Recursive Filter Research Articles

A Novel Robust Nonlinear Kalman Filter Based on Multivariate Laplace Distribution

In this brief, we investigate the robust state estimation of nonlinear systems with heavy-tailed noise. Based on the fact that the multivariate Laplace (ML) distribution has heavier tails than Gaussian distribution but is only determined by its mean and covariance, we utilize the ML distribution to model the heavy-tailed measurement noise. Based on the Gaussian mixture form of ML distribution, the system state and the covariance of ML distribution are inferred by variational Bayesian method, and then a closed recursive robust nonlinear Kalman filter is obtained with the nonlinear integrations calculated by numerical integration methods. Simulation results demonstrate that the proposed algorithm is insensitive to its free parameters and can obtain better estimation accuracy than related robust algorithms.

Role of recursive cubic spline interpolation method and convolution filter in image processing

During this article, we suggested a RCSIM through Convolution filter. This filter explores the images to enhance and improve the efficiency of both gray scale and color images. Initially we identified the noises in the images and simultaneously, the corresponding pixels are noticed to improve that particular part of that image using edge detection algorithm. The pixel values of the image is converted as the window size of the matrix. This matrix should be a (n X n) square matrix and then we applied the convolution filtering techniques to the (« X n) matrix. The development of the (input) image through the convolution filter yields the feature map. The feature map accentuates the uniqueness of the original image. At the same time, the RCSIMis used to interrupt the mathematical data to the feature map. The proposed approach reduces the sound and protects the efficiency of the unique image.

Detection of fetal arrhythmia by adaptive single channel electrocardiogram extraction.

Fetal arrhythmia, the abnormal heartbeat of a fetus is broadly classified as tachy arrhythmia (too fast > 160 beats/min) and brady arrhythmia (too slow < 120 beats/min). Detection of this irregular heart beat rhythm of the fetus during pregnancy is still a challenging task for the clinicians. Heart rate detection through electrocardiography has always been accurate for identifying cardiac defect in humans. Adult ECG has achieved several developments in the modern medicine whereas noninvasive fetal ECG (FECG) continues to be a big challenge. Automatic detection of fetal heart rate is vital for monitoring the unborn infant during pregnancy. The non-invasive placement of electrodes over the abdomen region of pregnant women records the ECG signal of both mother and fetus. The arrhythmia affected FECG signals (n = 14) are processed from the physionet database. This raw ECG signal is preprocessed using a Savitzky-Golay filter and symlet wavelet transform to remove the basic noises. Adaptive recursive least square filter is preferably chosen for extracting the FECG, using mother's thorax ECG as a reference. An accurate PQRST wave-shape of the FECG is required for the proper diagnosis of fetal cardiac defects. Using a single channel abdominal ECG signal, the proposed work generates extracted fetal ECG and an automated visual display of fetal heart rate. The presence of arrhythmia and fetal distress can be analyzed through fetal heart rate display and abnormal conductivity of PQRST wave respectively. We have analyzed fetal arrhythmias through ECG extraction and the same was compared with the echocardiograph results given by pediatric cardiologist. This study helps to identify the fetal distress at early gestational age that helps the obstetricians to make quick decisions before or immediately after delivery.

Performance Investigation of Digital Lowpass IIR Filter Based on Different Platforms

The work presented in this paper illuminates the design and simulation of a recursive or Infinite Impulse Response (IIR) filter. The proposed design algorithm employs the Genetic Algorithm to determine the filter coefficients to satisfy the required performance. The effectiveness of different platforms on filter design and performance has been studied in this paper. Three different platforms are considered to implement and verify the designed filter’s work through simulation. The first platform is the MATLAB/SIMULINK software package used to implement the Biquad form filter. This technique is the basis for the software implementation of the designed IIR filter. The HDL – Cosimulation technique is considered the second one; it inspired to take advantage of the existing tools in SIMULINK to convert the designed filter algorithm to the Very high-speed integrated circuit Hardware Description Language (VHDL) format. The System Generator is employed as the third technique, in which the designed filter is implemented as a hardware structure based on basic unit blocks provided by Xilinx System Generator. This technique facilitates the implementation of the designed filter in the FPGA target device. Simulation results show that the performance of the designed filter is remarkably reliable even with severe noise levels.

Maximum mixture correntropy based outlier-robust nonlinear filter and smoother

In this paper, we are dedicated to studying the robust filtering and smoothing problem for a nonlinear non-Gaussian system. Considering the advantage of mixture correntropy with two kernel bandwidths in dealing with non-Gaussian noise, we propose the novel robust recursive filter and smoother based on the cost functions induced by the maximum mixture correntropy criterion, where the nonlinear dynamic model function and measurement model function are linearized by using the statistical linear regression (SLR) method. In the proposed robust recursive filter and smoother, we apply a third-order spherical cubature rule to obtain the prior estimation of the state and covariance matrix, and approximate the multi-dimensional Gaussian integrals encountered in the SLR method. Furthermore, two additional weights are introduced into the proposed robust recursive filter and smoother to modify the filtering and smoothing gains, respectively. The simulation results of manoeuvring target tracking under different non-Gaussian noise scenarios illustrate the effectiveness of the proposed robust recursive filter and smoother.

Forecasting daily new infections, deaths and recovery cases due to COVID-19 in Pakistan by using Bayesian Dynamic Linear Models.

The COVID-19 has caused the deadliest pandemic around the globe, emerged from the city of Wuhan, China by the end of 2019 and affected all continents of the world, with severe health implications and as well as financial-damage. Pakistan is also amongst the top badly effected countries in terms of casualties and financial loss due to COVID-19. By 20th March, 2021, Pakistan reported 623,135 total confirmed cases and 13,799 deaths. A state space model called 'Bayesian Dynamic Linear Model' (BDLM) was used for the forecast of daily new infections, deaths and recover cases regarding COVID-19. For the estimation of states of the models and forecasting new observations, the recursive Kalman filter was used. Twenty days ahead forecast show that the maximum number of new infections are 4,031 per day with 95% prediction interval (3,319-4,743). Death forecast shows that the maximum number of the deaths with 95% prediction interval are 81 and (67-93), respectively. Maximum daily recoveries are 3,464 with 95% prediction interval (2,887-5,423) in the next 20 days. The average number of new infections, deaths and recover cases are 3,282, 52 and 1,840, respectively, in the upcoming 20 days. As the data generation processes based on the latest data has been identified, therefore it can be updated with the availability of new data to provide latest forecast.

Simple Behavioral Model of Baseband Pulse Devices in the Form of a Second-Order Nonlinear Recursive Filter

A minimalistic nonlinear dynamic model, which still reflects the main aspects of the devices response to baseband pulse signals, is considered. The model is built as “black-box” and does not require knowing the structure and physical properties of the device. Since the model should reflect the exponential-type transient response, it is based on a nonlinear recursive filter. In the recursive loops the integrators are placed, because the main effect in the response of the simulated devices is the smoothing of the signal edge. The model reflects the nonlinear amplitude characteristic of the device (at the flat top of pulse), the dependence of the transient process duration on the input signal, and the nonlinear properties of the overshoot at the flat top of the pulse. We consider the realization of this model in CAD system and the methods for extracting the model parameters. The simulation error with the proposed model is 2-10% depending on the similarity of the test signal and signal at which the parameters were extracted.

River water level prediction in coastal catchment using hybridized relevance vector machine model with improved grasshopper optimization

Modelling river water level (WL) of a coastal catchment is much complex due to the tidal influences on river WL. A hybrid machine learning model based on relevance vector machine (RVM) and improved grasshopper optimization (IGOA) is proposed in this study for modelling hourly WL in a catchment located in the east coast of tropical peninsular Malaysia. Considering the non-linear relationship between inputs and output, a recursive elimination filter based on support vector machine (SVM-RFE) was employed for the selection of the best combination of inputs from antecedent WL and rainfall data for the prediction of WL one hour ahead. The performance of IGOA was compared with classical GOA and particle swarm optimization (PSO) algorithms. Besides, the performance of the hybrid RVM model was compared with the artificial neural network (ANN) models hybridized with the same optimization algorithms. The SVM-RFE selected 1-, 12- and 24-lags WL data and 1-lag rainfall data as the most potential inputs. The relative performance of the models revealed the reliability of RVM-IGOA in WL prediction of a coastal catchment. Significant improvement of model performance was noticed after optimization using IGOA with Nash-Sutcliff Efficiency (NSE) of 0.986 and 0.981, and Kling-Gupta Efficient (KGE) of 0.981 and 0.974 for RVM-IGOA and ANN-IGOA respectively, compared to the models hybridized using other optimization algorithms with NSE between 0.969 and 0.971, and KGE between 0.890 and 0.908. The study indicates the selection of predictors based on their non-linear relations with WL and better optimization of model parameters can improve model performance in simulation of highly complex hydrological phenomena like tidal river WL in a tropical coastal catchment.

Mass estimation of ground vehicles based on longitudinal dynamics using IMU and CAN-bus data

This paper considers the problem of real-time estimation of ground vehicle mass, based on longitudinal dynamics. Compared to previous contributions, this work relies on basic data from the vehicle controller area network bus. This allows for application to a very broad range of vehicles, by not using vehicle specific parameters such as current gear indicator and engine torque. The current gear ratio is predicted based on the engine and vehicle speeds. The engine torque is modelled by the mass air flow rate of the engine. The road gradient is estimated with an inertial measurement unit, with fusion of gyroscope and accelerometer using a complementary filter. To handle prolonged dynamic conditions affecting the performance of the filter, compensation of external accelerations is made by use of the vehicle speed from the controller area network bus. The mass is estimated with a recursive least squares filter with forgetting factor. The model is validated experimentally with data obtained from test drives with two different petrol powered passenger cars, equipped with a manual transmission and dual clutch automatic transmission respectively. The test drives consist of various driving conditions with different vehicle loads. The resulting mass estimates are generally good for both vehicles with variations within ±5% of the actual masses.

How to train your differentiable filter

In many robotic applications, it is crucial to maintain a belief about the state of a system, which serves as input for planning and decision making and provides feedback during task execution. Bayesian Filtering algorithms address this state estimation problem, but they require models of process dynamics and sensory observations and the respective noise characteristics of these models. Recently, multiple works have demonstrated that these models can be learned by end-to-end training through differentiable versions of recursive filtering algorithms. In this work, we investigate the advantages of differentiable filters (DFs) over both unstructured learning approaches and manually-tuned filtering algorithms, and provide practical guidance to researchers interested in applying such differentiable filters. For this, we implement DFs with four different underlying filtering algorithms and compare them in extensive experiments. Specifically, we (i) evaluate different implementation choices and training approaches, (ii) investigate how well complex models of uncertainty can be learned in DFs, (iii) evaluate the effect of end-to-end training through DFs and (iv) compare the DFs among each other and to unstructured LSTM models.

GPU efficient 1D and 3D recursive filtering

This work presents strategies to massively parallelize recursive filters on inputs of one dimension (1D) or three dimensions (3D), complementing and improving on previous state-of-the-art algorithms on two dimensions (2D). Each strategy is reusable on different algorithms for parallel processing with feedback data dependencies, allowing to develop highly optimized algorithms for computing digital filters in general, with double-pass causal-anticausal feedbacks, in one or multiple dimensions. The algorithms are linear in time and memory, exposes a high number of parallel tasks, and they are implemented on graphics processing units, i.e. GPUs. One major barrier in this area is to have such algorithms faster than generic counterparts in available libraries, and another is to have them in an easy-to-use manner. To overcome the latter, the implementation of the presented strategies is available as open source, and, to overcome the former, timing performance and comparison results are provided, including a range of publicly available source codes and libraries, showing that this work outperforms fastest prior algorithms.

A random patches based edge preserving network for land cover classification using Polarimetric Synthetic Aperture Radar images

ABSTRACT A random patches-based edge-preserving network (RPEP) is proposed for polarimetric synthetic aperture radar (PolSAR) image classification in this paper. An initial spatial feature extraction is firstly done using the transform domain recursive filtering. From the filtered images, several random patches are chosen and used as convolutional kernels. The designed random patches-based network uses these fix kernels without doing any training process. The multi-scale features extracted by both shallow and deep layers are given to a support vector machine to get an initial classification map. The binary probability maps obtained from the initial classification map are then smoothed using the guided filter as an edge preserving filter. The final classification map is achieved by applying the maximum decision rule. The proposed RPEP method with extraction of robust, consistent, invariant and multi-scale polarimetric-spatial features and also by doing noise reduction with edge preserving filters provides superior classification results compared to several state-of-the-art methods especially in small sample size situations. In addition, RPEP has a simple and fast implementation that makes it a powerful classifier for real applications.

Can the two-parameter recursive digital filter baseflow separation method really be calibrated by the conductivity mass balance method?

Abstract. The two-parameter recursive digital filter method (Eckhardt) and the conductivity mass balance (CMB) method are two widely used baseflow separation methods favored by hydrologists. Some divergences in the application of these two methods have emerged in recent years. Some scholars believe that deviation of baseflow separation results of the two methods is due to uncertainty of the parameters of the Eckhardt method and that the Eckhardt method should be corrected by reference to the CMB method. However, other scholars attribute the deviation to the fact that they contain different transient water components. This study aimed to resolve this disagreement by analyzing the effectiveness of the CMB method for correcting the Eckhardt method through application of the methods to 26 basins in the United States by comparison of the biases between the generated daily baseflow series. The results showed that the approach of calibrating the Eckhardt method against the CMB method provides a “false” calibration of total baseflow by offsetting the inherent biases in the baseflow sequences generated by the two methods. The baseflow sequence generated by the Eckhardt method usually includes slow interflow and bank storage return flow, whereas that of the CMB method usually includes high-conductivity water flushed from swamps and depressions by rainfall, but not low-conductivity interflow and bank storage return flow. This difference results in obvious peak misalignment and periodic deviation between the baseflow sequences obtained by the two methods, thereby preventing calibration. However, multi-component separation of streamflow can be achieved through comparison. Future research should recognize the deviations between the separation results obtained by the different methods, identify the reasons for these differences, and explore the hydrological information contained therein.

Improved Design Method for Nearly Linear-Phase IIR Filters Using Constrained Optimization

In this paper, the design of nearly linear-phase recursive digital filters using a constrained optimization method is investigated. The method is based on existing constrained optimization techniques for nearly linear-phase IIR digital filters, and it is expected to be useful in applications where both magnitude and phase response specifications are required to be satisfied. Starting from an initial filter, the proposed method minimizes the group delay deviation under a set of linear constraints in terms of the magnitude response and filter stability. Improved sampling functions are introduced to the optimization problem, which are used to control the sampling points that are used for approximating the group delay and the rest of the constraints in various frequency bands. By using the proposed sampling functions we get an improved IIR filter response.

Recursive filter based GPU algorithms in a Data Assimilation scenario

Data Assimilation process is generally used to estimate the best initial state of a system in order to improve accuracy of future states prediction. This powerful technique has been widely applied in investigations of the atmosphere, ocean, and land surface. In this work, we deal with the Gaussian convolution operation which is a central step of the Data Assimilation approach, as well as in several data analysis procedures. In particular, we consider the use of recursive filters to approximate the Gaussian convolution. In [1] we presented an accelerated first-order recursive filter to compute the Gaussian convolution kernel, in a very fast way. We present theory and results, and we provide a new GPU-parallel implementation which is based on the third order recursive filter. To observe the benefits in terms of performance, tests and experiments complete our work.

Recursive Filtering for Time-Varying Discrete Sequential Systems Subject to Deception Attacks: Weighted Try-Once-Discard Protocol

In this article, recursive filtering is investigated for time-varying discrete sequential systems (DSSs) under weighted try-once-discard (WTOD) protocols, which are employed to govern the access authorization of a shared network in order to remit the communication burden. A transmission model, dependent on a Bernoulli distributed white sequence, is developed to describe the phenomenon of deception attacks. In light of the adopted protocol and the attack model, a recursive algorithm with the form of Riccati-like difference equations is developed to optimize the filtering performance in the mean square sense. Furthermore, by resorting to the mathematical induction, the convergence of the proposed recursive algorithm is discussed profoundly. Finally, a simulation example is presented to verify the availability of the designed recursive filter.

Estimator for Multirate Sampling Systems With Multiple Random Measurement Time Delays

The optimal linear estimation problem is studied for multirate sampling systems with multiple random measurement time delays (TDs). The considered multirate sampling scheme is that the sensor uniformly samples at a slow rate and the state uniformly updates at a fast rate. Known stochastic variable sequences obeying Bernoulli distributions are adopted to depict random measurement TDs, including missing measurements as a special case. First, using a state iterating method, the original system with multirate sampling and delayed measurements is transformed into a state-space model with single-rate sampling and delay-free measurements at measurement sampling (MS) instants. Then, by utilizing projection theory, a nonaugmented recursive optimal linear state filter is presented based on the established model in the linear minimum variance sense, where the estimators for the process noise are involved. Furthermore, the state estimator at state update instants is achieved through filtering or prediction based on the filter at MS instants. Finally, the centralized fusion estimator and the distributed covariance intersection fusion estimator are proposed for the multisensor case. Simulation research on a vehicle suspension system verifies the effectiveness of the algorithms.

Passive Synthetic Aperture Radar Imaging Using Kalman Reflection Coefficients Estimation Algorithm with DVB-T Signal

In this paper, a new method is presented for image formation in a Multistatic Passive Synthetic Aperture Radar (SAR), whose receiver is moving and transmitters are stationary in a multistatic structure, and the signal used to create the image is DVB-T. The proposed method uses multiple transmitters of opportunity to improve the range resolution of a Passive SAR. First, a linear observation model is developed for multistatic structure of the Passive SAR system. Then, the image of the underlying scene is obtained through a new Kalman-based estimation algorithm. In this algorithm, range migration error is completely corrected, and the use of Kalman recursive filter reduces the computational complexity of the reflection coefficients estimation algorithm. Experimental results indicate that the proposed algorithm is effective.

High-Resolution SMAP-Derived Root-Zone Soil Moisture Using an Exponential Filter Model Calibrated per Land Cover Type

Root-zone soil moisture (RZSM) plays a key role for most water and energy budgets, as it is particularly relevant in controlling plant transpiration and hydraulic redistribution. RZSM data is needed for a variety of different applications, such as forecasting crop yields, improving flood predictions and monitoring agricultural drought, among others. Remote sensing provides surface soil moisture (SSM) retrievals, whose key advantage is the large spatial coverage on a systematic basis. This study tests a simple method to retrieve RZSM estimates from high-resolution SSM derived from SMAP (Soil Moisture Active Passive). A recursive exponential filter using a time constant τ is calibrated per land cover type, which uses as an intermediate step a long-term ISBA-DIF (Interaction Soil Biosphere Atmosphere—Diffusion scheme) dataset over an area located in Catalonia, NE of Spain. The τ values thus obtained are then used as an input to the same recursive exponential filter, to derive 1 km resolution RZSM estimates from 1 km SMAP SSM, which are obtained from the original data by downscaling to a 1 km resolution, through the DISPATCH (DISaggregation based on a Physical and Theoretical scale CHange) methodology. The results are then validated with scaled in situ observations at different depths, over two different areas, one representative of rainfed crops, and the other of irrigated crops. In general, the estimates agree well with the observations over the rainfed crops, especially at a 10 cm and 25 cm depth. Nash–Sutcliffe (NS) scores ranging between 0.33 and 0.58, and between 0.37 and 0.56 have been found, respectively. Correlation coefficients for these depths are high, between 0.76 and 0.91 (10 cm), and between 0.71 and 0.90 (25 cm). For the irrigated sites, results are poorer (partly due to the extremely high heterogeneity present), with NS scores ranging between −2.57 and 0.16, and correlations ranging between −0.56 and 0.48 at 25 cm. Given the strong correlations and NS scores found in the surface, the sensitivity of the filter to different τ values was investigated. For the rainfed site, it was found, as expected, with increasing τ, increasing NS and correlations with the deeper layers, suggesting a better coupling. Nevertheless, a strong correlation with the surface (5 cm) or shallower depths (10 cm) observed over certain sites indicates a certain lack of skill of the filter to represent processes which occur at lower levels in the SM column. All in all, a calibration accounting for the vegetation was shown to be an adequate methodology in applying the recursive exponential filter to derive the RZSM estimates over large areas. Nevertheless, the relative shallow surface at which the estimates correlate in some cases seem to indicate that an effect of evapotranspiration in the profile is not well captured by the filter.

Robust Recursive Filtering for Stochastic Systems With Time-Correlated Fading Channels

This article is concerned with the robust recursive filtering (RF) problem for a class of stochastic uncertain systems subject to time-correlated fading channels. The measurement received by the sensor is transmitted to the remote filter through the time-correlated fading channel where the channel coefficient evolves according to a certain dynamics and hence exhibits a time-correlated nature. The parameter uncertainties of the system are described by norm-bounded unknown matrices. By introducing a class of auxiliary variables, an augmented system is constructed to reflect the dynamics of the fading coefficient and state simultaneously. Then, a recursive filter is designed which is capable of online computation. Furthermore, an upper bound is guaranteed for the filtering error covariance (FEC) for the possible parameter uncertainties as well as the time-correlated fading channels. With the help of the completing-the-squares technique, filter gains are parameterized by minimizing the obtained upper bound. Finally, two examples are employed to verify the effectiveness of the proposed robust RF method.