Nonlinear Adaptive Filter Research Articles

Three-dimensional adaptive dynamic surface guidance law for missile with terminal angle and field-of-view constraints

In this paper, an adaptive dynamic surface (DSC) guidance law for missile is designed to intercept the maneuvering target with field-of-view (FOV) and terminal angle constraints in three-dimensional(3D) space, and the missile autopilot dynamics is considered. Firstly, the time-varying transformation function related to line of sight (LOS) is used to replace the FOV constraints, transforming the process-constrained control problem into the output-constrained control problem. Meanwhile, the 3D coupled relative kinematics model considering missile autopilot dynamics and maneuvering target acceleration is established. Secondly, a novel time-varying asymmetric barrier Lyapunov function (TABLF) with dead-zone characteristics is introduced to the adaptive dynamic surface guidance law design process to improve the robustness of parameter debugging. Thirdly, with the help of a nonlinear adaptive filter, the ‘explosion of complexity’ problem can be avoided effectively, which is caused by analytic computation of virtual signal derivatives. Furthermore, aiming at the problem of autopilot dynamic errors, target acceleration disturbances, and unmeasurable parameters in the model, a novel adaptive law is used to evaluate online. Then, the stability of the closed-loop system is rigorously proven using Lyapunov criteria. Ultimately, Numerical simulations with various constraints and comparison studies have been considered to show the feasibility and effectiveness of the proposed missile guidance law.

An evolutionary algorithm-based approach for efficient design of Wiener spline non-linear adaptive filter and its experimental validation

An evolutionary algorithm-based approach for efficient design of Wiener spline non-linear adaptive filter and its experimental validation

A Joint Logarithmic based nonlinear Adaptive filter for load balancing in electric power distribution system

When nonlinear loads are introduced to a distribution system, various power quality challenges emerge, such as load unbalance, harmonic distortion, and reactive power mismatch. This study presents a novel solution utilizing a joint logarithmic hyperbolic cosine adaptive filter-operated distribution static compensator to mitigate these issues. The cost function of the adaptive filter is designed to be smooth for minor errors and resilient to significant errors. The proposed control technique computes fundamental active and reactive currents, generating reference signals for the distribution static compensator. A comparative analysis with conventional adaptive control techniques is also conducted. The distribution system undergoes comprehensive testing under various dynamics to ensure compliance with IEEE-519 standards. Real-time simulation-based experiments are employed to showcase the algorithm's performance.

Improved performance of a shunt hybrid active power filter by a robust exponential functional link network-based nonlinear adaptive filter control to enhance power quality

This research article details the design and implementation of a nonlinear adaptive filtering (NAF) technique using an exponential functional link network (EFLN) for a shunt hybrid active power filter (SHAPF) control to solve the current-associated power quality issues on the utility side at the distribution level of electrical power systems. Separation of the fundamental component from the harmonics, achieving unity power factor operation, reducing the reactive power drawn from the source, balancing the currents during transients, and reduction of total harmonic distortion (THD) of the source current are the issues considered to resolve. The proposed technique solves these issues by generating the sinusoidal reference current and separating the fundamental current from the harmonics. When compared to conventional and existing adaptive filtering techniques such as least mean square (LMS), least mean fourth (LMF), and variable step size LMS (VSS-LMS), the proposed EFLN-NAF method excels in terms of speedy convergence, adaptability in noise-specific environments and reduced steady-state coefficient error. MATLAB/Simulink software is utilized to perform the simulations to examine the suggested strategy for the chosen SHAPF topology both in static and dynamic scenarios. For a 15 kW and 3kVAr requirement of the nonlinear load, simulation results proved that the designed PPF for 2kVAr is able to share the reactive power with the APF, thereby reducing its rating and cost. The proposed method of filtering has been proven to be fast converging with 0.049 s, and the THD in steady state is brought to 1.32 % in steady-state and to 3.77 % during transient conditions, which are under standard limits. A hardware prototype of the experimental setup is constructed at the laboratory scale with OPAL-RT (OP4510) as the controller. With an active and reactive power demand of 1.1 kW and 210VAr, the designed PPF supplies 110 VAr, whereas the rest is supplied by the APF. The practical THD in source current is observed to be 2.081 %, which meets the standards. The results from both simulations and experiments are validated, and the efficacy of the proposed technique in mitigating the aforementioned power quality issues is proved.

Adaptive nonlinear Kalman filters based on credibility theory with noise correlation

To solve the divergence problem and overcome the difficulty in guaranteeing filtering accuracy during estimation of the process noise covariance or the measurement noise covariance with traditional new information-based nonlinear filtering methods, we design a new method for estimating noise statistical characteristics of nonlinear systems based on the credibility Kalman Filter (KF) theory considering noise correlation. This method first extends credibility to the Unscented Kalman Filter (UKF) and Extended Kalman Filter (EKF) based on the credibility theory. Further, an optimization model for nonlinear credibility under noise related conditions is established considering noise correlation. A combination of filtering smoothing and credibility iteration formula is used to improve the real-time performance of the nonlinear adaptive credibility KF algorithm, further expanding its application scenarios, and the derivation process of the formula theory is provided. Finally, the performance of the nonlinear credibility filtering algorithm is simulated and analyzed from multiple perspectives, and a comparative analysis conducted on specific experimental data. The simulation and experimental results show that the proposed credibility EKF and credibility UKF algorithms can estimate the noise covariance more accurately and effectively with lower average estimation time than traditional methods, indicating that the proposed algorithm has stable estimation performance and good real-time performance.

A robust adaptive decomposable Volterra filter based on the hyperbolic tangent Leclerc function and its performance analysis

SummaryMost of the existing adaptive filter algorithms pay more attention to improving performance while ignoring the computational complexity and the impact of the impulsive environment. When encountering the impulsive noise environments, the performance of traditional nonlinear adaptive filter may be significantly reduced and usually needs high computational cost. Therefore, this article proposes a hyperbolic tangent Leclerc robust nonlinear adaptive filter based on the low complexity decomposable Volterra model (HTLNAF‐DVM). The filter is implemented by imposing a rank‐one structure on the full Volterra model to get a product of linear filters, and employs a hyperbolic tangent Leclerc function as a robust norm to effectively improve the robustness against the impulsive noise. In addition, we give the theoretical analyses of the steady‐state mean‐square performance of the proposed HTLNAF‐DVM. Finally, the simulation results prove that the proposed HTLNAF‐DVM algorithm has better performance than the existing algorithms and fit well with the theory.

A novel hybrid method for calculating the fetal heart rate from the non-invasive abdominal Electrocardiogram signal

Continuous monitoring of fetal health requires the accurate calculation of the Fetal Heart Rate (FHR) by efficiently isolating fetal Electrocardiogram (fECG) from non-invasive abdominal Electrocardiogram (aECG). There are numerous solutions proposed for this problem, having its own restrictions. This paper introduces a novel three-stage hybrid adaptive approach for fECG extraction and FHR determination from aECG. The proposed framework is an amalgamation of independent component analysis (ICA), adaptive exponential functional link network (AEFLN), and novel wavelet thresholding (NWT). The proposed work aims to determine the best quality fetal R-peaks for calculating fetal heart rate (FHR). ICA is a blind source separation technique that uses all the information from the multichannel inputs to determine the maternal Electrocardiogram (mECG) and enhanced aECG. In the next stage, a non-linear adaptive filter, AEFLN, is used for the extraction of fECG. This approach requires no additional algorithm for polarity reversal and time alignment before AEFLN. At last, NWT determines the fetal R-peak envelopes from the residual fECG. The R-peak envelopes are used to analyze FHR, and its accuracy was accessed using the FHR trace. So far, FastICA-AEFLN-NWT has not been used as a hybrid method for fECG extraction and fetal R-peak detection. The algorithm’s effectiveness was tested on both real databases from Daisy and Physionet and synthetic databases from Physionet. The proposed hybrid method attains 95.29 % of sensitivity (SE), 96.68 % of Positive Predictive Value (PPV), 95.92 % of F1 score, and FHR measurement (FHRmeas) is 29.72 bpm2. The proposed methodology outperforms the state-of-art methods in fECG extraction.

RunDAE model: Running denoising autoencoder models for denoising ECG signals

Background:The denoising autoencoder (DAE) is commonly used to denoise bio-signals such as electrocardiogram (ECG) signals through dimensional reduction. Typically, the DAE model needs to be trained using correlated input segments such as QRS-aligned segments or long ECG segments. However, using long ECG segments as an input can result in a complex deep DAE model that requires many hidden layers to achieve a low-dimensional representation, which is a major drawback. Methods:This work proposes a novel DAE model, called running DAE (RunDAE), for denoising short ECG segments without relying on the R-peak detection algorithm for alignment. The proposed RunDAE model employs a sample-by-sample processing approach, considering the correlation between consecutive, overlapped ECG segments. The performance of both the classical DAE and RunDAE models with convolutional and dense layers, respectively, is evaluated using corrupted QRS-aligned and non-aligned ECG segments with physical noise such as motion artifacts, electrode movement, baseline wander, and simulated noise such as Gaussian white noise. Results:The simulation results indicate that 1. QRS-aligned segments are preferable to non-aligned segments, 2. the RunDAE model outperforms the classical DAE model in denoising ECG signals, especially when using dense layers and QRS-aligned segments, 3. training the RunDAE models with normal and arrhythmic ECG signals enhance model’s properties/capabilities, and 4. the RunDAE is a multistage, non-causal, nonlinear adaptive filter. Conclusion:A shallow learning model, which consists of a couple of hidden layers, could achieve outstanding denoising performance using only the correlation among neighboring samples.

Underwater four-quadrant dual-beam circumferential scanning laser fuze using nonlinear adaptive backscatter filter based on pauseable SAF-LMS algorithm

The phenomenon of a target echo peak overlapping with the backscattered echo peak significantly undermines the detection range and precision of underwater laser fuzes. To overcome this issue, we propose a four-quadrant dual-beam circumferential scanning laser fuze to distinguish various interference signals and provide more real-time data for the backscatter filtering algorithm. This enhances the algorithm loading capability of the fuze. In order to address the problem of insufficient filtering capacity in existing linear backscatter filtering algorithms, we develop a nonlinear backscattering adaptive filter based on the spline adaptive filter least mean square (SAF-LMS) algorithm. We also designed an algorithm pause module to retain the original trend of the target echo peak, improving the time discrimination accuracy and anti-interference capability of the fuze. Finally, experiments are conducted with varying signal-to-noise ratios of the original underwater target echo signals. The experimental results show that the average signal-to-noise ratio before and after filtering can be improved by more than 31 dB, with an increase of up to 76% in extreme detection distance.

A robust adaptive linear parameter-varying gain-scheduling controller for aeroengines

This paper presents an on-board model-based adaptive linear parameter-varying (LPV) gain-scheduling controller for aeroengines exhibiting strong nonlinearity, uncertainty, and component performance degradation. A novel hybrid on-board adaptive model is proposed using a dual-loop (fast-slow) structure, which consists of an adaptive LPV model as the fast loop to guarantee the on-board performance, and a component-level model as the slow loop to provide accurate model information at a slow update frequency, without violating the real-time requirement of the fast loop. An innovative mixed adaptive extended Kalman filter is designed to estimate and update the model, by introducing an extended-Kalman-filter-based covariance scaling mechanism and updating the system noise covariance matrix by employing full covariance estimation. The component-level adaptive nonlinear model and mixed adaptive extended Kalman filter increase the accuracy of the on-board model, while the adaptive LPV model enhances its real-time performance. Finally, a robust polytopic adaptive LPV gain-scheduling controller is designed based on the adaptive LPV model by introducing a new scheduling variable, i.e., health parameters estimated by the on-board adaptive model. The proposed adaptive model and controller are implemented to a high fidelity nonlinear aeroengine model. Simulation results demonstrate that the estimation error of health parameters and component degradation level of the proposed method is 0.0763%, which gives an order of magnitude higher health parameter and component degradation level estimation accuracy compared with the other commonly applied models. The proposed model-based adaptive LPV gain scheduling control scheme has a steady-state error of 0.0028%, gives one order of magnitude higher control accuracy than that of three state-of-the-art baseline controllers while demonstrating significantly reduced overshoot and adjustment time. This verifies the robustness and effectiveness of the proposed controller, and verifies that the model can meet the technical requirements of the engine control system and significantly improve the engine control performance.

A novel adaptive nonlinear Kalman filter scheme for DVL-aided SINS alignment in underwater vehicles

The rapid and accurate initial alignment of a strapdown inertial navigation system (SINS) aided by a Doppler velocity logger (DVL) still poses a significant challenge in unmanned underwater vehicle navigation. In this study, a novel adaptive nonlinear filtering alignment scheme is developed for a SINS with a large misalignment angle. In previous studies, the frame-inconsistency problem of the nonlinear SINS error model was neglected. Thus, a modified nonlinear error model of a SINS is derived here rigorously as the process model of the nonlinear Kalman filter. In addition, the noise amplification of applying Sage-Husa adaptive Kalman filter (SHAKF) in alignment is analyzed, and a novel arctangent fading memorial factor is introduced to dynamically adjust the weight of current measurements. Simulations and field experiments indicate that the proposed algorithm is efficient in underwater DVL/SINS in-motion alignment. The alignment accuracy and convergence rate of the modified model are significantly improved compared to those of the traditional model. The arctangent fading memorial SHAKF can reliably estimate the measurement noise and improve the performance of alignment.

Algorithm and Architecture Design of Random Fourier Features-Based Kernel Adaptive Filters

Numerous real-life systems exhibit complex nonlinear input-output relationships. Kernel adaptive filters, a popular class of nonlinear adaptive filters, can efficiently model these nonlinear input-output relationships. Their growing network structure, however, poses considerable challenges in terms of their hardware implementation, making them inefficient for real-time applications. Random Fourier features (RFF) facilitate the development of kernel adaptive filters with a fixed network structure. For the first time, this paper attempts to implement the RFF-based kernel least mean square (RFF-KLMS) algorithm on hardware. To this end, we propose several reformulations of the feature functions (FFs) that are computationally expensive in their native form so that they can be implemented in real-time VLSI. Specifically, we reformulate inner product evaluation, cosine, and exponential functions that appear in the implementation of FFs. With these reformulations, the proposed delayed RFF-KLMS (DRFF-KLMS) is then synthesized using 45-nm CMOS technology with 16-bit fixed-point representations. According to the synthesis results, pipelined DRFF-KLMS architectures require minimal hardware increase over the state-of-the-art conventional delayed LMS architecture while significantly improving estimation performance for the nonlinear model. Our results suggest that the cosine feature function-based DRFF-KLMS is appropriate for applications requiring high accuracy, whereas the exponential function-based DRFF-KLMS may be well suited for resource-constrained applications.

Asymmetric integral barrier Lyapunov function-based dynamic surface control of a state-constrained morphing waverider with anti-saturation compensator

To satisfy wide-speed and long-range mission requirements, morphing aircraft can maintain optimal flight performance by changing their configuration during flight. As an advanced morphing aircraft, a cross-domain morphing waverider can change its wing geometry to maintain a high lift-to-drag ratio across the subsonic, transonic, and supersonic to hypersonic speed ranges. During the highly dynamic morphing process, the trajectory tracking problem of the morphing waverider is characterized by strong coupling, time-varying characteristics, parameter uncertainties, input saturation, and asymmetric state constraints. To address these problems, this paper proposes an asymmetric integral barrier Lyapunov function (AIBLF) based dynamic surface controller consisting of two loops, based on the six-degrees-of-freedom partial decoupled control-oriented model of a symmetric-sweep-wing morphing waverider. Specifically, a virtual control signal of three-axis angular rates is provided by the AIBLF-based flight controller to satisfy the predefined asymmetric constraints of the angle of attack, sideslip angle, and bank angle, combined with a disturbance observer to approximate the disturbances of multiple parameter uncertainties. Subsequently, the desired virtual control signal consisting of three-axis angular rates is derived by passing the above virtual control signal through a nonlinear adaptive filter to avoid the problem of complexity explosion. The control command is generated by the dynamic surface controller and a finite-time anti-saturation compensator to overcome input saturation. Additionally, a nonlinear disturbance observer is applied to estimate the lumped disturbance to realize feedforward compensation. According to the stability analysis, all signals in the closed-loop system are uniformly ultimately bounded while the states remain in the constraint sets. Finally, the performance of the proposed controller is evaluated through extensive and comparative numerical simulations under multiple disturbances. The proposed controller has a small tracking error and high convergence speed and can prevent states from exceeding the given bounds.

A comparative study of the performance of methods for f-wave extraction

Objective. This study proposes a novel technique for atrial fibrillatory waves (f-waves) extraction and investigates the performance of the proposed method comparing with different f-wave extraction methods. Approach. We propose a novel technique combining a periodic component analysis (PiCA) and echo state network (ESN) for f-waves extraction, denoted PiCA-ESN. PiCA-ESN benefits from the advantages of using both source separation and nonlinear adaptive filtering. PiCA-ESN is evaluated by comparing with other state-of-the-art approaches, which include template subtraction technique based on principal component analysis, spatiotemporal cancellation, nonlinear adaptive filtering using an echo state neural network, and a source separation technique based on PiCA. Quality assessment is performed on a recently published reference database including a large number of simulated ECG signals in atrial fibrillation (AF). The performance of the f-wave extraction methods is evaluated in terms of signal quality metrics (SNR, ΔSNR) and robustness of f-wave features. Main results. The proposed method offers the best signal quality performance, with a ΔSNR of approximately 22 dB across all 8 sets of the reference database, as well as the most robust extraction of f-wave features, with 75% of all estimates of dominant atrial frequency well below 1 Hz.

Efficient nonlinear filter stabilization of the Leray-α model

In this work we study a novel adaptive nonlinear filtering applied to the Leray-α model. Unlike its classical counterpart, the new filtering requires the solution of a linear elliptic problem, with constant coefficients, at each time step. The action of the adaptive nonlinear filter throughout the integration time is refactorized as the solution of a linear system, with the same matrix and multiple right hand-sides. We discuss the theoretical properties of the new filtering approach applied to the BDF2 approximation of the Leray-α model. Theoretical results and numerical tests demonstrate that the linear system arising from spatial discretization is well-conditioned and the accuracy of the filter is comparable with the classical one. Some benchmark results are also presented.

Re-weighted zero attracting adaptive exponential FLAF with maximum correntropy criterion for robust sparse nonlinear system identification

The profoundly employed linear-in-the-parameter nonlinear adaptive filtering techniques of functional link adaptive filter (FLAF) and adaptive exponential FLAF (AEFLAF) often exhibit deteriorated performances in the wake of varying sparsity conditions and impulsive noise interferences. In this regard, a robust nonlinear adaptive filtering technique is introduced leveraging the benefits of nonlinear similarity index maximum correntropy criterion (MCC). Additionally a log sum penalty function is included in the derived cost function in response for sparse system identification. The entire robust nonlinear adaptive filter in this paper is constructed upon the framework of AEFLAF based on affine projection algorithm (APA) as MCC based reweighted zero attracting AEFLAF (MR-AEFLAF). Besides, steady state analysis of the proposed MR-AEFLAF is carried out establishing the condition for stability. Simulations with white, colored noise and speech segment illustrate the efficacy of the proposed technique for robust nonlinear adaptive filtering in system identification and acoustic feedback cancellation in hearing aids scenario. The performance of the designed adaptive filter is assessed quantitatively and qualitatively both.

Adaptive Gaussian filters for nonlinear state estimation with one‐step randomly delayed measurements

AbstractThis paper proposes new algorithms of adaptive Gaussian filters for nonlinear state estimation with maximum one‐step randomly delayed measurements. The unknown random delay is modeled as a Bernoulli random variable with the latency probability known a priori. However, a contingent situation has been considered in this work when the measurement noise statistics remain partially unknown. Due to unavailability of the complete knowledge of measurement noise statistics, the unknown measurement noise covariance matrix is estimated along with states following: (i) variational Bayesian approach, (ii) maximum likelihood estimation. The adaptation algorithms are mathematically derived following both of the above approaches. Subsequently, a general framework for adaptive Gaussian filter is presented with which variants of adaptive nonlinear filters can be formulated using different rules of numerical approximation for Gaussian integrals. This paper presents a few of such filters, viz., adaptive cubature Kalman filter, adaptive cubature quadrature Kalman filter with their higher degree variants, adaptive unscented Kalman filter, and adaptive Gauss–Hermite filter, and demonstrates the comparative performance analysis with the help of a nontrivial Bearing only tracking problem in simulation. Additionally, the paper carries out relative performance comparison between maximum likelihood estimation and variational Bayesian approaches for adaptation using Monte Carlo simulation. The proposed algorithms are also validated with the help of an off‐line harmonics estimation problem with real data.

An adaptive nonlinear filter with missing measurements compensation for manoeuvring target tracking

To solve the problem of missing measurements in highly manoeuvring target tracking, an expected-mode-augmentation-based unscented Kalman filter with missing measurements compensation (EMA-MMCUKF) is designed based on the variable-structure multiple model method. In the proposed EMA-MMCUKF, the random missing measurements are described by the Bernoulli distribution, and the one-step prediction is used as the compensation. Based on the proposed EMA-MMCUKF, a Bayesian estimation-based expected-mode-augmentation unscented Kalman filter with missing measurements compensation (BE-EMA-MMCUKF) is proposed for adaptive estimation of the sensor measurement reception rate, where the unknown measurement reception rate can be estimated by fully utilising prior information. Simulation results demonstrate that the proposed EMA-MMCUKF can effectively track the manoeuvring target at different measurement reception rates. Moreover, when the sensor prior information differs significantly from the true measurement reception rate, the proposed BE-EMA-MMCUKF can effectively estimate the unknown sensor measurement reception rate and improve the accuracy of manoeuvring target tracking compared with non-estimation of the sensor measurement reception rate.

The formation algorithm of errors models for satellite navigation systems and correction algorithm for aircraft navigation systems

An aircraft navigation complex as a part of an inertial navigation system, a satellite navigation system and an adaptive nonlinear Kalman filter is considered. In the Kalman filter, when the estimation process diverges, the model is constructed using an evolutionary algorithm. The used divergence indicators analyze the measured signals; the directly unmeasured state variables are not examined. A divergence criterion of directly unmeasured state variables is proposed on the grounds of the reduced measurements and the variances of the reduced measurement noises. The algorithm modification effectiveness is demonstrated by using the flight experiment data. Keywords navigation complex, adaptive nonlinear Kalman filter, divergence indicator, reduced measurements, flight experiment data

Lecture series 5 (The Final): Nonlinear adaptive filter and applications: Where reproducing kernel meets fixed-point iteration

Lecture series 5 (The Final): Nonlinear adaptive filter and applications: Where reproducing kernel meets fixed-point iteration