A family of robust adaptive filtering algorithms based on sigmoid cost

Using the generalized Gaussian probability density function as the kernel, a generalized correntropy has been proposed. A generalized maximum correntropy criterion (GMCC) algorithm is then developed by maximizing the generalized correntropy. However, the GMCC algorithm has a high steady-state misalignment and involves a high calculation cost of the exponential term (generalized Gaussian kernel). In this brief, we propose a maximum Versoria criterion (MVC) algorithm, which is derived by maximizing the generalized Versoria function, to reduce steady-state misalignment and computational effort as compared to the GMCC algorithm. The MVC algorithm is then tested in system identification and acoustic echo cancellation scenarios, which have demonstrated that the proposed algorithm is robust against non-Gaussian impulsive noises and performs much better than the LMP and GMCC algorithms.

A substantial body of literature has been devoted to the development of novel cost functions for robust adaptive filtering algorithms. These algorithms differ in computational complexity, the number of hyperparameters, convergence speed, and steady-state misalignment. Popular algorithms such as the least-mean fourth (LMF), logarithmic least mean square (LMLS), and generalized maximum correntropy criterion (GMCC) primarily rely on statistical and information-theoretic measures of the error signal. However, a significant portion of recent literature does not provide an explicit theoretical foundation for the proposed cost functions. In this work, we present a simple yet powerful approach for designing robust cost functions for adaptive algorithms, wherein the cost function is expressed as a composition of two functions that satisfy specific properties of monotonicity and convexity. Using this method, many standard robust cost functions can be represented within this framework. Additionally, we propose two new families of robust cost functions based on the hyperbolic tangent and hyperbolic secant functions. Theoretical closed-form expressions for the bounds on the adaptation parameter rate and the steady-state misalignment of the adaptive filtering algorithms based on the proposed cost function families have been derived and validated through simulations. Extensive simulations, involving channel estimation and direction-of-arrival (DOA) estimation tasks, demonstrate that the proposed algorithm family outperforms state-of-the-art cost functions.

Robust adaptive signal processing algorithms based on a generalized maximum correntropy criterion (GMCC) suffers from high steady state misalignment. In an endeavour to achieve lower steady state misalignment, in this letter we propose a generalized hyperbolic secant function (GHSF) as a robust norm and derive the generalized hyperbolic secant adaptive filter (GHSAF). The new algorithm is seen to offer robust system identification performance over the conventional GMCC algorithm. To further improve the convergence performance under non-Gaussian noise environments, we propose the nearest Kronecker product decomposition based GMCC and GHSAF algorithms. Extensive simulation study show the improved convergence performance provided by the proposed algorithms for system identification.

We introduce a novel family of adaptive filtering algorithms based on a relative logarithmic cost inspired by the “competitive methods” from the online learning literature. The competitive or regret based approaches stabilize or improve the convergence performance of adaptive algorithms through relative cost functions. The new family elegantly and gradually adjusts the conventional cost functions in its optimization based on the error amount. We introduce important members of this family of algorithms such as the least mean logarithmic square (LMLS) and least logarithmic absolute difference (LLAD) algorithms. However, our approach and analysis are generic such that they cover other well-known cost functions as described in the paper. The LMLS algorithm achieves comparable convergence performance with the least mean fourth (LMF) algorithm and enhances the stability performance significantly. The LLAD and least mean square (LMS) algorithms demonstrate similar convergence performance in impulse-free noise environments while the LLAD algorithm is robust against impulsive interferences and outperforms the sign algorithm (SA). We analyze the transient, steady-state and tracking performance of the introduced algorithms and demonstrate the match of the theoretical analyses and simulation results. We show the enhanced stability performance of the LMLS algorithm and analyze the robustness of the LLAD algorithm against impulsive interferences. Finally, we demonstrate the performance of our algorithms in different scenarios through numerical examples.

As an important component of autonomous intelligent systems, the research on autonomous positioning algorithms used by UAVs is of great significance. In order to resolve the problem whereby the GNSS signal is interrupted, and the visual sensor lacks sufficient feature points in complex scenes, which leads to difficulties in autonomous positioning, this paper proposes a new robust adaptive positioning algorithm that ensures the robustness and accuracy of autonomous navigation and positioning in UAVs. On the basis of the combined navigation model of vision/inertial navigation and satellite/inertial navigation, based on ESKF, a multi-source fusion model based on a federated Kalman filter is here established. Furthermore, a robust adaptive localization algorithm is proposed, which uses robust equivalent weights to estimate the sub-filters, and then uses the sub-filter state covariance to adaptively assign information sharing coefficients. After simulation experiments and dataset verification, the results show that the robust adaptive algorithm can effectively limit the impact of gross errors in observations and mathematical model deviations and can automatically update the information sharing coefficient online according to the sub-filter equivalent state covariance. Compared with the classical federated Kalman algorithm and the adaptive federated Kalman algorithm, our algorithm can meet the real-time requirements of navigation, and the accuracy of position, velocity, and attitude measurement is improved by 2–3 times. The robust adaptive localization algorithm proposed in this paper can effectively improve the reliability and accuracy of autonomous navigation systems in complex scenes. Moreover, the algorithm is general—it is not intended for a specific scene or a specific sensor combination– and is applicable to individual scenes with varied sensor combinations.

Widely linear complex-valued hyperbolic secant adaptive filtering algorithm and its performance analysis

Robust adaptive algorithm for widely-linear Hammerstein system and its application

Recently, an affine projection generalized maximum correntropy criterion (APGMCC) algorithm was developed to process the colored input signal and impulsive noise. However, the non-convexity of the generalized correntropic loss (GC-Loss) function causes the APGMCC algorithm suffers from high steady-state misalignment. In this brief, a new robust adaptive filtering algorithm called affine projection kernel risk-sensitive mean <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${p}$ </tex-math></inline-formula> -power error loss (APKRSMPL) is proposed, which is deduced by minimizing the sum of the KRSMPL functions of the a posteriori error vector elements under a bounded energy constraint on the filter weights fluctuation. Since no matrix inversion is required, the proposed APKRSMPL algorithm is computationally efficient. In addition, the convexity of the KRSMPL function ensures faster convergence and lower steady-state misalignment of the APKRSMPL algorithm. Then, the mean-square stability as well as the steady-state excess mean square error (EMSE) of the APKRSMPL algorithm are analyzed and an approximate steady-state EMSE solution is derived. Finally, system identification and acoustic echo cancellation (AEC) computer simulations verify the accuracy of the steady-state EMSE solution and the effectiveness of the proposed APKRSMPL algorithm.

The adaptive kernel algorithms usually achieve a good convergence performance and a tracking performance due to the universal approximator, offering an excellent solution to many problems with nonlinearities. However, as is well known, the convergence rate and steady-state error of adaptive filtering algorithm are a pair of inherent contradictions, and the kernel method is not exceptional. For this problem, a robust kernel adaptive filtering algorithm, called the variable-scaling factor kernel fractional lower power adaptive filtering algorithm based on the Sigmoid function, is developed by creating a new framework of cost function which combines the kernel fractional low power error criterion with the Sigmoid function for system identification of different noise environments. This new cost framework incorporates a scaling factor into the cost function of the Sigmoid kernel fractional lower power adaptive filtering algorithm (VS-SKFLP) in this paper. One of the main features in the new framework is its scaling factor. This scaling factor is used to control the steepness of the Sigmoid function, and the steepness can affect the convergence speed of filtering algorithm. The scaling factor provides a tradeoff between the convergence rate and the steady-state mean square error (MSE), which improves the convergence rate under the same steady-state mean square error. However, it is also an important problem to choose an appropriate scale factor. Therefore, a variable-scale factor SKFLP algorithm is also proposed to improve the convergence rate and steady-state MSE, simultaneously. The proposed variable-scale factor structure consists of a function of error, featuring the adaptive updates of their parameter estimated by making discerning use of the error. In this paper, the nonlinear saturation characteristic of the Sigmoid function and low order norm criterion are used to overcome the performance degradation of training data destroyed by non-Gaussian impulse noise and colored noise. Through the convergence analysis, the parameter estimation sequence of our proposed algorithm proves convergent. Simulation results show that the proposed algorithm (VS-SKFLP) outperforms other kernel adaptive filtering algorithms in system recognition with different noise environments.

Sparse adaptive filtering algorithms are utilized to exploit system sparsity as well as to mitigate interferences in many applications such as channel estimation and system identification. In order to improve the robustness of the sparse adaptive filtering, a novel adaptive filter is developed in this work by incorporating a correntropy-induced metric (CIM) constraint into the least logarithmic absolute difference (LLAD) algorithm. The CIM as an $$l_{0}$$l0-norm approximation exerts a zero attraction, and hence, the LLAD algorithm performs well with robustness against impulsive noises. Numerical simulation results show that the proposed algorithm may achieve much better performance than other robust and sparse adaptive filtering algorithms such as the least mean p-power algorithm with $$l_{1}$$l1-norm or reweighted $$l_{1}$$l1-norm constraints.

The unmanned aerial vehicle (UAV) and the unmanned ground vehicle (UGV) can complete complex tasks through information sharing and ensure the mission execution capability of multiple unmanned carrier platforms. At the same time, cooperative navigation can use the information interaction between multi‐platform sensors to improve the relative navigation and positioning accuracy of the entire system. Aiming at the problem of deviation of the system model due to gross errors in sensor measurement data or strong manoeuvrability in complex environments, a robust and adaptive UGV‐UAV relative navigation and positioning algorithm is proposed. In this paper, the relative navigation and positioning of UGV‐UAV is studied based on inertial measurement unit (IMU)/Vision. Based on analyzing the relative kinematics model and sensor measurement model, a leader (UGV)‐follow (UAV) relative navigation model is established. In the implementation of the relative navigation and positioning algorithm, the robust adaptive algorithm and the non‐linear Kalman filter (extended Kalman filter [EKF]) algorithm are combined to dynamically adjust the system state parameters. Finally, a mathematical simulation of the accompanying and landing process in the UGV‐UAV cooperative scene is carried out. The relative position, velocity and attitude errors calculated by EKF, Robust‐EKF and Robust‐Adaptive‐EKF algorithms are compared and analyzed by simulating two cases where the noise obeys the Gaussian distribution and the non‐Gaussian distribution. The results show that under the non‐Gaussian distribution conditions, the accuracy of the Robust‐Adaptive‐EKF algorithm is improved by about two to three times compared with the EKF and Robust‐EKF and can almost reach the relative navigation accuracy under the Gaussian distribution conditions. The robust self‐adaptive relative navigation and positioning algorithm proposed in this paper has strong adaptability to the uncertainty and deviation of system modelling in complex environments, with higher accuracy and stronger robustness.

The most popular robust adaptive beamforming technique is diagonal loading. However, no clear guidelines can be applied to choose the optimal diagonal loading factor, and beamforming techniques based on the uncertainty set of array steering vector still need to specify the bound of the uncertainty set. In this paper, we develop a novel robust adaptive algorithm. Firstly, we modify covariance fitting criteria (CFC) via replacing the conventional sample covariance matrix used in CFC by the general linear combination (GLC) covariance matrix estimates. Then we use the modified CFC to estimate the covariance matrix of array observation data in the standard capon beamforming formulation. The merits of our method we term GLC-CFC include applicability to arbitrary number of snapshots, robustness to the correlated sources and without the requirement of specifying any user-parameters. The excellent performance of our method in small snapshots size is demonstrated via numerical examples and compared with other classical adaptive beamforming algorithms.

Robust adaptive beamforming for MIMO radar

A two-step robust adaptive filtering algorithm for GNSS kinematic precise point positioning

In this paper, by inserting the logarithm cost function of the normalized subband adaptive filter algorithm with the step-size scaler (SSS-NSAF) into the sigmoid function structure, the proposed sigmoid-function-based SSS-NSAF algorithm yields improved robustness against impulsive interferences and lower steady-state error. In order to identify sparse impulse response further, a series of sparsity-aware algorithms, including the sigmoid L0 norm constraint SSS-NSAF (SL0-SSS-NSAF), sigmoid step-size scaler improved proportionate NSAF (S-SSS-IPNSAF), and sigmoid L0 norm constraint step-size scaler improved proportionate NSAF (SL0-SSS-IPNSAF), is derived by inserting the logarithm cost function into the sigmoid function structure as well as the L0 norm of the weight coefficient vector to act as a new cost function. Since the use of the fix step size in the proposed SL0-SSS-IPNSAF algorithm, it needs to make a trade-off between fast convergence rate and low steady-state error. Thus, the convex combination version of the SL0-SSS-IPNSAF (CSL0-SSS-IPNSAF) algorithm is proposed. Simulations in acoustic echo cancellation (AEC) scenario have justified the improved performance of these proposed algorithms in impulsive interference environments and even in the impulsive interference-free condition.