Doppler frequency shift are used for source localization. First, a received array signal model with a small time delay that can incorporate the Doppler frequency information is formed. Subsequently, the corresponding maximum likelihood estimation criterion is established. An effective alternating minimization algorithm is developed to solve the optimization problem. Subsequently, we also derive the Cramér–Rao bound expressions for parameter estimation. It is proved that the CM property of the signals is useful in reducing the lower bound for location estimation. Simulation results demonstrate that the proposed method is asymptotically efficient. Moreover, it is also shown that the estimation accuracy of direct localization can be greatly increased if the CM characteristics of the radiated signals are adequately exploited. [ABSTRACT FROM AUTHOR]

A new multicomponent multitone amplitude and frequency-modulated signal model for parametric modelling of speech phoneme (voiced and unvoiced) is presented in this paper. As the speech signal is a multicomponent non-stationary signal, the Fourier–Bessel expansion is used to separate all individual components from the multicomponent speech signal. The parameter estimation is done by analysing the amplitude envelope (AE) and instantaneous frequency (IF) of the signal component separately. The AE and IF functions for separated components are extracted by using the discrete energy separation algorithm. The amplitude-modulated signal parameters and the amplitude of the signal are estimated by analysing the AE function, whereas the frequency-modulated signal parameters and the carrier frequency of the signal are estimated by analysing the IF function. This technique is found to be quite efficient for accurate parameter estimation of the speech phoneme. As an illustration of model-based speech processing, the proposed model is used for various speech signal processing applications. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of fault estimation and fault-tolerant control for a class of Markovian jump systems with mode-dependent interval time-varying delay and Lipschitz nonlinearities. In this paper, a new adaptive fault observer is designed to solve the problem of fault estimation. The proposed observer can estimate the states and faults simultaneously, whether faults are of time-varying or constant characterization. Based on the fault estimation, a fault-tolerant controller is designed to stabilize the closed-loop system. Sufficient conditions for the existence of the observer gain and fault-tolerant controller gain are got by a set of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the proposed fault-tolerant control method. [ABSTRACT FROM AUTHOR]

This paper takes an Alpha-stable distribution as the noise model to solve the parameter estimation problem of bistatic multiple-input multiple-output (MIMO) radar system in the impulsive noise environment. For a moving target, its echo often contains a time-varying Doppler frequency. Furthermore, the echo signal may be corrupted by a non-Gaussian noise. It causes the conventional algorithms and signal models degenerating severely in this case. Thus, this paper proposes a new signal model and a novel method for parameter estimation in bistatic MIMO radar system in the impulsive noise environment. It combines the fractional lower-order statistics (FLOS) and fractional power spectrum density (FPSD), for suppressing the impulse noise and estimating parameters of the target in fractional Fourier transform domain. Firstly, a new signal array model is constructed based on the $$\alpha $$ -stable distribution model. Secondly, Doppler parameters are jointly estimated by peak searching of the FLOS-FPSD. Furthermore, two modified algorithms are proposed for the estimation of direction-of-departure and direction-of-arrival (DOA), including the fractional power spectrum density based on MUSIC algorithm (FLOS-FPSD-MUSIC) and the fractional lower-order ambiguity function based on ESPRIT algorithm (FLOS-FPSD-ESPRIT). Simulation results are presented to verity the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the parameter estimation problem of dual-frequency signals disturbed by stochastic noise. The signal model is a highly nonlinear function with respect to the frequencies and phases, and the gradient method cannot obtain the accurate parameter estimates. Based on the Newton search, we derive an iterative algorithm for estimating all parameters, including the unknown amplitudes, frequencies, and phases. Furthermore, by using the parameter decomposition, a hierarchical least squares and gradient-based iterative algorithm is proposed for improving the computational efficiency. A gradient-based iterative algorithm is given for comparisons. The numerical examples are provided to demonstrate the validity of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper is concerned with the identification problem for multivariable equation-error systems with autoregressive moving average noise using the hierarchical identification principle and the multi-innovation identification theory. We propose a hierarchical gradient-based iterative (HGI) identification algorithm and give a gradient-based iterative (GI) identification algorithm for comparison. Meanwhile, the multi-innovation theory is used to derive the hierarchical multi-innovation gradient-based iterative (HMIGI) identification algorithm. The analysis shows that the HGI algorithm has smaller computational burden and can give more accurate parameter estimates than the GI algorithm and the HMIGI algorithm can track time-varying parameters. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a novel method, which employs the fractional Fourier transform and the Sigmoid transform, is proposed to estimate parameters of the linear frequency modulation (LFM) signal under the alpha stable distribution noise environment. Two novel functions, Sigmoid fractional correlation function and Sigmoid fractional power spectrum density (Sigmoid-FPSD), are defined. Basing on these two definitions, a novel method based on Sigmoid-FPSD under alpha stable distribution noise is proposed to estimate parameters of the LFM signal. Moreover, boundedness of Sigmoid-FPSD to the S α S noise and the feasibility analysis of the Sigmoid-FPSD are presented to evaluate the performance of the proposed method. Both theoretical analysis and simulations demonstrate the superior performances of the proposed approach over other existing methods. Furthermore, the proposed method does not need a priori knowledge of noise with higher estimation accuracy in alpha stable distribution noise environment. [ABSTRACT FROM AUTHOR]

This paper proposes an Aitken-based stochastic gradient algorithm for ARX models with time delay. By using the redundant rule, the ARX model can be transformed into an augmented model. Based on the Aitken method, the parameters of the augmented model can be estimated, and then, the unknown parameters of the ARX model and the time delay can be computed. The performance of the Aitken-based stochastic gradient algorithm is then analyzed. Furthermore, a numerical example and a real system example are provided to show the effectiveness of the proposed algorithm. Compared with the traditional stochastic gradient algorithm, the Aitken-based stochastic gradient algorithm achieves better convergence performance that the parameter estimation errors converge below 3% in both examples after 400 steps. [ABSTRACT FROM AUTHOR]

This paper considers the parameter estimation problem of stochastic systems (i.e., controlled autoregressive systems) by adopting the projection method and the hierarchical identification principle. To improve the performance of the projection identification algorithm, a generalized projection algorithm is proposed by introducing a data window length. By means of the hierarchical identification principle, we divide the system into two fictitious subsystems and derive a two-stage generalized projection identification algorithm. The simulation example tests the effectiveness of the proposed identification algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose an approximate Kalman filter of measurements following Student's t-distribution by using the variational Bayes approach. This approach can decompose the estimation of multivariate parameters into a univariate estimation. The recursive formula for the approximate posterior densities of parameters and states is derived in detail. Then, the asymptotic Bayesian Cramer–Rao lower bounds are derived for the proposed filter. Numerical simulations verify both the performance of the proposed filter and the variance lower bounds under time-varying noise. The efficiency of the proposed filter is also demonstrated in a real application, namely an integrated strapdown inertial navigation system/Doppler velocity log shipborne test for navigation. [ABSTRACT FROM AUTHOR]

Underdetermined reverberant audio-source separation is an important issue in speech and audio processing. To solve this problem, many separation algorithms have been proposed, in which model parameter estimation is performed in the time–frequency domain, leading to permutation ambiguity and poor separation performance. Additionally, in the existing expectation–maximization (EM) algorithms, one of the crucial problem is that updating the model parameters at each iterative step is time-consuming. In this paper, we present an improved EM algorithm that combines nonnegative matrix factorization (NMF) and time differences of arrival (TDOA) estimation, avoiding the time consumption by properly selecting initial values of the EM algorithm. In the proposed algorithm, NMF source model is used to avoid the permutation ambiguity problem, and acoustic localization can be achieved by transforming the TDOA. Then, model parameters are updated to obtain better separation results. Finally, the source signals are separated using Wiener filters. The experimental results show that compared with existing blind separation methods, the proposed algorithm achieves better performance on source separation. [ABSTRACT FROM AUTHOR]

This paper presents a new nonlinear output and virtual error feedback control technique for stabilization of switched uncertain nonlinear systems using a continuous differentiable nonlinear feedback function (NFF). The merits of the proposed method are threefold: (i) there is no assumption that the switching signals must satisfy the (average) dwell time, (ii) the feedback amplitude self-adjusts under different state levels to guarantee better dynamic performance using the NFF, and (iii) the number of parameters that needs online tuning is 1, i.e., the proposed control method is computationally inexpensive. Moreover, the closed-loop signals are kept bounded using the rigorously proved Lyapunov and Invariant-set theorems, and the output signal converges to a sufficiently small region around zero by choosing proper design parameters. Finally, simulation and comparative results are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]