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Abstract Recently, adaptive filtering algorithms have attracted much more attention in the field of signal processing. By studying the shortcoming of the traditional real‐valued fixed step size adaptive filtering algorithm, this paper proposed the novel approach to adaptive filtering with variable step size based on Sigmoid function and geometric algebra (GA). First, the proposed approach to adaptive filtering with variable step size based on geometric algebra represents the multi‐dimensional signal as a GA multi‐vector for the vectorization process. Second, the proposed approach to adaptive filtering with variable step size based on geometric algebra solves the contradiction between the steady‐state error and the convergence rate by establishing a non‐linear function relationship between the step size and the error signal. Finally, the experimental results demonstrate that the proposed approach to adaptive filtering with variable step size based on geometric algebra achieves better performance than that of the existing adaptive filtering algorithms.

Abstract This study suggests a dynamic current cut‐off frequency‐based pole‐zero cancellation speed controller for permanent magnet synchronous motors (PMSMs). The proposed self‐tuning algorithm automatically increases the current cut‐off frequency during only the transient periods and restores it as approaching the steady‐state operation. The outer loop control injects the active damping effect, resulting in a closed‐loop order reduction by pole‐zero cancellation from the particularly structured feedback gain. These two benefits contribute to the following advantages: (a) lowering the steady‐state current cut‐off frequency to improve the relative stability margin and (b) securing the capability of assigning the desired cut‐off frequency to both the inner and outer loops in the first‐order low‐pass filter form. A 500‐W PMSM experimental prototype platform confirms the effectiveness of the proposed controller.

Abstract This paper is concerned with the recursive fusion estimation‐based mobile robot localization (RL) problem by employing multiple energy harvesting sensors (EHSs). In the addressed RL problem, multiple sensors with energy harvesting capacity are deployed to produce measurements used for RL. When the sensors own sufficient energy, the sensors can output measurements and then send them to the corresponding local filter. Otherwise, the sensor energy‐induced missing measurement phenomenon will occur. In order to obtain the missing measurement rate, at each time instant, the relationship between the totality of the sensor energy and its probability distribution is derived recursively. This paper aims at seeking out a practicable solution to the addressed mobile RL problem. First, in the presence of the sensor energy‐induced measurement missing phenomenon, an upper bound (UB) of the local localization error covariance is recursively acquired. Then, such a derived UB is minimized by suitably devising the desired local filter parameter. Subsequently, the covariance intersection fusion method is adopted to achieve the addressed RL problem. In the end, a simulation is conducted to verify the practicability of the developed RL scheme.

Abstract Magnetic anomaly detection (MAD) is a technique to find ferromagnets hiding in strong and complicated magnetic background. In many practical cases, the targets are very far from the detection sensor, which leads to low signal‐to‐noise ratio (SNR) and high detection difficulty. Most of the current methods determine the existence of target by some approaches based on signal analysis, such as the orthogonal basis function (OBF) and the minimum entropy (ME). However, although these methods consume low resources, the detection performances are not satisfactory enough. In recent years, due to the increase of computer capability, complex methods become applicable in MAD. In this study, a deep neural network (DNN) is adopted to detect the magnetic anomalies. The DNN has shown its better ability to represent natural data in many applications. A feature automatically learned by a DNN from data in the raw form is more effective for detecting target signals and suppressing irrelevant variations. Herein, a convolutional network with residual structure to implement the feature extraction is designed and an MAD method based on it is proposed. Through the semi‐real tests, the proposed method exhibits a strong capability to extract features and shows excellent performances on detection.

Abstract For matrix Lie groups attitude estimation problems with the trouble of unknown/inaccurate process noise covariance, by elaborating the proportion based covariance regulation scheme, this work proposes a novel version of adaptive invariant Kalman filter (AIKF). Invariant Kalman filter (IKF) takes into account the group geometry and can give better results than Euclidean Kalman filters, but it still heavily depends on the accuracy of noise statistics parameters. To ease this constraint, IKF's covariance propagation step is removed and a proportional regulation scheme is elaborated for the proposed AIKF: the feedback of posterior sequence is introduced to construct a closed‐loop structure of covariance propagation, and then a proportional regulator is employed to amplify the feedback and accelerate the convergence of covariance calibration. As the main benefit, implementation of new AIKF does not require the accurate knowledge of noise statistics, which is also the main advantage over IKF. The mathematical derivation of proposed covariance regulation scheme is presented and the numerical simulations of the Lie groups attitude estimation problem are used to certify the filtering performance of the new approach.

Abstract This paper uses the shift‐invariance property of uniform linear array in root‐MUSIC estimator for obtaining signal and noise subspaces by applying multistage Wiener filter (MSWF) procedure. Also, the MSWF root‐MUSIC based on the pseudo‐noise resampling process for estimating the direction of arrival (DOA) of signals is proposed. By this process, a root estimator bank and a corresponding DOA estimator bank are constructed. Then, a hypothesis test is applied to the DOA estimator bank to detect the normal DOA estimators from abnormal DOA estimators called outliers. By averaging the corresponding root estimators of normal DOA estimators, the final DOAs can be determined more accurately. When all the DOA estimators fail to pass the hypothesis test, the criterion based on the Gaussian weight average of the root estimator bank is introduced. By applying this criterion, better outlier‐free performance of MSWF root‐MUSIC can be obtained. Simulations show that our method can improve the DOA estimations, especially in small sample sizes and low signal‐to‐noise ratios.

Abstract This paper conveys attitude and rate estimation without rate sensors by performing a critical comparison, validated by extensive simulations. The two dominant approaches to facilitate attitude estimation are based on stochastic and set‐membership reasoning. The first one mostly utilizes the commonly known Gaussian‐approximate filters, namely the EKF and UKF. Although more conservative, the latter seems to be more promising as it considers the inherent geometric characteristics of the underline compact state space and accounts—from first principles—for large model errors. The set‐theoretic approach from a control point of view is addressed, and it is shown that it can overcome reported deficiencies of the Bayesian architectures related to this problem, leading to coordinate‐free optimal filters. Lastly, as an example, a modified predictive filter is derived on the tangent bundle of the special orthogonal group TSO(3).

Abstract Unmanned aerial vehicles as an important role for 5G and beyond networks are becoming more and more popular and have been equipped with various sensors to enable diverse emerging applications, e.g. locating sound‐emitting targets. Multi‐channel blind source separation algorithm has been applied into the unmanned aerial vehicles and micro aerial vehicles, where underdetermined mixture blind source separation is a challenging problem, i.e. the number of sources is more than the number of microphones. An optimization underdetermined blind source separation algorithm to separate the multi‐channel audio mixture signals recorded by an unmanned aerial vehicle is proposed. In the algorithm, firstly a hierarchical clustering to estimate channel as the mixing matrix initialization is employed, while using direction of arrival permutation algorithm to deal with the permutation alignment and update the mixing matrix using multiplication update method. Then the model parameters are estimated using improved expectation‐maximization update rules for the fast convergence. Finally, the frequency‐domain sources are estimated through Wiener filtering and time‐domain sources are obtained via inverse short‐time Fourier transform. Experimental results covering synthetic and real‐recorded speech source mixtures show that the proposed algorithm achieves better separation results than the state‐of‐the‐art methods.

Abstract Here, a novel off‐grid direction‐of‐arrival (DOA) estimation algorithm for nested arrays in the context of sparse recovery is proposed. The framework of existing off‐grid approaches is to correct the on‐grid parameter with a grid mismatch variable. From another perspective, we treat the direction‐of‐arrival deviation as the steering vector deviation equivalently, and the concept of steering vector uncertainty set is introduced to approximate the desired steering vector. Based on this idea, an optimization problem with respect to the uncertainty set for the purpose of steering vector reconstruction is formulated. After that, phase‐ambiguity resolving and phase‐difference approximation are orderly performed on the optimized uncertainty set to extract the off‐grid direction of arrival. Even though a coarse grid is given, simulation results are presented to demonstrate the performance advantage of the proposed direction‐of‐arrival estimation algorithm compared with several existing approaches.

Abstract A joint analysis method is proposed for source separation from multiple datasets. In this method, sources with the greatest impact on the multiple datasets are identified and then are sequentially separated. The method utilizes the advantage of structure singular value decomposition through a novel approach that extracts only one unified left eigenvector. The Lagrangian multipliers are determined in two steps. In the first step, a projection procedure on optimal subspaces provides dimension reduction through singular value decomposition. In the second step, the number of main sources is automatically derived by minimizing the mean square error between the desired noiseless eigenvalues and estimated eigenvalues of the observations. The results show that the highest accuracy in source separation belongs to the proposed unified left eigenvector (ULEV) method compared to some of most popular approaches including ICA, jICA, MCCA and jICA+MCCA.

Abstract This paper proposes a modified fast off‐grid L1‐SVD (M‐FOGL1SVD) method for direction of arrival (DOA) estimation. Unlike FOGL1SVD, after obtaining the positions of the nonzero rows of the signal sources, the off‐grid overcomplete basis matrix is used to update the signal sources, thus improving the estimation accuracy of it. In addition, to reduce the approximate error of the first‐order off‐grid model, a second‐order off‐grid model is introduced through a further Taylor expansion of the steering vector. Finally, the formula for solving the off‐grid gap under the novel model is derived. Extensive simulation results indicate that the proposed algorithm has better performance than FOGL1SVD in terms of DOA estimation precision.

Abstract When there is the coexistence of uncorrelated and coherent signals in sparse arrays, the conventional algorithms using coarray are fail. In order to solve this problem, the letter proposes a novel method based on compressed sensing. Firstly, the authors vectorize the covariance matrix and establish a sparse representation model through constructing a two‐dimensional redundant dictionary. Then, the authors use an improved orthogonal matching pursuit algorithm for off‐grid sources to recover the sparse vector. Through analysing location of non‐zero elements in sparse vector, the direction‐of‐arrivals of both uncorrelated and coherent signals can be obtained. The proposed method has no strict limitation by the structure of the existing sparse arrays. Moreover, it makes full use of vectorized data and can estimate more number of signals than that of sensors. Numerical experiments prove the effectiveness and favourable performance of the proposed method.

Abstract Most existing Bayesian compressive sensing (BCS) algorithms are developed in real numbers. This results in many difficulties in applying BCS to solve complex‐valued problems. To overcome this limitation, this letter extends the existing real‐valued BCS framework to the complex‐valued BCS framework. Within this framework, the multitask learning setting, where L tasks are statistically interrelated and share the same prior, is considered. It is verified by numerical examples that the developed complex multitask compressive sensing (CMCS) algorithm is more accurate and effective than the existing algorithms for the complex sparse signal reconstructions

Abstract This paper proposes a non‐iterative procedure for flaw(s) characterization based on Pulsed Eddy Current Testing (PECT) signals analysis. The adopted inversion strategy is based on the use of supervised statistical learning algorithms. A numerical forward solver, based on the Finite Integration Technique (FIT), is used for the generation of the training data (the input‐targets couples of the learning algorithm). Predictions are then carried out in almost real‐time using a non‐linear kernel based regression method, known as kernel ridge regression. It turns out that the direct fit of the regression model to the raw PECT signals may lead to poor prediction accuracy due to the large cardinality of PECT signals. To remedy this problem, an adaptive sampling strategy has been adopted in this work. The performance of the proposed methodology is discussed and compared with solutions proposed in the literature.

Abstract Here, agents learn how often to exchange information with neighbours in cooperative multi‐agent systems (MASs) such that their linear quadratic regulator (LQR)‐like performance indices are minimized. The investigated LQR‐like cost functions capture trade‐offs between the energy consumption of each agent and MAS local control performance in the presence of exogenous disturbances, delayed and noisy data. Agent energy consumption is critical for prolonging the MAS mission and is composed of both control (e.g. acceleration, velocity) and communication efforts. Taking provably stabilizing upper bounds on broadcasting intervals as optimization constraints, an online off‐policy model‐free learning algorithm based on least square policy iteration (LSPI) to minimize the cost function of each agent is employed. Consequently, the obtained broadcasting intervals adapt to the most recent information (e.g. delayed and noisy agents' inputs and/or outputs) received from neighbours whilst provably stabilize the MAS. Chebyshev polynomials are utilized as the approximator in the LSPI whereas Kalman filtering handles sampled, corrupted, and delayed data. Subsequently, convergence and near‐optimality of our LSPI scheme are inspected. The proposed methodology is verified experimentally using an inexpensive motion capture system and nano quadrotors.

Abstract In order to reduce the mutual coupling ratio of sparse linear array, a new linear array structure with two sparse uniform linear arrays interleaved nested, is proposed in this paper. The new sparse linear array structure is consisted of two subarrays which have N and M physical sensors, respectively. By setting appropriate interelement spacing and interleaving, the degrees‐of‐freedom, uniform degrees‐of‐freedom and array aperture of the proposed sparse array can reach 2NM+2N, 2(N+2M)+1 and max{(N−1)R1,(M−1)R2+d}, respectively. On one hand, the proposed sparse array has closed‐form expressions for the sensor locations. On the other hand, through comparative analysis, although the proposed array structure has lower uniform degrees‐of‐freedom, it can greatly increase the degrees‐of‐freedom, extend the array aperture, and reduce the mutual coupling ratio between physical sensors, which means better estimation performance of direction‐of‐arrival estimation can be achieved. Finally, the direction‐of‐arrival estimation performance of the proposed array structure is verified by numerical simulations.

Abstract The problem of state estimation for non‐linear systems with unknown inputs is discussed. The objective is to construct a non‐linear filter where the unknown input affects both the state equation and measurement equation. An auto‐calibration Kalman filter is proposed with three stages, where the first and second stages are the extension of the two‐stage Kalman filter in non‐linear system cases, and the third stage is the extended Kalman filter with correlated noise. Compared with the two‐stage extended Kalman filter, the presented algorithm conducts a more reasonable linearization of the measurement equation in the third stage. As a result, auto‐calibration is realized and more accurate and more stable state estimation can be obtained. Simulative and practical examples both demonstrate the validity and superiority of the presented auto‐calibration Kalman filter. Furthermore, positioning experiments illustrate that the auto‐calibration Kalman filter can obtain an accurate long‐term heading estimation in pedestrian navigation and is easy to apply in engineering applications.

Abstract In this study, a novel fast wideband direction of arrival (DOA) estimation algorithm is proposed to reduce the computational complexity. First, a multiple measurement vector (MMV)‐based compact structure for a wideband signal is established. Combined with the focus operation, the array manifolds of different frequency bins are transformed into the dictionary of the reference frequency. Then, two efficient novel methods named adaptive step‐size‐based null space tuning with hard thresholding and feedback (ASNHF) and MMV‐ASNHF are proposed to process single measurement vector and MMV problem, respectively. Finally, wideband DOA estimation can be achieved by MMV‐ASNHF algorithm. Compared with other algorithms, the proposed algorithm has higher accuracy at a low signal‐to‐noise ratio and lower computational complexity. Simulation results show that the proposed estimator is effective and feasible.

Abstract Oscillation method is the most effective approach to determine the inertia properties of rigid bodies. This paper proposes a new signal processing method to determine the moment of inertia (MoI) accurately in the presence of high frictional damping when using a torsion pendulum setup. A mathematical model of damped oscillation is established, and the analytic form of Fourier transformation of the damped torsional oscillation is derived. A formula for calculating the MoI in relation to the dominant frequency and damping ratio is also derived. An algorithm regarding periodic extension and normalization of torsional oscillation signal is proposed to calculate the dominant frequency and damping ratio of torsional oscillation in the frequency domain. The feasibility and accuracy of this algorithm are verified by both numerical simulations and measurement experiments. The experimental results show that the proposed method has good measurement repeatability, and the relative error of measurement is within 0.80%.

Abstract In adaptive filtering applications, the Gaussian distribution cannot be used to model the signal/noise with frequent spikes accurately. In fact, the rational model to simulate the behaviour of such signal/noise is the α‐stable distribution process. In this letter, a fractional‐order complex correntropy algorithm is proposed to deal with the case that both signal and noise processes are modelled as complex‐valued α‐stable signals. Compared with the classical approaches, the proposed fractional‐order complex correntropy extends the Gaussian assumption of signal/noise in the complex domain to the assumption of α‐stable distributions without second‐order and higher order statistical moments. Benefitting from the fractional‐order calculus and correntropy criterion, fractional‐order complex correntropy shows great robustness to the jittery behaviour of complex‐valued α‐stable signal/noise. In addition, a convergence analysis for fractional‐order complex correntropy has been carried out. Simulations on system identification revealed that the filtering performance is significantly improved by using fractional‐order complex correntropy.

Abstract In practical applications, communication emitters are often carried by low orbit satellites aircraft, ships, and other moving carriers. Doppler phenomenon usually exists due to the relative motion between the emitter and the receiver, which seriously affects the identification performance. Given this situation, a method based on the signal vector decomposition and the multi‐feature fusion is proposed. By normalizing and demodulating the target signal, the signal vector diagram is decomposed into four parts. We present a multi‐feature fusion model with varying features extracted from each diagram by a deep learning network. Experimental results show that the proposed method is effective in the presence of Doppler effect.

Abstract A polynomial filtering algorithm is designed for estimating a Markov sequence based on linear measurements. The feature of the estimation problem is that the Markov sequence is described by a nonlinear shaping filter, which is a second‐order polynomial with respect to the state vector components. The algorithm efficiency is illustrated by three examples of navigation data processing. It is shown that the polynomial filter provides accuracy close to the best potential one calculated using the particle filter. At the same time, the amount of computation required to implement this algorithm is much smaller than that for the particle filter. In addition, the polynomial filter provides a consistent calculated accuracy characteristic.

Abstract This paper develops particle filtering for multi‐sensor systems with randomly delayed measurements, where the general case that random delay can be multi‐step rather than one‐step or two‐step is considered. Moreover, different sensors can have different delay steps and delay probabilities. Random delays are assumed to be mutually independent for different sensors and modelled by a separate sequence of random variables obeying discrete distributions. Since random delay leads to the actual measurements being dependent rather than independent given states, and this dependence becomes more complicated with the increase of random delay step, a new formula of the local likelihood density is proposed and then a new weighting scheme is adopted in particle filtering to deal with these difficulties. The proposed method is applied to two examples to testify its effectiveness and superiority.

Abstract Adaptive filtering algorithms are widespread today owing to their flexibility and simplicity. Due to environments in which they are normally immersed, their robustness against noise has been a topic of interest. Traditionally, in the literature it is assumed that noise is mainly active in the reference signal. Since this hypothesis is often violated in practice, recently some papers have advanced strategies to compensate the bias introduced by noisy excitation data. The contributions of this paper are twofold. The first one establishes that, in some conditions, the bias‐compensated least mean square algorithm implements an optimum estimator, in the sense that it presents the smallest variance of the set of unbiased estimators. Since the asymptotic mean‐square performance of this algorithm has not yet been investigated in detail, the second contribution adopts an energy conservation relationship to derive its theoretical steady‐state mean squared distortion. The final result is presented in a closed form, is consistent with simulations and is able to provide important guidelines to the designer.

Abstract The stochastic gradient descent (SGD) method is one of the most prominent first‐order iterative optimisation algorithms, enabling linear adaptive filters as well as general nonlinear learning schemes. It is applicable to a wide range of objective functions, while featuring low computational costs for online operation. However, without a suitable step‐size normalisation, the convergence and tracking behaviour of the stochastic gradient descent method might be degraded in practical applications. In this letter, a novel general normalisation approach is provided for the learning of (non‐)holomorphic models with multiple independent parameter sets. The advantages of the proposed method are demonstrated by means of a specific widely‐linear estimation example.

Abstract To solve the difficult problem of line spectrum detection with a low signal‐to‐noise ratio, a line spectrum extraction algorithm based on a hidden Markov model (HMM) is proposed. The forward–backward algorithm was used to track single and multiple spectral lines in a lofargram, and a new algorithm for the state transition probability matrix was proposed to handle the large amount of HMM calculation and the uncertainty difficulty in processing real signals. Finally, a median fitting algorithm was used to correct the few outlier points in the line spectrum estimation process. Simulation and sea trial data showed that the algorithm had good line spectrum tracking ability for a low signal‐to‐noise ratio.

Abstract The bit error rate (BER) computation for coherently detected orthogonal signals in additive white Gaussian noise requires numerical integration, which can be cumbersome in low‐complexity devices. Here, a BER computation approach that circumvents the need for repeated numerical integration is proposed. First, a low‐complexity BER approximation formula is selected, with unknown parameters to be determined. Second, this letter determines the unknown parameters by fitting the BER approximation to a few BER values known in advance. The BER comparison with the exact results shows that the accuracy of the proposed low‐complexity approach is satisfactory for several constellation sizes of interest. This enables the possibility of BER self‐computation in low‐complexity devices that use orthogonal signals, like those used in the Internet of Things (IoT).

Abstract In multi‐target tracking, sensor with finite resolution generates merged measurements, which means that a group of targets might produce only one measurement, and such phenomenon could lead to degraded tracking performance if it is not considered. The generalised labelled multi‐Bernoulli filter for merged measurement (GLMB‐M) provides a promising solution for such problem. However, the merged measurement likelihood it used was modelled as a Gaussian density with its mean being the uniform weighted mean of the measurements generated by the merging targets. Such uniform weighting strategy might fail if the merged measurements deviate severely from the uniform weighted position due to significant difference of the strengths of the merging targets. To avoid such deviation, an adaptive weighting strategy for estimation of the mean of the merged bearing measurement is proposed, which uses the bearing measurement error to obtain the adaptive weighting factors. Simulation results show that the proposed adaptive weighting strategy outperforms the uniform weighting strategy when the strengths of the targets vary greatly, although both strategies provide similar performance when the strengths of the target are equal.

Abstract Sparse frequency waveform is widely used to suppress the narrowband interferences. The performance that can be achieved with a single waveform is limited. The authors study the approach to design a pair of matching waveforms with low autocorrelation sidelobes and arbitrary frequency stopbands. Two algorithms based on the minimum mean square error (MMSE) between the actual waveform characteristics and the desired waveform characteristics are proposed to deal with this problem. The constrained optimization problem is solved by an alternating iteration method. Numerical experiments show that the proposed algorithms can provide better performance than the existing methods.

Purpose - The purpose of this paper is to study the effectiveness of multiple signals. Specifically, the paper investigates how the individual strength of a marketplace signal varies as a function of whether consumers are exposed to that signal alone or in combination with another signal. Design/methodology/approach - The research uses experimental designs to empirically address the research questions. Hypotheses are formulated primarily based on signaling theory and these hypotheses are tested with laboratory experiments using real consumers. Findings - The key finding is that a signal's stand-alone credibility largely determines whether its individual strength would be diluted or augmented by the coexistence of another signal. Further, when signals with different stand-alone strengths coexist, the individual strength of the weaker signal is higher than when that signal is present alone. These effects are observed in brick-and-mortar and online shopping media. Originality/value - Past research reports mixed findings about whether the individual strength of a signal is diluted (dilution effect) or augmented (augmentation effect) by the presence of another signal. This research attempts to resolve this issue, for the first time, by demonstrating that whether dilution effect or augmentation effect occurs depends on the stand-alone credibility of the individual signals in a mix. [ABSTRACT FROM AUTHOR]

In this article, an analysis of Adleman's experiment and a review of DNA computing applications from a signal-processing point of view are provided. In addition, certain key parts of DNA computing are emphasized, such as the code word design, to which the application of signal processing theory and techniques can offer significant advantages. The goal of this article is to introduce to the signal processing community a new unexplored area of research. [ABSTRACT FROM PUBLISHER]

Today's Internet is a massive, distributed network which continues to explode in size as e-commerce and related activities grow. The heterogeneous and largely unregulated structure of the Internet renders tasks such as dynamic routing, optimized service provision, service-level verification, and detection of anomalous/malicious behavior increasingly challenging tasks. The problem is compounded by the fact that one cannot rely on the cooperation of individual servers and routers to aid in the collection of network traffic measurements vital for these tasks. In many ways, network monitoring and inference problems bear a strong resemblance to other "inverse problems" in which key aspects of a system are not directly observable. Familiar signal processing problems such as tomographic image reconstruction, system identification, and array processing all have interesting interpretations in the networking context. This article introduces the new field of network tomography, a field which we believe will benefit greatly from the wealth of signal processing theory and algorithms [ABSTRACT FROM PUBLISHER]

Over the last decade or so, wavelets have had a growing impact on signal processing theory and practice, both because of the unifying role and their successes in applications. Filter banks, which lie at the heart of wavelet-based algorithms, have become standard signal processing operators, used routinely in applications ranging from compression to modems. The contributions of wavelets have often been in the subtle interplay between discrete-time and continuous-time signal processing. The purpose of this article is to look at wavelet advances from a signal processing perspective. In particular, approximation results are reviewed, and the implication on compression algorithms is discussed. New constructions and open problems are also addressed [ABSTRACT FROM PUBLISHER]