Recursive Filter Research Articles

Linear prediction coefficients correction method for digital speech processing systems with data compression based on the autoregressive model of a voice signal

The problem of distortion of the autoregressive model of the voice signal under the influence of additive background noise in digital speech processing systems with data compression based on linear prediction is considered. In the frequency domain, these distortions are observed in the weakening of the main formants responsible for the intelligibility of the speaker’s speech. To compensate for formant attenuation, it is proposed to modify the parameters of the autoregressive model (linear prediction coefficients) using the impulse response of a recursive shaping filter. Along with the amplitude amplification of the formants, their frequencies remain unchanged to make the speaker’s voice recognizable. The effectiveness of the method was studied experimentally using specially developed software. Based on the experimental results, conclusions were drawn about a significant increase in the relative level of formants in the power spectrum of the corrected voice signal.

A high precision vital signs detection method based on millimeter wave radar

Millimeter wave (mmWave) radar technology has potential applications in vital signs detection and medicine. In order to minimize the influence of human micro-movements and respiratory harmonics on heart rate estimation, the vital signs detection method based on mmWave radar is studied in this paper. First, we use median filtering to eliminate baseline drift caused by human micromotion. Next, a differential recursive least squares multiple classification (DR-MUSIC) algorithm is proposed based on the combination of recursive least squares-based adaptive filter (RLS) and multiple signal classification (MUSIC) algorithm. This algorithm effectively suppresses respiratory harmonics and separates respiratory and heartbeat signals. Finally, heart rate value can be precisely estimated using spectral peak search. We invite a number of people to participate in the experiment, which demonstrate that the method successfully suppresse the impact of respiratory harmonics at low SNR. The error rate between the estimated heart rate and the reference heart rate is only 1.69% to 2.61%, which is significantly better than the existing algorithms.

Hydrological dynamics of the shire river: Insights from baseflow and recession analysis

The Shire River, a vital waterway in Malawi, plays a pivotal role in the country's economy, serving as a source of electrical power and irrigation for surrounding communities. This study investigates the hydrological dynamics of the Shire River by examining its flow components and the influence of baseflow under varying climatic conditions. Through meticulous baseflow separation using the Eckhardt recursive digital filter and recession analysis, Lake Malawi emerges as the primary contributor to the river's baseflow, sustaining approximately 80%–82% of total flows annually of which about 78% is contributed during wet seasons. Moreover, an inverse relationship between baseflow and rainfall is observed, highlighting the significance of baseflow augmentation during drier periods. Baseflow analysis of wettest and driest years further elucidates precipitation's impact on baseflow fluctuations, emphasizing the intricate interplay between precipitation patterns and baseflow dynamics. Therefore, to ensure the sustainable management of the Shire River, it is crucial to implement policies that support the conservation of groundwater resources and the efficient allocation of water during varying climatic conditions. Overall, this study provides valuable insights into the hydrological processes of the Shire River, contributing to enhanced understanding and sustainable management of this essential water resource.

A novel constrained skew-Gaussian filter and its application to maneuverable reentry vehicle tracking

The state of the system generally satisfies specific constraints imposed by material properties or physical laws, so the application of these constraints can improve the accuracy of state estimation. In this paper, a novel recursive filter referred as constrained high-degree cubature skew-Gaussian filter (CHCSGF) is proposed, which achieves soft-constrained state estimation by compressing the probability density of unconstrained states with constraint information. First, the probability density of the state under inequality soft constraints is modeled as a skew-Gaussian (SG) distribution, rather than truncated or single Gaussian distributions. Then, a recursive constrained SG filter is developed to handle inequality soft constraints in linear systems. Addressing nonlinear challenges, a 5th-degree spherical-radial cubature approximation method is presented to numerically calculate SG-weighted integrals for the nonlinear transformation of SG distribution. Finally, the CHCSGF algorithm is proposed using this method to tackle nonlinear filtering problems. The CHCSGF is applied to reentry trajectory tracking to improve estimation accuracy by dealing with heat flow, dynamic pressure and overload constraints during reentry flight. Simulation results demonstrate that the CHCSGF achieves higher estimation accuracy than unconstrained methods under nonlinear inequality soft constraints, and is robust to the constraints with a prior error. Compared to particle filter and moving horizon estimation, the computational complexity of CHCSGF is significantly reduced.

Calibrated Eckhardt’s filter versus alternative baseflow separation methods: A silica-based approach in a Brazilian catchment

The Eckhardt’s filter, a recursive digital filter widely used in hydrology to separate baseflow, relies on two parameters: the recession constant (a) and the maximum allowable long-term ratio of baseflow to streamflow (BFImax). While a can be determined through regression analyses, BFImax is often assigned an arbitrary value because of limited catchment information for a more objective determination. This study aimed to assess and calibrate BFImax for a 1.2 km2 rural catchment in southern Brazil using dissolved silica data. Calibration involved minimizing differences between filter-generated baseflow hydrographs and those derived from dissolved silica measurements and mass balance across 13 monitored rainfall-runoff events. The calibrated model was compared to three established models: a modified graphical method based on local minima, a backward filter model, and a one-parameter filter. The results yielded an optimal BFImax of 0.653 with high model performance (PBias ≈ 0, NSE = 0.85, KGE = 0.74, and NRMSD = 13 %) against silica-derived baseflow. Applying the calibrated filter to a six-year streamflow dataset yielded a long-term baseflow index (BFI) value of 54 %, aligned with regional and global averages. Comparisons with other models showed that the backward filter model produced unrealistic baseflow values nearly identical to streamflow values; the local minima method overestimated baseflow by +19 % and failed to accurately represent the smoothness and peaks of the baseflow hydrographs; and the one-parameter filter represented the shape and timing of the baseflow hydrographs well, but underestimated magnitude by −19 %. These findings validate the effectiveness of the Eckhardt’s filter in generating accurate baseflow hydrographs and confirm the importance of calibrating BFImax for optimal performance. The research also endorses the use of dissolved silica measurements and the mass balance method as a reliable approach for calibrating BFImax for long-term assessment of baseflows.

A semantic edge-aware parameter efficient image filtering technique

The success of a structure preserving filtering technique has relied on its capability to recognize structures and textures present in the input image. In this paper a novel structure preserving filtering technique is presented that first, generates an edge-map of the input image by exploiting semantic information. Then, an edge-aware adaptive recursive median filter is utilized to produce the filter image. The technique provides satisfactory results for a wide variety of images with minimal fine-tuning of its parameters. Moreover, along with the various computer graphics applications the proposed technique also shows its robustness to incorporate spatial information for spectral-spatial classification of hyperspectral images. A MATLAB implementation of the proposed technique is available at-https://www.github.com/K-Pradhan/A-semantic-edge-aware-parameter-efficient-image-filtering-technique

Unscented recursive three-step filter based unbiased minimum-variance estimation for a class of nonlinear systems

For the direct feedthrough system where unknown input affects both process equation and measurement equation, an unscented recursive three-step filter based unbiased minimum-variance (URTSF-UMV) estimation algorithm is proposed. The algorithm is based on the unbiased minimum-variance (UMV) method and uses statistical linearisation technology to approximate the nonlinear system and the nonlinear measurement function to linear regression form. The estimation of unknown input is obtained from innovation through weighted least-squares (WLS) estimation. The approximate linear regression form allows us to process the nonlinear system with unknown input direct feedthrough by using the UMV state estimation framework, and derive the filter by minimising the trace of the state error covariance of the measurement update under the unbiased condition. The URTSF-UMV requires that the unknown input distribution matrix is full column rank. We use the full rank decomposition method to deal with the nonlinear system containing the unknown input rank-deficient distribution matrix. The effectiveness of the URTSF-UMV algorithm is demonstrated through an illustrative simulation example.

Using natural tracers and calibrated analytical filter to highlight baseflow contribution to mountainous Mediterranean rivers in a context of climate change

Baseflow defined as the contribution of groundwater and delayed subsurface flow, is generally described by indices such as the baseflow index (BFI), the long-term ratio of baseflow to streamflow. Characterizing baseflow is challenging because it is not directly accessible, particularly in sensitive areas to climate change like the mountainous Mediterranean regions with hard-rock aquifers. In these areas, little is known about the temporal and spatial contribution of baseflow to streamflow. This study aimed to address this scientific gap by using the first calibrated and validated recursive digital filter with natural tracers for such regions. Two watersheds of Corsica (France), the Tavignanu and the Fiumaltu, were chosen as application models for calibration and validation, respectively, due to their representative characteristics of these regions. Various methods exist for baseflow analysis, including empirical, analytical and physical methods. Empirical and analytical methods, such as digital filters, are easy to use but lack physical significance. Conversely, physical methods using natural tracers, such as isotopes and ions, are more physically representative but are difficult to implement. By calibrating and validating analytical methods with tracers in this specific context, we were able to leverage the strengths of both approaches for effective long-term baseflow analysis. This innovative approach confirmed that baseflow was the main contributor to river flow during dry months, with a contribution of 88–90 % for both watersheds. Notably, baseflow remained a significant contributor during periods of high flow, averaging 54 % for the Tavignanu and 60 % for the Fiumaltu. Over a 25-year period, the mean annual contribution was substantial, at 73 % for the Tavignanu and 77 % for the Fiumaltu. In a particularly dry year, which are expected to become more common with climate change, baseflow contribution was even higher, confirming its origin from deep groundwater and delayed subsurface components. Our results demonstrate that, in the context of climate change, groundwater and delayed subsurface flow will play an increasingly important role in sustaining rivers, connected ecosystems, as well as many human activities in the mountainous Mediterranean regions.

Hybrid six sigma based on recursive kalman filter and weibull distribution to estimate the lifespan of Bulb LEDs

The durability of LED bulbs ensures that the lights can operate for a long time without needing to be replaced or maintained too often. The brightness of high-power LED bulbs provides a strong and efficient light source, saves energy, and has a long lifespan. The traditional method of testing LED bulb life span has limitations such as long testing time, limited accuracy, high cost, inability to predict accurately, and failure to respond quickly. Therefore, the development of new and improved testing methods is necessary to effectively and accurately evaluate and ensure the durability of LED bulbs. This research paper proposes a hybrid Six Sigma method based on the recursive Kalman filter and Weibull distribution to estimate the lifespan of Bulb LEDs. The goal of the new method for evaluating LED bulb life is to provide accurate, reliable, and multi-dimensional information about the life of LED lamps, meeting the requirements of accuracy, diversity, time-saving, resources, credibility, and the ability to evaluate from a variety of perspectives. As a result of the research, the recursive Kalman filter method has strengths such as high accuracy, flexibility, saving computational resources, the ability to handle inaccurate data, and scalability. When applied to LED bulb life assessment, it provides an accurate and reliable estimate of LED lamp life. Research results on longevity testing were reduced from 1650 h to 710 h. The end-of-life test time is 710 h, and the aging time per life test cycle is 135 h. The cost of life testing is reduced from 2100.17 USD to 410.12 USD. This LED bulb lifespan testing method can be applied to similar types of LED products to improve the company's productivity and business efficiency.

Global-local manifold embedding broad graph convolutional network for hyperspectral image classification

Graph convolutional neural networks (GCNs) with domain-specific feature aggregation capabilities have unique advantages in hyperspectral image (HSI) classification. However, current GCN-based approaches frequently encounter the issue of node characteristics being over-smoothed while aggregating in higher-order domains. Furthermore, GCN linear classifiers focus solely on sample separability and ignore the potential manifold information of graph features, resulting in a failure to fully investigate extracted features. To address these problems, we propose a global-local manifold embedding broad graph convolutional network (GLMBG) for HSI classification. In GLMBG, we designed two modules from feature extraction and classification perspectives: The graph convolutional edge feature fusion extractor (GEFF) and the broad classifier of global-local manifold embedding (BGLME). GEFF is designed to learn graph node and local edge features from HSI through GCN and recursive filtering, combining them in a weighted manner to construct fused graph features. BGLME is designed to replace traditional linear classifiers with broad learning classifiers through manifold regularized embedding, fully utilizing the global and local manifold discriminant information of graph node features. The combination of GEFF and BGLME effectively reduces over-smoothing of graph node features while maximizing the utilization of manifold discriminant information, hence improving model feature discriminative ability. Experimental evaluations of three commonly used hyperspectral datasets show that our method surpasses state-of-the-art methods.

Rejection of parametric model errors in a recursive Kalman filter for virtual sensing applications

The performance of the Kalman filter is often hindered by the discrepancies between a model used to realize the filter and the true model of the data-generating system. While some methods to account for those errors exists, the majority is restricted to Luenberger's observers. The objective of this work is to develop a Kalman filter where the effect of parametric model errors is rejected from the state and observation equations before the development of the state estimate, and without the explicit knowledge of the error terms. For this purpose, errors in a physical parameter of a parametrized mechanical system are modelled as additive terms in the state and observation equations by means of first-order perturbation analysis. The rejection step is achieved with an injection of a shaped output nullifying the effect of the added terms. A state observer is then derived under the assumption that the injected shaped outputs and the system states are uncorrelated. The performance of the proposed approach is illustrated on an experimental data of a plate system.

Neural Network Signal Integration from Thermogas-Dynamic Parameter Sensors for Helicopters Turboshaft Engines at Flight Operation Conditions.

The article's main provisions are the development and application of a neural network method for helicopter turboshaft engine thermogas-dynamic parameter integrating signals. This allows you to effectively correct sensor data in real time, ensuring high accuracy and reliability of readings. A neural network has been developed that integrates closed loops for the helicopter turboshaft engine parameters, which are regulated based on the filtering method. This made achieving almost 100% (0.995 or 99.5%) accuracy possible and reduced the loss function to 0.005 (0.5%) after 280 training epochs. An algorithm has been developed for neural network training based on the errors in backpropagation for closed loops, integrating the helicopter turboshaft engine parameters regulated based on the filtering method. It combines increasing the validation set accuracy and controlling overfitting, considering error dynamics, which preserves the model generalization ability. The adaptive training rate improves adaptation to the data changes and training conditions, improving performance. It has been mathematically proven that the helicopter turboshaft engine parameters regulating neural network closed-loop integration using the filtering method, in comparison with traditional filters (median-recursive, recursive and median), significantly improve efficiency. Moreover, that enables reduction of the errors of the 1st and 2nd types: 2.11 times compared to the median-recursive filter, 2.89 times compared to the recursive filter, and 4.18 times compared to the median filter. The achieved results significantly increase the helicopter turboshaft engine sensor readings accuracy (up to 99.5%) and reliability, ensuring aircraft efficient and safe operations thanks to improved filtering methods and neural network data integration. These advances open up new prospects for the aviation industry, improving operational efficiency and overall helicopter flight safety through advanced data processing technologies.

A score-based filter for nonlinear data assimilation

We propose a score-based generative sampling method for solving the nonlinear filtering problem with superior accuracy. A major drawback of existing nonlinear filtering methods, e.g., particle filters, is the low accuracy in handling high-dimensional nonlinear problems. To overcome this issue, we incorporate the score-based diffusion model into the recursive Bayesian filter framework to develop a novel score-based filter (SF). The key idea of SF is to store the information of the recursively updated filtering density function in the score function, instead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). By leveraging the reverse-time diffusion process, SF can generate unlimited samples to characterize the filtering density. An essential aspect of SF is its analytical update step, gradually incorporating data information into the score function. This step is crucial in mitigating the degeneracy issue faced when dealing with very high-dimensional nonlinear filtering problems. Three benchmark problems are used to demonstrate the performance of our method. In particular, SF provides surprisingly impressive performance in reliably capturing/tracking the 100-dimensional stochastic Lorenz system that is a well-known challenging problem for existing filtering methods.

ℓ1${\ell }_1$ norm‐based recursive estimation for non‐linear systems with non‐Gaussian noises

AbstractThis study addresses the state estimation problem of discrete‐time non‐linear stochastic systems with non‐Gaussian noises, particularly impulsive noises. Instead of minimizing the mean square error of the state estimate, which tends to excessively focus on outliers caused by non‐Gaussian noises, the norm‐based non‐linear recursive filter (L1KF) is put forward in this paper. Here, minimizing the norm of model errors is actually to pursue the minimum sum of absolute values of all errors, which is equitable to all model errors rather than paying much attention on outliers. To further improve estimation accuracy, a recursive nonlinear smoother (L1KS) is proposed, based on minimizing the norm of model errors. The proposed norm‐based filter and smoother are implemented using unscented transformation for statistical linear regression applied to nonlinear models. Additionally, the computational complexity of the proposed method is analysed. Simulation results of tracking a radar target with impulsive noises demonstrate the effectiveness and robustness of the proposed estimator.

Method for testing the stability of an autoregressive model of the vocal tract and adjusting its parameters

Within the framework of the traditional direction of research in the field of acoustic measurements, an autoregressive model of the vocal tract as a key link in the human speech apparatus is considered. The acute problem of ensuring the stability of the autoregressive model in systems with adaptation of its parameters to the observed speech signal of short duration is pointed out. To overcome this problem, the task was set of testing the stability of the autoregressive model and adjusting its parameters based on the results of this testing. The study is based on the author’s method of formant analysis of vowel sounds of speech through the synthesis of a recursive shaping filter in the free oscillation mode. To solve sated task, a method is proposed for testing the stability and adjusting the parameters of the autoregressive model of the vocal tract based on a two-stage algorithm for its transformation. At the first stage of transformation, the stability of the autoregressive model is tested using the impulse response of the shaping filter. At the second stage, if the stability of the autoregressive model is violated, its impulse response is modified by element-by-element multiplication by a variable exponential value that asymptotically converges to zero. A regular algorithm has been developed for recalculating the modified impulse response into an adjusted vector of autoregressive parameters at the second stage of transformation. Based on the results of experimental testing of the proposed method, it was concluded that guaranteed stability of the autoregressive model of the vocal tract has been achieved with minimal distortion in the frequency domain. The results obtained are useful in the development and modernization of automatic speech recognition systems, digital speech communications, artificial intelligence and other information systems that use data compression and speech coding based on an autoregressive model of the vocal tract in automatic speech signal processing.

Robust Recursive Least-Squares Fixed-Point Smoother and Filter using Covariance Information in Linear Continuous-Time Stochastic Systems with Uncertainties

This study develops robust recursive least-squares (RLS) fixed-point smoothing and filtering algorithms for signals in linear continuous-time stochastic systems with uncertainties. The algorithms use covariance information, such as the cross-covariance function of the signal with the observed value and the autocovariance function of the degraded signal. A finite Fourier cosine series expansion approximates these functions. Additive white Gaussian noise is present in the observation of the degraded signal. A numerical simulation compares the estimation accuracy of the proposed robust RLS filter with the robust RLS Wiener filter, showing similar mean square values (MSVs) of the filtering errors. The MSVs of the proposed robust RLS fixed-point smoother are also compared to those of the proposed robust RLS filter.

Detail-preserving noise suppression post-processing for low-light image enhancement

Low-light image enhancement is a challenging task for high-quality image display and visual applications. However, most of the existing methods are difficult to effectively improve brightness and suppress noise. To solve the problem of greatly amplifying noise in many low-light image enhancement methods, this paper presents a detail-preserving noise-suppressing post-processing method for low-light image enhancement. The main idea is that Gamma correction has good performance in noise suppression, by extending the single global parameter of Gamma correction to a Gamma correction map with the same size as the low-light image, we propose an improved domain transform recursive filter to optimize Gamma correction maps, aiming to smooth the Gamma correction map while preserving structural edges, thereby achieving the goal of suppressing noise levels in the enhanced image and preserving the details and contrast of the enhanced image. The proposed post-processing approach addresses the concern of enhancing noise when enhancing low-light images, and the results show that the proposed post-processing method has good detail preservation and noise suppression performance for different advanced low-light image enhancement methods.

Frame-wise speech extraction with recursive expectation maximization for partially deformable microphone arrays

Large-apertured wearable and deformable microphone arrays have shown their better performance than conventional small wearable and rigid microphone arrays for speech extraction tasks, especially when the desired speech is far away from the arrays or there exist a great number of directional noises in practical applications. Most existing beamforming methods that require the information of the desired sound direction often cannot be used directly on deformable arrays because their shape might continuously change over time. To tackle the problem of utilizing partially deformable microphone arrays for target speech extraction, this paper derives a frame-wise speech extraction method, which is referred to as the recursive multichannel Wiener filter with generalized Gamma priors. In this method, the complex spectrum of the desired speech is assumed to follow a zero-mean complex Gaussian distribution with time-varying variance, and the reciprocal of this time-varying variance known as the precision is further assumed to follow a Gamma distribution, while the complex spectrum of the noise is assumed to follow a zero-mean complex Gaussian distribution. Under these two assumptions, we derive the recursive expectation maximization algorithm to extract the desired speech in a frame-by-frame manner. Experimental results show the promising performance of the proposed method in terms of multiple objective metrics.

Fusion estimation against mixed network attacks for systems with random parameter matrices, correlated noises, and quantized measurements

This paper is concerned with the information fusion estimation problems for stochastic uncertain systems with quantized measurements and mixed network attacks including random deception attack and denial-of-service (DoS) attack. The cross-correlated random parameter matrices and addictive noises simultaneously exist in the studied system. By resorting to the optimal prediction compensation mechanism for DoS attack, an optimal centralized fusion filter in the linear minimum variance sense is proposed using an innovation analysis approach. In addition, the Kalman-like recursive distributed optimal linear fusion predictor and filter without feedback are presented based on local estimators from single-sensor subsystems. The estimation error cross-covariance matrices between two arbitrary local estimators, and those between local and prior fusion estimators are derived. They have good flexibility due to the parallel structure. However, they have lower accuracy than the centralized fusion estimators. To further improve the estimation accuracy, the distributed optimal linear fusion predictor and filter with feedback are also presented. They avoid the calculation of cross-covariance matrices. Moreover, it has been mathematically proved that they have the same estimation accuracy as the centralized fusion estimators. A simulation example demonstrates the effectiveness of the proposed algorithms.

Detection and repair of BDS six-frequency cycle slips based on recursive filtering and integer constraint method

The multi-frequency signals of the Beidou system are very helpful for positioning, but in data processing, the detection and repair of multi-frequency cycle slips also face certain challenges. A recursive filtering and integer constraint cycle slip detection and repair method for the Beidou six-frequency is proposed in this paper. This method utilises five sets of combination coefficients of six-frequency and three sets of dual-frequency combinations, and detects and repairs cycle slips through integer constraints of cycle slip estimation. The proposed method has been validated by data with a sampling rate of 1 Hz, and can detect the position and size of cycle slips at various frequencies, whether it is random cycle slips or small cycle slips of equal size less than 2 cycles, with a detection success rate of 100%.