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One technique that is widely used in various fields, including nonlinear target tracking, is the extended Kalman filter (EKF). The well-known minimum mean square error (MMSE) criterion, which performs magnificently under the assumption of Gaussian noise, is the optimization criterion that is frequently employed in EKF. Further, if the noises are loud (or heavy-tailed), its performance can drastically suffer. To overcome the problem, this paper suggests a new technique for maximum correntropy EKF with nonlinear regression (MCCEKF-NR) by using the maximum correntropy criterion (MCC) instead of the MMSE criterion to calculate the effectiveness and vitality. The preliminary estimates of the state and covariance matrix in MCKF are provided via the state mean vector and covariance matrix propagation equations, just like in the conventional Kalman filter. In addition, a newly designed fixed-point technique is used to update the posterior estimates of each filter in a regression model. To show the practicality of the proposed strategy, we propose an effective implementation for positioning enhancement in GPS navigation and radar measurement systems. [ABSTRACT FROM AUTHOR]

The cubature Kalman filter (CKF) based on maximum correntropy criterion (MCC) is robust under non‐Gaussian noises, but it may encounter numerical problems when there are large outliers. First, based on the MCC and weighted least square (WLS) methods, a new cost function is introduced to calculate the state and covariance updates, which can better solve numerical problems caused by large outliers. Then, a nonlinear measurement function is used, and the measurement information is updated through the latest iterative values, which can obtain more accurate results under various non‐Gaussian noises. In addition, the Gauss–Newton, Levenberg–Marquardt, and Quasi–Newton methods are used, and three iterative algorithms named GN‐IMCC‐CKF, LM‐IMCC‐CKF, and QN‐IMCC‐CKF are respectively derived for the updating steps. Compared with the existing algorithms, the simulation results of two classical models show that the proposed algorithms have better numerical stability and estimation accuracy under non‐Gaussian systems. [ABSTRACT FROM AUTHOR]

Summary: The cubature Kalman filter (CKF) based on the maximum correntropy criterion (MCC) has been widely used in the target tracking. However, numerical problems usually occur when there are outliers in the measurement noise. In order to solve the problems of state estimation under the non‐Gaussian measurement noise, a new combined cost function is defined based on the weighted least squares (WLS) method and MCC. In addition, a new method is also used to adaptively adjust the kernel size, then the improved maximum correntropy CKF (PMCCKF) and its corresponding improved maximum correntropy cubature information filter (PMCCIF) are proposed. Compared with the existing algorithms, the new method can not only obtain similar or even better estimation performance, but also avoid numerical problems. Moreover, when the kernel size is infinite, the performance of proposed algorithms will reduce to the standard CKF and corresponding cubature information filter (CIF) respectively, but the classical maximum correntropy CIF (MCCIF) will not, and even the performance is poor in this case. The advantages of the proposed algorithms are verified by four classical nonlinear models. [ABSTRACT FROM AUTHOR]

In ship navigation, the most widely used technology is global navigation satellite systems (GNSS), which provide the ship's position and velocity continuously over a period of time. However, when ships are blocked by port buildings or bridges, the quality of signals received from shipborne GNSS receivers may be reduced, resulting in inaccurate ship positioning that poses a risk to navigational safety. In an occluded environment, the measurement process during the signal processing of shipborne GNSS receivers is nonstationary and prone to measurement anomalies, which can contaminate measurement noise with outliers. To address this problem, a cascaded non-coherent vector tracking loop is designed, with the maximum correntropy Kalman filter serving as a cascaded carrier/code pre-filter for shipborne GNSS receivers. The measurement noise covariance matrix of the pre-filter is adaptively calculated and corrected using the carrier-to-noise ratio and the maximum correntropy criterion, respectively. The algorithm proposed is more sensitive to outliers than the traditional tracking methods and can effectively solve the state estimation problem under the condition of measurement anomalies. Specifically, the algorithm offers ships with more precise position and velocity estimations and lower signal tracking errors than traditional tracking methods under both static and dynamic conditions, as demonstrated by shipboard experiments. The horizontal positioning is increased by 88.4% and the horizontal velocity error is reduced by 62.1% in the occluded environment under dynamic conditions. [ABSTRACT FROM AUTHOR]

One technique that is widely used in various fields, including nonlinear target tracking, is the extended Kalman filter (EKF). The well-known minimum mean square error (MMSE) criterion, which performs magnificently under the assumption of Gaussian noise, is the optimization criterion that is frequently employed in EKF. Further, if the noises are loud (or heavy-tailed), its performance can drastically suffer. To overcome the problem, this paper suggests a new technique for maximum correntropy EKF with nonlinear regression (MCCEKF-NR) by using the maximum correntropy criterion (MCC) instead of the MMSE criterion to calculate the effectiveness and vitality. The preliminary estimates of the state and covariance matrix in MCKF are provided via the state mean vector and covariance matrix propagation equations, just like in the conventional Kalman filter. In addition, a newly designed fixed-point technique is used to update the posterior estimates of each filter in a regression model. To show the practicality of the proposed strategy, we propose an effective implementation for positioning enhancement in GPS navigation and radar measurement systems.

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, an adaptive and robust Kalman filter algorithm based on the maximum correntropy criterion (MCC) is proposed to solve the problem of integrated navigation accuracy reduction, which is caused by the non-Gaussian noise and time-varying noise of GPS measurement in complex environment. Firstly, the Grubbs criterion was used to remove outliers, which are contained in the GPS measurement. Then, a fixed-length sliding window was used to estimate the decay factor adaptively. Based on the fixed-length sliding window method, the time-varying noises, which are considered in integrated navigation system, are addressed. Moreover, a MCC method is used to suppress the non-Gaussian noises, which are generated with external corruption. Finally, the method, which is proposed in this paper, is verified by the designed simulation and field tests. The results show that the influence of the non-Gaussian noise and time-varying noise of the GPS measurement is detected and isolated by the proposed algorithm, effectively. The navigation accuracy and stability are improved. [ABSTRACT FROM AUTHOR]

For multiple sensor estimation in nonlinear Gaussian environment, the traditional Gauss-Hermite quadrature information filter (GHQIF) has great performance. However, due to the precision loss caused by rounding errors, GHQIF may cause a series of problems such as system divergence. Therefore, the square root GHQIF (SRGHQIF) is first proposed in this paper; it ensures the symmetry and semipositive quality of covariance matrices, also improves the numerical stability and estimation accuracy. Furthermore, practical systems are usually non-Gaussian, and the GHQIF and SRGHQIF under the minimum mean square error (MMSE) rule both deteriorate seriously in this situation. Therefore, replacing MMSE rule with robust maximum correntropy criterion (MCC) as the optimal criterion, a new information filter called the maximum correntropy SRGHQIF (MCSRGHQIF) is proposed, which can improve the robustness of the SRGHQIF against impulsive noise. The predicted information matrix and vector of the SRGHQIF are calculated and then corrected and reconstructed with the MCC. In addition, fixed-point theory is used to iteratively update the estimation information vector, which can obtain better estimation results. Finally, the target tracking simulation results verify that the MCSRGHQIF is a very effective algorithm for multiple sensor estimation in nonlinear non-Gaussian environment, and the newly proposed MCSRGHQIF retains the frameworks and advantages of the SRGHQIF and MCC. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive and robust Kalman filter algorithm based on the maximum correntropy criterion (MCC) is proposed to solve the problem of integrated navigation accuracy reduction, which is caused by the non-Gaussian noise and time-varying noise of GPS measurement in complex environment. Firstly, the Grubbs criterion was used to remove outliers, which are contained in the GPS measurement. Then, a fixed-length sliding window was used to estimate the decay factor adaptively. Based on the fixed-length sliding window method, the time-varying noises, which are considered in integrated navigation system, are addressed. Moreover, a MCC method is used to suppress the non-Gaussian noises, which are generated with external corruption. Finally, the method, which is proposed in this paper, is verified by the designed simulation and field tests. The results show that the influence of the non-Gaussian noise and time-varying noise of the GPS measurement is detected and isolated by the proposed algorithm, effectively. The navigation accuracy and stability are improved.

Abstract Most of the cost functions of adaptive filtering algorithms include the square error, which depends on the current error signal. When the additive noise is impulsive, we can expect that the square error will be very large. By contrast, the cross error, which is the correlation of the error signal and its delay, may be very small. Based on this fact, we propose a new cost function called the mean square cross error for adaptive filters, and provide the mean value and mean square performance analysis in detail. Furthermore, we present a two-stage method to estimate the closed-form solutions for the proposed method, and generalize the two-stage method to estimate the closed-form solution of the information theoretic learning methods, including least mean fourth, maximum correntropy criterion, generalized maximum correntropy criterion, and minimum kernel risk-sensitive loss. The simulations of the adaptive solutions and closed-form solution show the effectivity of the new method.

When the disturbance of impulsive noise exists in the multitask network, the convergence behavior of the traditional multitask diffusion affine projection (AP) algorithm (MD-APA) is significantly suppressed. To alleviate this problem, in this brief, a robust MD-APA is proposed based on maximum correntropy criterion (MCC), which is called MD-APMCC algorithm. Due to the shortcomings of the fixed kernel width, this brief adopts a robust adaptive kernel width strategy to increase the estimation behavior of the MD-APMCC algorithm. Besides, the convergence behavior of MD-APMCC algorithm is studied to derive the convergence range of step-size and the theoretical steady-state mean square deviation (MSD) of the whole network. The simulation verification demonstrates that the proposed MD-APMCC algorithm appears better estimation behavior than MD-APA and MD-APSA for multitask distributed estimation under impulsive noise interference, and the theoretical steady-state MSD of MD-APMCC algorithm is obtained through mean square analysis, which has been well verified by several simulations. [ABSTRACT FROM AUTHOR]

The geometric unscented Kalman filter (GUF) is an effective method for state estimation due to its advantages of high precision, reasonable efficiency, and good stability. In order to further improve the filtering performance of GUF, multiple rotation matrices are first designed by optimizing the rotation angles of their corresponding sampling points with maximum likelihood estimation, leading to a novel sampling strategy, namely, rotating geometric unscented sampling (RGUS). Then, applying RGUS to the GUF framework generates a rotating geometric unscented Kalman filter (RGUF). Since observable measurements are generally corrupted by non-Gaussian noise, RGUF may suffer from performance degradation due to the used minimum mean square error (MMSE) criterion. To improve the robustness of RGUF against non-Gaussian noises, we propose a novel maximum correntropy rotating geometric unscented Kalman filter (MCRGUF) using the maximum correntropy criterion (MCC). Finally, a Cramér–Rao lower bound (CRLB) of MCRGUF is introduced as a performance indicator. Simulations on three examples validate the high filtering accuracy and strong robustness of MCRGUF in the presence of non-Gaussian noise. [ABSTRACT FROM AUTHOR]

For distributed Position and Orientation System (POS), multi-node motion information are measured mainly by transfer alignment technology. The KF-based non-linear filtering algorithm provides optimal integrated solution for transfer alignment. However, on account of uncertain external environment and flexible lever arm compensation error, the noises of transfer alignment exhibit non-Gaussian property and further cause lower accuracy of distributed POS. In this paper, Correntropy-based CDKF is proposed by combining central difference Kalman filter (CDKF) and maximum correntropy criterion (MCC), which aims to decrease the effect of non-Gaussian noises. We rebuild a linear regression model and define a cost function under MCC to modify measurement information, and finally accurate state estimation is achieved. Meanwhile, the error model of nonlinear transfer alignment is formulated where flexible deformation and lever arm effect are considered, and the attitude and velocity information of main POS are transferred to slave IMU to improve its performance. Based on a semi-physical simulation, the performance of proposed method is proved to outperform the standard CDKF in term of estimation accuracy. [ABSTRACT FROM AUTHOR]

Coprime arrays have been widely adopted for direction-of-arrival (DOA) estimation since it can achieve an increased number of degrees of freedom (DOF). To utilize all information received by the coprime array, array interpolation methods are developed, which construct a virtual uniform linear array (ULA) with the same aperture from the non-uniform coprime array. However, the conventional non-robust DOA estimation algorithms for coprime arrays, including the interpolation based methods, suffer from degraded performance or even failed operation when some sensors are miscalibrated. In this paper, a novel maximum correntropy criterion (MCC) based virtual array interpolation algorithm for robust DOA estimation is developed to address this problem. The proposed approach treats the miscalibrated sensor observations as outliers, and by exploiting the property of MCC, the interpolated virtual array covariance matrix is reconstructed via nuclear norm minimization (NNM) with less influence of these outliers. In this manner, the robust DOA estimation is enabled by the robustly reconstructed covariance matrix. Simulation results demonstrate that the proposed algorithm can effectively the mitigate effect of the miscalibrated sensors while maintaining the enhanced DOF offered by coprime arrays.

Copyright of Systems Engineering & Electronics is the property of Journal of Systems Engineering & Electronics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The performance of ellipse fitting may significantly degrade in the presence of outliers, which can be caused by occlusion of the object, mirror reflection or other objects in the process of edge detection. In this paper, we propose an ellipse fitting method that is robust against the outliers, and thus maintaining stable performance when outliers can be present. We formulate an optimization problem for ellipse fitting based on the maximum entropy criterion (MCC), having the Laplacian as the kernel function from the well-known fact that the $\ell _{1}$ -norm error measure is robust to outliers. The optimization problem is highly nonlinear and non-convex, and thus is very difficult to solve. To handle this difficulty, we divide it into two subproblems and solve the two subproblems in an alternate manner through iterations. The first subproblem has a closed-form solution and the second one is cast as a convex second-order cone program (SOCP) that can reach the global solution. By so doing, the alternate iterations always converge to an optimal solution, although it can be local instead of global. Furthermore, we propose a procedure to identify failed fitting of the algorithm caused by local convergence to a wrong solution, and thus, it reduces the probability of fitting failure by restarting the algorithm at a different initialization. The proposed robust ellipse fitting method is next extended to the coupled ellipses fitting problem. Both simulated and real data verify the superior performance of the proposed ellipse fitting method over the existing methods. [ABSTRACT FROM AUTHOR]

Recently, maximum correntropy criterion (MCC) has been widely and successfully used in robust signal processing and machine learning, in which the correntropy is maximized instead of minimizing the popular mean square error (MSE) to improve the robustness with respect to outliers or impulsive noises. A lot of efforts have been devoted to derive different adaptive algorithms under MCC, but to date, little insight has been gained as to how the MCC solution will be influenced by outliers. In this paper, we investigate this problem and our focus is mainly on the parameter estimation of a simple linear errors-in-variables (EIVs) model with scalar variables. Under some conditions, we derive an upper bound on the absolute value of the estimation error and show that the MCC solution can get very close to the true value of the unknown parameter even with arbitrarily large outliers in both the input and output variables. Illustrative examples are provided to verify and clarify the theory. [ABSTRACT FROM AUTHOR]

In this paper, a new direction of arrival (DOA) and the number of signals of interest (SOIs) estimation method is proposed for wideband sources in impulsive noise environments. By evaluating the cyclic correntropy function (CCF) of the received signals at a certain cycle frequency, the impulsive noise and all co-channel interferences with different cycle frequencies can be suppressed. In this approach, a theorem of the CCF is proposed, and a linear prediction (LP) model of the CCF of the array data, which is important for both DOA and number of SOIs estimations, is built by the theorem. Additionally, we introduce multiple regularization parameters into the LP model and derive an analytical expression of the maximum correntropy criterion (MCC) of the parameters for obtaining the optimal regularization parameters expression. Furthermore, by the expression of regularization parameters and the estimation error of the CCF in a limited number of snapshots, an iterative algorithm is proposed for joint estimation of the DOA and the number of SOIs with only knowledge of the cycle frequency of the SOIs.

The adaptive algorithms have been widely studied in Gaussian environment. However, the impulsive noise and other non-Gaussian noise may largely deteriorate the performance of algorithm in practical applications. To address this problem, in this paper, we propose two novel adaptive algorithms for system identification problem with mixed noise scenarios. Both proposed algorithms are based on the framework of the affine projection (AP) algorithm. The first proposed algorithm, termed as VS-APMCCA, combines variable step-size (VS) strategy and maximum correntropy criterion (MCC) to obtain improved performance. For further performance improvement, the VC-VS-APMCCA is developed, which is based on the variable center (VC) scheme of MCC. The convergence analysis of the VC-VS-APMCCA is conduced. Finally, simulation results demonstrate the superior performance of the VS-APMCCA and VC-VS-APMCCA.

Most of the cost functions of adaptive filtering algorithms include the square error, which depends on the current error signal. When the additive noise is impulsive, we can expect that the square error will be very large. By contrast, the cross error, which is the correlation of the error signal and its delay, may be very small. Based on this fact, we propose a new cost function called the mean square cross error for adaptive filters, and provide the mean value and mean square performance analysis in detail. Furthermore, we present a two-stage method to estimate the closed-form solutions for the proposed method, and generalize the two-stage method to estimate the closed-form solution of the information theoretic learning methods, including least mean fourth, maximum correntropy criterion, generalized maximum correntropy criterion, and minimum kernel risk-sensitive loss. The simulations of the adaptive solutions and closed-form solution show the effectivity of the new method. [ABSTRACT FROM AUTHOR]

The extended Kalman filter (EKF) is a method extensively applied in many areas, particularly, in nonlinear target tracking. The optimization criterion commonly used in EKF is the celebrated minimum mean square error (MMSE) criterion, which exhibits excellent performance under Gaussian noise assumption. However, its performance may degrade dramatically when the noises are heavy tailed. To cope with this problem, this paper proposes two new nonlinear filters, namely the linear regression maximum correntropy EKF (LRMCEKF) and nonlinear regression maximum correntropy EKF (NRMCEKF), by applying the maximum correntropy criterion (MCC) rather than the MMSE criterion to EKF. In both filters, a regression model is formulated, and a fixed-point iterative algorithm is utilized to obtain the posterior estimates. The effectiveness and robustness of the proposed algorithms in target tracking are confirmed by an illustrative example. [ABSTRACT FROM AUTHOR]

The kernel maximum-correntropy-criterion (KMCC) algorithm with kernel learning outperforms that with constant kernel, in terms of estimate accuracy and convergence. However, KMCC has limited performance when it is used for sparse system identification since it cannot exploit the sparse structure. This brief proposes $\ell _{0}$ -norm constraint KMCC (KMCC-L0) algorithm to improve the estimate accuracy and the convergence rate of KMCC method. Specifically, an approximated $\ell _{0}$ -norm constraint is integrated into KMCC cost function. Then we derive its iterative optimization process via stochastic gradient method. Furthermore, the analysis including parameter choice, computational complexity, and steady-state misalignment are provided in this brief. The proposed KMCC-L0 method is used for identifying and tracking for unknown sparse systems. The simulation results confirm its superior performance. [ABSTRACT FROM AUTHOR]

• We present a regularization norm of MVC for block sparse system identification (BS MVC). • We study the theoretical steady state EMSE in two cases: the Gaussian case and the non Gaussian case. • Numerical example s illustrate the effectiveness of the proposed BS MVC approach. The maximum Versoria criterion algorithm (MVC) exhibits lower steady-state misalignment and less complexity as compared to the maximum correntropy criterion (MCC) algorithm in the scenario of non-Gaussian impulsive noises. However, few scholars have discussed improving the MVC algorithm in sparse channels. This paper presents a block-sparse MVC (BS-MVC) algorithm by introducing the regularization norm, which has desirable performance in block-sparse channels and has excellent robustness to non-Gaussian conditions with impulsive noises. The steady-state excess mean-square error (EMSE) is discussed in Gaussian and non-Gaussian noise conditions. The effectiveness of BS-MVC and the theoretical expression is validated using multiple simulations. The BS-MVC achieves a lower steady-state mean-square deviation (MSD) and maintains a fast convergence rate compared with MCC and MVC algorithms. [ABSTRACT FROM AUTHOR]

For linear systems, the original Kalman filter under the minimum mean square error (MMSE) criterion is an optimal filter under a Gaussian assumption. However, when the signals follow non-Gaussian distributions, the performance of this filter deteriorates significantly. An efficient way to solve this problem is to use the maximum correntropy criterion (MCC) instead of the MMSE criterion to develop the filters. In a recent work, the maximum correntropy Kalman filter (MCKF) was derived. The MCKF performs very well in filtering heavy-tailed non-Gaussian noise, and its performance can be further improved when some prior information about the system is available (e.g., the system states satisfy some equality constraints). In this paper, to address the problem of state estimation under equality constraints, we develop a new filter, called the MCKF with state constraints, which combines the advantages of the MCC and constrained estimation technology. The performance of the new algorithm is confirmed with two illustrative examples.

For high-precision positioning and navigation systems, the positioning precision of receiver is jeopardized by multipath interference. Multipath suppression methods based on data processing have drawn much attention recently. The critical step of data processing-based method is to estimate multipath parameters. However, most multipath suppression methods falling into the category of data processing-based methods are limited to Gaussian noises, which means the performance of these methods may be degraded in non-Gaussian noises which are encountered quite often in reality. Besides, only static multipath case is studied in most existing literature, which is not sufficient for potential applications since the occurrence and the disappearance of multipath are always changeable along the movement of receiver. To address these problems, the maximum correntropy criterion(MCC) and the generalized maximum correntropy criterion(GMCC) are integrated into the traditional adaptive multipath estimation(AME) algorithm, named as MCC-AME and GMCC-AME, to handle the dynamic multipath estimation problem in non-Gaussian noises. Furthermore, MCC-AME and GMCC-AME are further improved by adopting forgetting factor, named as RMCC-AME and RGMCC-AME, to improve estimation accuracy and reduce time consumption in a recursive way. The four proposed algorithms also address the problems that the formerly proposed entropy-based multipath estimation algorithms are sensitive to the initial estimation and that the assumption of fixed number of multipath is required. The performance of the four proposed algorithms are analyzed and compared. The analytical results show that GMCC-AME outperforms MCC-AME regarding convergent speed, estimation accuracy and robustness, and RGMCC-AME performs even better than RMCC-AME in the same regard. [ABSTRACT FROM AUTHOR]

Correntropy is a local similarity measure defined in kernel space, and the maximum correntropy criterion (mcc) has been successfully applied in many areas of signal processing and machine learning in recent years. The kernel function in correntropy is usually restricted to the Gaussian function with the center located at zero. However, the zero-mean Gaussian function may not be a good choice for many practical applications. In this letter, we propose an extended version of correntropy, whose center can be located at any position. Accordingly, we propose a new optimization criterion called maximum correntropy criterion with variable center (MCC-VC). We also propose an efficient approach to optimize the kernel width and center location in the MCC-VC. Simulation results of regression with linear-in-parameter (LIP) models confirm the desirable performance of the new method. [ABSTRACT FROM AUTHOR]

High-dimensional data contain not only redundancy but also noises produced by the sensors. These noises are usually non-Gaussian distributed. The metrics based on Euclidean distance are not suitable for these situations in general. In order to select the useful features and combat the adverse effects of the noises simultaneously, a robust sparse subspace learning method in unsupervised scenario is proposed in this paper based on the maximum correntropy criterion that shows strong robustness against outliers. Furthermore, an iterative strategy based on half quadratic and an accelerated block coordinate update is proposed. The convergence analysis of the proposed method is also carried out to ensure the convergence to a reliable solution. Extensive experiments are conducted on real-world data sets to show that the new method can filter out the outliers and outperform several state-of-the-art unsupervised feature selection methods. [ABSTRACT FROM AUTHOR]

Abstract A robust cyclic array beamforming method is proposed for cyclostationary signals to counter against the cycle frequency error (CFE) in Gaussian and impulsive noise environments. In this approach, the maximum correntropy criterion (MCC) is employed as the cost function to compute an appropriate weight vector for performing cyclic adaptive array beamforming. We show that a closed form solution of weighting vector yields a weighted least-square-like formulation by using the MCC. The corresponding performances of unbiasedness and consistency are evaluated. Further, in order to solve the performance degradation caused by the CFE, an optimization method is developed based on the fact that the correntropy-based correlation (CRCO) function of the output signals will approach its maxima without any CFE. Finally, a robust iterative algorithm without the prior knowledge of the direction vector of the signal of interest (SOI) is proposed for robust adaptive array beamforming. [ABSTRACT FROM AUTHOR]

In this letter, we propose a maximum correntropy criterion-based low-rank preserving projection (MCC-LRPP) for hyperspectral image (HSI) classification, seeking a low-dimensional subspace via low-rank correntropy graph where spectral band structure can be preserved as much as possible. Unlike the sparse and low-rank-based techniques available, MCC-LRPP introduces maximum correntropy criteria (MCC) to model individual band reconstruction error and noise discriminately instead of $l_{2}$ and Frobenius related norms. It is equivalent to a row-weighting regularization problem. It puts more emphasis on bands with less noise and indirectly increase their importance and vice versa. MCC-LRPP enhances band difference and thus preserves their local structure as well as global structure. Indeed, more local structure means more discriminant ability. The experimental results on several popular HSI data sets prove its effectiveness and superiority when compared to other existing dimension reduction means. [ABSTRACT FROM AUTHOR]

Abstract For a nonlinear system, the cubature Kalman filter (CKF) and its square-root version are useful methods to solve the state estimation problems, and both can obtain good performance in Gaussian noises. However, their performances often degrade significantly in the face of non-Gaussian noises, particularly when the measurements are contaminated by some heavy-tailed impulsive noises. By utilizing the maximum correntropy criterion (MCC) to improve the robust performance instead of traditional minimum mean square error (MMSE) criterion, a new square-root nonlinear filter is proposed in this study, named as the maximum correntropy square-root cubature Kalman filter (MCSCKF). The new filter not only retains the advantage of square-root cubature Kalman filter (SCKF), but also exhibits robust performance against heavy-tailed non-Gaussian noises. A judgment condition that avoids numerical problem is also given. The results of two illustrative examples, especially the SINS/GPS integrated systems, demonstrate the desirable performance of the proposed filter. Highlights • A square-root nonlinear filter based on maximum correntropy criterion is proposed. • A nonlinear regression model is reconstructed to obtain the optimal solution. • A judgment condition that avoids numerical problem is given. • The superior performance of proposed filter is confirmed by illustrative examples. [ABSTRACT FROM AUTHOR]

Ultrasonic positioning technology is being used in a wide range of application areas. In an ultrasonic positioning system, the noise of an ultrasound wave may not follow a Gaussian distribution but has a strong impulse because of many factors. A traditional extended Kalman filter based on the minimum mean square error would produce a linear estimation error and cannot handle a non-Gaussian noise effectively. Therefore, we propose a novel maximum correntropy criterion extended Kalman filter weighted centroid positioning algorithm based on a new Kalman gain formula to determine the maximum correntropy criterion. The maximum correntropy criterion maps the signal to a high-dimensional space and effectively deals with the non-Gaussian noise in ultrasonic positioning. In addition, the weighted centroid uses the results of the extended Kalman filter as inputs and reduces the impact of the linear estimation error on the positioning results. Experimental results show that the maximum correntropy criterion extended Kalman filter weighted centroid algorithm can improve the positioning accuracy by 60.06% over the extended Kalman filter and 22.83% compared with the maximum correntropy criterion extended Kalman filter. Overall, the proposed algorithm is more robust and effective. [ABSTRACT FROM AUTHOR]

Low frequency communication, taking advantage of the features of low frequency electromagnetic signals in near field, is widely used in through-the-earth (TTE) wireless applications. However, the low frequency non-Gaussian noise severely limits the communication performance. In this paper, an adaptive noise cancellation algorithm based on time delay estimation (ANC-TDE) and maximum correntropy criterion (MCC) is proposed. The explicit time delay estimation algorithm based on MCC (MCC-ETDE) is used to estimate the time-varying delay and the noise correlationship between the primary input and reference inputs. With a reference noise selected and time delay compensated, the non-Gaussian noise is canceled by adaptive filter based on MCC. The proposed algorithm is implemented on field programmable gate array (FPGA) and the performance is evaluated by simulation and experiment. As shown in the results, the ANC-TDE algorithm can reduce the complexity of ANC filter and adaptively compensate the varied time delay between the primary input and reference input. With the time delay compensated, the ANC-TDE algorithm has better performance in non-Gaussian noise environment and is more suitable for real-time systems. [ABSTRACT FROM AUTHOR]

• An optimization problem about the state mean of multi-agent systems with impulsive noise based on MCC derived from information theoretic learning is investigated in this paper, where the half-quadratic(HQ) strategy is used to simplify the solving process of the optimization problem. • A problem interfered by impulsive noise on the states of multi-agent systems is studied in this paper, where the adverse effect of impulsive noise on the states is eliminated by the MCC algorithm. • An event-triggered consensus problem of discrete-time multi-agent systems with random impulsive noise is addressed in this paper, where an event-triggering condition is derived for the system to achieve consensus. An event-triggered consensus problem of discrete-time multi-agent systems with impulsive noise under directed switching topology is investigated in this paper, where the control input of each agent is determined by its own state information and the state information of its neighbors that may be corrupted by impulsive noise. Firstly, to reduce the adverse effect of impulsive noise on consensus performance of the discrete-time multi-agent systems, maximum correntropy criterion (MCC) derived from information theoretic learning is introduced to calculate the communication weights among the agents, and an event-triggered strategy is adopted to drive the state variables of each agent to eventually converge to a same value. Secondly, the condition to guarantee consensus of the discrete-time multi-agent systems is derived by graph theory and Lyapunov stability theorem. Finally, the effectiveness of the theory is verified by several numerical simulations. [ABSTRACT FROM AUTHOR]

Coprime array with M + N sensors can achieve an increased degrees-of-freedom (DOF) of O ( M N ) for direction-of-arrival (DOA) estimation. Utilizing the compressive sensing (CS)-based DOA estimation methods, the increased DOF offered by the coprime array can be fully exploited. However, when some sensors in the array are miscalibrated, these DOA estimation methods suffer from degraded performance or even failed operation. Besides, the key to the success of CS-based DOA estimation is that every target falls on the predefined grid. Thus, a coarse grid may cause the mismatch problem, whereas a fine grid requires great computational cost. In this paper, a robust CS-based DOA estimation algorithm is proposed for coprime array with miscalibrated sensors. In the proposed algorithm, signals received by the miscalibrated sensors are viewed as outliers, and correntropy is introduced as the similarity measurement to distinguish these outliers. Incorporated with maximum correntropy criterion (MCC), an iterative sparse reconstruction-based algorithm is then developed to give the DOA estimation while mitigating the influence of the outliers. A multiresolution grid refinement strategy is also incorporated to reconcile the contradiction between computational cost and the mismatch problem. The numerical simulation results verify the effectiveness and robustness of the proposed method.

In this letter, we propose a robust direction-of-arrival (DOA) estimation algorithm in the context of sparse reconstruction, where some array sensors are miscalibrated. In this case, conventional DOA estimation algorithms suffer from degraded performance or even failed operations. In the proposed approach, the miscalibrated sensor observations are treated as outliers, and a weighting factor is adaptively optimized and applied to each sensor in order to effectively mitigate the effect of the outliers. An algorithm based on the maximum correntropy criterion is then developed to yield robust DOA estimation. The simulation results are presented to verify the effectiveness and superiority of the proposed approach compared with conventional DOA estimation algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a robust state estimator based on maximum exponential absolute value (MEAV) is proposed by using the maximum correntropy criterion with Laplace kernel function as the objective function of state estimation. Since the objective function of MEAV model is continuous but nondifferentiable, its equivalent model is given, which is then solved based on the primal–dual interior point method. To further improve the computational efficiency, a new correction equation with much lower order is presented and the number of fill-ins in the solving process is reduced by a systematic method. Simulations based on the IEEE benchmark systems and two real grids of China demonstrate that the proposed MEAV estimator is very robust with high efficiency. [ABSTRACT FROM PUBLISHER]

The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilising a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman filter type estimator leads to the well-known unscented Kalman filter (UKF). Although the UKF works very well in Gaussian noises, its performance may deteriorate significantly when the noises are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises. To improve the robustness of the UKF against impulsive noises, a new filter for non-linear systems is proposed in this work, namely the maximum correntropy unscented filter (MCUF). In MCUF, the UT is applied to obtain the prior estimates of the state and covariance matrix, and a robust statistical linearisation regression based on the maximum correntropy criterion is then used to obtain the posterior estimates of the state and covariance matrix. The satisfying performance of the new algorithm is confirmed by two illustrative examples. [ABSTRACT FROM AUTHOR]

Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate seriously. To improve the robustness of KF against impulsive noises, we propose in this work a new Kalman filter, called the maximum correntropy Kalman filter (MCKF), which adopts the robust maximum correntropy criterion (MCC) as the optimality criterion, instead of using the MMSE. Similar to the traditional KF, the state mean vector and covariance matrix propagation equations are used to give prior estimations of the state and covariance matrix in MCKF. A novel fixed-point algorithm is then used to update the posterior estimations. A sufficient condition that guarantees the convergence of the fixed-point algorithm is also given. Illustration examples are presented to demonstrate the effectiveness and robustness of the new algorithm. [ABSTRACT FROM AUTHOR]

The state space recursive least squares (SSRLS) filter is a new addition to the well-known recursive least squares (RLS) family filters, which can achieve an excellent tracking performance by overcoming some limitations of the standard RLS algorithm. However, when the underlying system is disturbed by some heavy-tailed non-Gaussian impulsive noises, the performance of SSRLS will deteriorate significantly. The main reason for this is that the SSRLS is derived under the minimum mean square error (MMSE) criterion, which is not well-suited to estimation problems under non-Gaussian noises. To overcome this issue, we propose in this paper a novel linear filter, called the state space maximum correntropy (SSMC) filter, which is derived under the maximum correntropy criterion (MCC) instead of the MMSE. Since MCC is very suited to non-Gaussian signal processing, the SSMC performs very well in non-Gaussian noises especially when the signals are corrupted by impulsive noises. A simple illustrative example is presented to demonstrate the desirable performance of the new algorithm. [ABSTRACT FROM AUTHOR]

In this brief, a robust and sparse recursive adaptive filtering algorithm, called convex regularized recursive maximum correntropy (CR-RMC), is derived by adding a general convex regularization penalty term to the maximum correntropy criterion (MCC). An approximate expression for automatically selecting the regularization parameter is also introduced. Simulation results show that the CR-RMC can significantly outperform the original recursive maximum correntropy (RMC) algorithm especially when the underlying system is very sparse. Compared with the convex regularized recursive least squares (CR-RLS) algorithm, the new algorithm also shows strong robustness against impulsive noise. The CR-RMC also performs much better than other LMS-type sparse adaptive filtering algorithms based on MCC. [ABSTRACT FROM AUTHOR]