Linear Filter Research Articles

High-speed recursive-separable image processing filters

The development of modern technologies in the field of image formation leads to an increase in the size of the generated images, as a result the question of reducing the processing computational costs arises, and this is an important factor in the creation of real-time systems. The study provides a description of high-speed recursive-separable filters for improving the quality of images, which, due to the peculiarities of their implementation, can reduce the number of computational operations required for the image processing process. This type of filters is obtained from two-dimensional linear digital filters, which are modified by applying recursive and separable properties to them. The MATLAB environment computing method for implementation of these filters is described. An extensive performance research of the developed filters has been carried out at various sizes of the test image and on various experimental installations. The comparison with the classical two-dimensional convolution method of the developed filters is demonstrated, and it shows the time gain required for the image processing. The results obtained can be applied in biomedical image processing systems or in vision systems working in heavy weather conditions.

A Gyroless Attitude Estimation for Ground Vehicle Under Severe Dynamic Conditions

In this paper, we propose an inertial measurement unit (IMU) based accurate attitude estimation algorithm for land vehicles using only accelerometer and magnetometer data along with a set of nonholonomic constraints on vehicle motion. Currently, most of the IMU based attitude estimation methods deploy gyroscopes along with accelerometer measurements which work efficiently only either for static or quasi-static conditions. However, during prolonged dynamic phases of vehicle motion, the accelerometer measurements are corrupted due to external acceleration which deteriorates the attitude estimation accuracy. In this paper, we illustrate that vehicle and sensor constraints allow the removal of external acceleration from accelerometer measurement in a magnetically clean environment. This, in turn, enables to design and use a linear Kalman filter (KF) using only accelerometer and magnetometer data for accurate attitude estimation. The proposed algorithm is tested and compared with three different state-of-the-art algorithms in simulation and real-world experiments under various dynamic conditions. The results illustrate that vehicle attitude information can be obtained accurately and reliably during long term fast dynamic conditions, using the designed KF.

Linear time-varying matched filter for known and unknown SOI generalized cyclostationary signal with multiple cyclic frequencies

Chirp cyclic matched filter has been designed for chirp cyclostationary (CCS) signals, a kind of generalized cyclostationary signals, recently. However, it is designed based on statistical prior information and waveform of the signal-of-interest (SOI) CCS signal, which works only for CCS signal with a single chirp cyclic frequency. As known, the prior information of SOI signal may not be exactly known or the measured waveform of SOI signal is noised in practical applications, which decreases performance of the algorithm. In this study, by decomposing the imprecisely known SOI signal as the summation of SOI signal and an unknown additive disturbance, three kinds of chirp cyclic matched filters are designed according to the value of signal-to-noise ratio (SNR). Furthermore, noticing the CCS signal usually contains multiple chirp cyclic frequencies, three kinds of combined chirp cyclic matched filter are designed for known/unknown SOI CCS signals by linearly combining the chirp cyclic matched filter at every chirp cyclic frequency. Moreover, ramifications of the truncation process and complexity of the proposed algorithms are analyzed. Finally, simulation results validate the improvement of the chirp cyclic matched filter based on multiple chirp cyclic frequencies than on a single chirp cyclic frequency in different SNR situations.

A general class of optimal nonlinear resonant controllers of fractional order with time-delay for active vibration control – theory and experiment

The present article generalizes the classical integer-order resonant controllers for active vibration control. The proposed controller utilizes a second-order linear filter with response feedback and a control input in the form of a nonlinear, time-delayed function of the fractional derivative of the filter variable. Thereby, the proposed controller encompasses the integer-order resonant controllers, like positive position feedback, acceleration feedback, negative velocity feedback, etc. as special cases and allows an extra degree of freedom in terms of choosing the optimum form of the control input function. Theoretical analysis of the system is performed by the method of multiple time scales and finally, the results are verified by numerical simulations and experiments. Two new numerical methods of parameters optimization are discussed. Detailed parametric studies are performed to reveal the effects of different design parameters, viz. the control gain, time-delay, and the fractional-order of the input function on the system performance. The theoretical and experimental studies demonstrate the supremacy of the fractional-order control over integer-order resonant control, especially for higher control gain and delay. The existence of an optimal value of the fractional order of the control function is established.

Autoregressive Modeling based ECG Cardiac Arrhythmias’ Database System

This article proposes an ECG (electrocardiography) database system based on linear filtering, wavelet transform, PSD analysis, and adaptive AR modeling technologies to distinguish 19 ECG beat types for classification. This paper uses the Savitzky-Golay filter and wavelet transform for noise reduction, and wavelet analysis and AR modeling techniques for feature extraction to design a database system of AR coefficients describing the ECG signals with different arrhythmia types. In the experimental part of this work, the proposed algorithm performance is evaluated using an ECG dataset containing 19 different types including normal sinus rhythm, atrial premature contraction, ventricular premature contraction, ventricular tachycardia, ventricular fibrillation, supraventricular tachycardia, and other types from the MIT-BIH Arrhythmia Database. The simulation is performed in a MATLAB environment.

Assessment of watermelon maturity using portable new generation NIR spectrophotometers

The non-destructive evaluation of internal maturity in watermelons, which are large fruits with a thick rind, during their development on the vine can be considered as a challenge for the growing sector. Near infrared spectroscopy (NIRS) was used to assess in situ soluble solid content (SSC), the main parameter to establish full maturity, in 249 intact watermelons, of which, 152 had a striped light green rind and 97 a solid dark green rind. Two handheld new generation spectrophotometers were compared for this purpose. Different pre-processing methods and the partial least squares (PLS) regression algorithm were used to build global calibration models and specific calibration models for each one of the two types of watermelon analysed. The results obtained for the global models showed that NIRS is a suitable technology for screening the fruit for maturity, and that the linear variable filters (LVF) sensor is the best equipment for this purpose (SECV = 1.02%; RPDp = 1.36). Moreover, the best results were obtained when different models were used depending on the type of watermelon. Additionally, near infrared (NIR) classification models were developed to discriminate the samples by stage of maturity for each type of watermelon available, using partial least squares discriminant analysis (PLS-DA). The optimum threshold values for the striped light green and solid dark green rind watermelons (0.82 and 0.65, respectively) were displaced from the mean value of the discriminant variable due to the differences in terms of number of samples per class used. A total of 66.4% and 82.2% of the striped light green and solid dark green rind watermelons, respectively, were correctly classified. The results of this study demonstrated the viability of using NIRS technology as a decision-making support tool to measure the maturity of watermelons and to establish the optimum harvest time of watermelons and therefore meet the consumers’ demand for sweet-tasting fruits. Further studies will be needed to improve calibration robustness, and to further interpret outdoor applications in fruits with thick rind.

Distributed filtering in sensor networks based on linear minimum mean square error criterion with limited sensing range

One of the fundamental problems in sensor networks is to estimate and track the target states of interest that evolve in the sensing field. Distributed filtering is an effective tool to deal with state estimation in which each sensor only communicates information with its neighbors in sensor networks without the requirement of a fusion center. However, in the majority of the existing distributed filters, it is assumed that typically all sensors possess unlimited field of view to observe the target states. This is quite restrictive since practical sensors have limited sensing range. In this article, we consider distributed filtering based on linear minimum mean square error criterion in sensor networks with limited sensing range. To achieve the optimal filter and consensus, two types of strategies based on linear minimum mean square error criterion are proposed, that is, linear minimum mean square error filter based on measurement and linear minimum mean square error filter based on estimate, according to the difference of the neighbor sensor information received by the sensor. In linear minimum mean square error filter based on measurement, the sensor node collects measurement from its neighbors, whereas in linear minimum mean square error filter based on estimate, the sensor node collects estimate from its neighbors. The stability and computational complexity of linear minimum mean square error filter are analyzed. Numerical experimental results further verify the effectiveness of the proposed methods.

Singular Spectrum Analysis and Circulant Maximum Variance Frames

Singular spectrum analysis (SSA) is a powerful method that is frequently used in dynamical systems theory and time series analysis. However, the algorithm itself is only partially understood. In this paper, we tackle the problem of a thorough interpretation of the complete basic SSA algorithm. We point out the relationship between SSA and Fourier analysis (FA), linear filtering (LF), principal component analysis (PCA), and power spectrum density estimation (PSDE). The main contribution is a reformulation and comprehensive interpretation of SSA by means of a novel class of data-adaptive circulant frames. Based on this class of frames, we introduce a formalism for time series decomposition and reconstruction. This mathematical framework generalizes principle component analysis and SSA. We show that SSA, PCA, FA, LF, and PSDE can be found from special cases of the proposed frame structures. This way we are able to provide a formal description of SSA and its relationship to the aforementioned methods. Whilst previous approaches to the interpretation of SSA relied on approximations, we provide exact mathematical descriptions of the relation between the above-mentioned techniques.

Simplified radius-directed linear Kalman filter algorithm for lightning-induced state of polarization compensation in optical ground wire

Lightning strokes can cause an ultrafast rotation of the state of polarization (RSOP) in an optical ground wire cable, which leads to communication interruptions. To address this, a simplified radius-directed linear Kalman filter (S-RD-LKF) for blind polarization demultiplexing was developed. The ultrafast RSOP under thunderstorm weather conditions was simulated based on the Heidler model, and the simulation results indicated that the proposed S-RD-LKF algorithm effectively compensated for the RSOP impairment caused by the first and subsequent lightning strokes. Moreover, the RD-LKF algorithm and the proposed S-RD-LKF algorithm exhibited a similar performance; however, the computation complexity of the proposed algorithm was lower.

State Estimation of Gas-Lifted Oil Well Using Nonlinear Filters.

The focus of this work is the extension of nonlinear state estimation methods to gas-lifted systems. The extended Kalman filter (EKF), unscented Kalman filter (UKF) and particle filter (PF) were used to estimate the nonlinear states. Brief descriptions of the filters were first presented starting from the linear Kalman filter. Hypothesis tests on the expectation of the residuals were performed to show how close to optimal the estimation methods are and it showed the UKF estimates to be slightly better than EKF while PF performs the worst. The PF has poor accuracy using residual visualisation, hypothesis test and the root mean squared error (RMSE) values of the residuals. The gas-lifted system exhibits casing heading instability where the states show oscillatory behaviour depending on the value of the input but the results here do not change in a known way for each filter as the input is changed from the non-oscillatory region to the oscillatory region. Therefore, for this noise distribution and model assumption, either the EKF or UKF can be used for nonlinear state estimation with UKF better preferred if computational cost is not considered when control solutions are used in gas-lifted system.

A hybrid 2D/4D-MRI methodology using simultaneous multislice imaging for radiotherapy guidance.

PurposeRespiratory motion management is important in abdominothoracic radiotherapy. Fast imaging of the tumor can facilitate multileaf collimator (MLC) tracking that allows for smaller treatment margins, while repeatedly imaging the full field‐of‐view is necessary for 4D dose accumulation. This study introduces a hybrid 2D/4D‐MRI methodology that can be used for simultaneous MLC tracking and dose accumulation on a 1.5 T Unity MR‐linac (Elekta AB, Stockholm, Sweden).MethodsWe developed a hybrid 2D/4D‐MRI methodology that uses a simultaneous multislice (SMS) accelerated MRI sequence, which acquires two coronal slices simultaneously and repeatedly cycles through slice positions over the image volume. As a result, the fast 2D imaging can be used prospectively for MLC tracking and the SMS slices can be sorted retrospectively into respiratory‐correlated 4D‐MRIs for dose accumulation. Data were acquired in five healthy volunteers with an SMS‐bTFE and SMS‐TSE MRI sequence. For each sequence, a prebeam dataset and a beam‐on dataset were acquired simulating the two phases of MR‐linac treatments. Prebeam data were used to generate a 4D‐based motion model and a reference mid‐position volume, while beam‐on data were used for real‐time motion extraction and reconstruction of beam‐on 4D‐MRIs. In addition, an in‐silico computational phantom was used for validation of the hybrid 2D/4D‐MRI methodology. MLC tracking experiments were performed with the developed methodology, for which real‐time SMS data reconstruction was enabled on the scanner. A 15‐beam 8× 7.5 Gy intensity‐modulated radiotherapy plan for lung stereotactic body radiotherapy with isotropic 3 mm GTV‐to‐PTV margins was created. Dosimetry experiments were performed using a 4D motion phantom. The latency between target motion and updating the radiation beam was determined and compensated. Local gamma analyses were performed to quantify dose differences compared to a static reference delivery, and dose area histograms (DAHs) were used to quantify the GTV and PTV coverage.ResultsIn‐vivo data acquisition and MLC tracking experiments were successfully performed with the developed hybrid 2D/4D‐MRI methodology. Real‐time liver–lung interface motion estimation had a Pearson's correlation of 0.996 (in‐vivo) and 0.998 (in‐silico). A median (5th–95th percentile) error of 0.0 (−0.9 to 0.7) mm and 0.0 (−0.2 to 0.2) mm was found for real‐time motion estimation for in‐vivo and in‐silico, respectively. Target motion prediction beyond the liver–lung interface had a median root mean square error of 1.6 mm (in‐vivo) and 0.5 mm (in‐silico). Beam‐on 4D MRI reconstruction required a median amount of data equal to an acquisition time of 2:21–3:17 min, which was 20% less data compared to the prebeam‐derived 4D‐MRI. System latency was reduced from 501 ± 12 ms to −1 ± 3 ms (SMS‐TSE) and from 398 ± 10 ms to −10 ± 4 ms (SMS‐bTFE) by a linear regression prediction filter. The local gamma analysis agreed within −3.8% to 3.3% (SMS‐bTFE) and −5.3% to 10% (SMS‐TSE) with a reference MRI sequence. The DAHs revealed a relative D98% GTV coverage between 97% and 100% (SMS‐bTFE) and 100% and 101% (SMS‐TSE) compared to the static reference.ConclusionsThe presented 2D/4D‐MRI methodology demonstrated the potential for accurately extracting real‐time motion for MLC tracking in abdominothoracic radiotherapy, while simultaneously reconstructing contiguous respiratory‐correlated 4D‐MRIs for dose accumulation.

Application of Continuous Non-Gaussian Mortality Models with Markov Switchings to Forecast Mortality Rates

The ongoing pandemic has resulted in the development of models dealing with the rate of virus spread and the modelling of mortality rates μx,t. A new method of modelling the mortality rates μx,t with different time intervals of higher and lower dispersion has been proposed. The modelling was based on the Milevski–Promislov class of stochastic mortality models with Markov switches, in which excitations are modelled by second-order polynomials of results from a linear non-Gaussian filter. In contrast to literature models where switches are deterministic, the Markov switches are proposed in this approach, which seems to be a new idea. The obtained results confirm that in the time intervals with a higher dispersion of μx,t, the proposed method approximates the empirical data more accurately than the commonly used the Lee–Carter model.

Angular Velocity Estimation and Error-Covariance Analysis from Accelerometers Using Least Squares

In this work angular velocity solutions are presented from accelerometers. Two main formulations are presented. The first is based on using multiple vector sets of accelerometers, and the second is based on using multiple single-axis accelerometers. Linear least-squares approaches are derived for both, along with error-covariance expressions for the angular velocity estimates. Nonlinear least-squares approaches are also derived for both, which also provide the Cramér–Rao lower bound as a byproduct. All approaches have a sign ambiguity in the angular velocity solutions, which is resolved using a simple linear Kalman filter. Simulation results are shown to compare the formulations, along with the linear and nonlinear least-squares solutions.

An Optimal H∞ Approach for Local Stability Analysis of Non Linear Digital Systems with Saturation Non Linearity and External Interference

An optimal [Formula: see text] criterion for the stability investigation of non linear digital filters with saturation non linearity and external interference is proposed in this paper. The proposed criterion can be used for overflow oscillation-free realization of the non linear digital system implemented with fixed wordlength machines like digital computers or special purpose embedded systems. The proposed approach ascertains the local asymptotic stability of non linear digital filtering schemes without external interference. Further, by employing [Formula: see text] performance criterion the conditions for local stability and performance measurement are proposed with external interference. In the proposed work, the stability conditions are proposed in linear matrix inequality (LMI) by exploiting energy-based Lyapunov theory, Lipschitz inequality, and saturation arithmetic. The proposed criterion is shown to be less conservative which will improve the operating region and obtain a better estimate of [Formula: see text] performance index compared to the existing local criterion. Moreover, the proposed criterion can be used in selecting the appropriate wordlength of a digital system for tolerable values of interference energy, [Formula: see text] performance level, and fixed-point resolution. This will be an additional advantage of this work compared with existing global criteria. Sufficient examples to show the efficacy of the proposed technique are also provided.

Microwave photonics broadband unambiguous frequency measurement based on a Sagnac loop and a linear optical filter.

We propose an instantaneous frequency measurement (IFM) scheme featured with unambiguous measurement utilizing a Sagnac loop with an embedded bi-directional phase modulator and an optical filter with a linear frequency response. The frequency of the microwave signal to be measured is instantaneously estimated by calculating an amplitude comparison function (ACF) of photocurrents from the upper and lower branches of the proposed structure. Compared to previous IFM schemes, the ACF in the proposed scheme is monotonic, by which the frequency of the unknown microwave signal can be uniquely confirmed without ambiguity. Only one laser source and a phase modulator are needed, which simplifies the measurement system. In addition, the monotonous ACF can guarantee measurement accuracy in a wide range, from low frequency to high frequency. The IFM system has robustness in optical and RF power shifts. Simulation results show that frequency measurement over the range of 30 GHz with a measurement error of 0.4 GHz is achieved.

Universal prediction algorithm in maneuvering target tracking

The paper considers the methods to increase the accuracy of trajectory processing of the results of radar measurements in automated air traffic management systems (AATMS). The recursive filters traditionally used in the secondary processing path of radar information of modern AATMS systems are briefly considered: alpha-beta filter, linear and extended Kalman filters, multi-model filter. Along with multi-model Kalman filters it is proposed to use a universal filter based on the universal prediction theorem, the accuracy of which is asymptotically no worse than any other filter in the class of continuous functions. The algorithm for the operation of a universal alpha-beta filter was developed. As a result of modeling, it was obtained that the mean square of the tracking error of the trajectory of a maneuvering target for the universal filter during the change of the motion model turned out to be lower than for traditional filters.

The stability investigation of variable viscosity control in the human-robot interaction.

BackgroundFor many co‐manipulative applications, variable damping is a valuable feature provided by robots. One approach is implementing a high viscosity at low velocities and a low viscosity at high velocities. This, however, is proven to have the possibility to alter human natural motion performance.MethodsWe show that the distortion is caused by the viscosity drop resulting in robot's resistance to motion. To address this, a method for stably achieving the desired behaviour is presented. It involves leveraging a first‐order linear filter to slow the viscosity variation down.ResultsThe proposition is supported by a theoretical analysis using a robotic model. Meanwhile, the user performance in human‐robot experiments gets significantly improved, showing the practical efficiency in real applications.ConclusionsThis paper discusses the variable viscosity control in the context of co‐manipulation. An instability problem and its solution were theoretically shown and experimentally evidenced through human‐robot experiments.

Multiplication and Accumulation Co-Optimization for Low Complexity FIR Filter Implementation

In multiplierless finite impulse response (FIR) filters, the product accumulation block (PAB) could be the major contributor to hardware complexity, especially for high-order filters. In this paper, an optimization scheme where the constant multiplication block and the PAB are jointly optimized at the bit-level is proposed to minimize the hardware complexity. In the proposed joint optimization, the multiple constant multiplications (MCM) block is rearranged into several MCM sub-blocks. The products are summed locally before accumulation to reduce the word-length of the structural adders. It is shown that the symmetric property of linear phase FIR filters can be utilized in some cases to further reduce the complexity of the constant multiplications. Quantitative analyses are also presented to study the relationship between the optimum group size and the coefficient values as well as the filter orders. It is shown that there is no fixed optimum structure for filters with different coefficient word-lengths and filter orders, and each filter needs to be optimized specifically to achieve the minimum hardware complexity. Implementation results are presented to validate the effectiveness of the proposed method.

Designing and validating a robust adaptive neuromodulation algorithm for closed-loop control of brain states

Objective. Neuromodulation systems that use closed-loop brain stimulation to control brain states can provide new therapies for brain disorders. To date, closed-loop brain stimulation has largely used linear time-invariant controllers. However, nonlinear time-varying brain network dynamics and external disturbances can appear during real-time stimulation, collectively leading to real-time model uncertainty. Real-time model uncertainty can degrade the performance or even cause instability of time-invariant controllers. Three problems need to be resolved to enable accurate and stable control under model uncertainty. First, an adaptive controller is needed to track the model uncertainty. Second, the adaptive controller additionally needs to be robust to noise and disturbances. Third, theoretical analyses of stability and robustness are needed as prerequisites for stable operation of the controller in practical applications. Approach. We develop a robust adaptive neuromodulation algorithm that solves the above three problems. First, we develop a state-space brain network model that explicitly includes nonlinear terms of real-time model uncertainty and design an adaptive controller to track and cancel the model uncertainty. Second, to improve the robustness of the adaptive controller, we design two linear filters to increase steady-state control accuracy and reduce sensitivity to high-frequency noise and disturbances. Third, we conduct theoretical analyses to prove the stability of the neuromodulation algorithm and establish a trade-off between stability and robustness, which we further use to optimize the algorithm design. Finally, we validate the algorithm using comprehensive Monte Carlo simulations that span a broad range of model nonlinearity, uncertainty, and complexity. Main results. The robust adaptive neuromodulation algorithm accurately tracks various types of target brain state trajectories, enables stable and robust control, and significantly outperforms state-of-the-art neuromodulation algorithms. Significance. Our algorithm has implications for future designs of precise, stable, and robust closed-loop brain stimulation systems to treat brain disorders and facilitate brain functions.

Linear Filtering with Fractional Noises: Large Time and Small Noise Asymptotics

The classical state-space approach to optimal estimation of stochastic processes is efficient when the driving noises are generated by martingales. In particular, the weight function of the optimal linear filter, which solves a complicated operator equation in general, simplifies to the Riccati ordinary differential equation in the martingale case. This reduction lies in the foundations of the Kalman--Bucy approach to linear optimal filtering. In this paper we consider a basic Kalman--Bucy model with noises, generated by independent fractional Brownian motions, and develop a new method of asymptotic analysis of the integro-differential filtering equation arising in this case. We establish existence of the steady-state error limit and find its asymptotic scaling in the high signal-to-noise regime. Closed form expressions are derived in a number of important cases.