Improving Performance of an Adaptive Equalizer using EKF Trained Multilayered Neural Networks

Developing mathematical models and estimating their parameters are fundamental issues for studying dynamic behaviors of traffic systems. METANET model is one of the most applicable models in traffic modeling in which the parameters have plenty of effects on the model behavior. In this paper, the effects of the model parameters on the model behavior and the estimation quality of the system states in the undetermined parameters are described. The extended Kalman filtering (EKF) algorithm instead of the error back-propagation (BP) algorithm is used to train artificial neural networks (ANNs) for dynamical traffic networks modeling. The basic idea is to prevent over fitting discrepancy occurrence caused by outliers in the training samples by the EKF. Numerical simulations show that the EKF algorithm is greater to the BP algorithm.

The power generation system with renewable energy supply is susceptible to the influence of external environment. Lithium battery and other energy storage devices need to be added in the new energy field to smooth the output of renewable energy generation system and improve the stability of the integrated system. Accurately estimating the state of charge (SOC) of energy storage batteries can effectively improve the use and reasonable scheduling of batteries. This paper takes ternary lithium battery pack as the research object and builds a second-order RC equivalent circuit model to estimate the SOC. According to the time-varying characteristics of battery model parameters, recursive least square method with forgetting factor was used to identify the parameters, the model parameters are modified using the current data. To solve the problem of accumulated error of extended Kalman filter (EKF) algorithm, an adaptive fading factor was introduced to correct prediction error covariance matrix and suppress the influence of historical data on the current state. Matlab simulation and dynamic stress testing experiments show that, compared with EKF algorithm, the adaptive fading EKF (AFEKF) algorithm has higher accuracy.

As a fundamental prerequisite for a variety of location-based services, indoor location information has received increasing attention in recent years. Under the line-of-sight condition, the positioning accuracy of the indoor positioning technology based on ultrawideband (UWB) is acceptable for many applications, but under the non-line-of-sight condition, it degrades dramatically. The positioning accuracy can be significantly improved by the fusion of inertial measurement units and UWB sensors based on the extended Kalman filter (EKF) algorithm. However, when UWB measurements are affected by large non-Gaussian noise, the assumption of the EKF algorithm that observations are subject to Gaussian distribution for noise is invalid. Although the non-Gaussian noise can be handled by the robust EKF algorithm, this algorithm only uses the prior information to judge the reliability of the observations, and the positioning result is not stable when the number of beacons is small. To solve this problem, a method for successive updating of the covariance and posterior state of the observations in iterations based on an iterated extended Kalman filter (IEKF) is proposed. The marginal distribution of the posterior distribution is constructed and iteratively optimized, inhibiting the effect of non-Gaussian noise on UWB under a complex environment. The positioning results of the proposed method, the standard EKF algorithm, and the robust EKF algorithm, using different numbers of beacons, are compared. The results show that the positioning accuracy of the proposed algorithm is the highest under all scenarios. The proposed algorithm shows the smallest decrease in accuracy and presents the most stable positioning when the number of beacons is small, which is a common situation in practical applications.

Estimating the state of charge (SOC) of Li-ion battery by the traditional extend Kalman filter (EKF), the unreasonable noise settings and inaccurate model parameters may decrease the accuracy. Here, an adaptive dual extended Kalman filter which can dynamically adjust the process noise covariance and battery model parameters is established by the second order RC model. The algorithm uses the EKF algorithm as the main body, fixes the measurement noise covariance, and adaptively adjusts the process noise covariance based on the maximum likelihood estimation criterion. Another Kalman filter (KF) is simultaneously used to estimate battery model parameter in real time to constitute a joint algorithm. In this paper, the charging and discharging experiments of lithium iron phosphate batteries are carried out. The SOC estimation by different adaptive adjustment strategies of noise covariance are compared and analyzed under actual operating condition. Meanwhile, the SOC under different aging conditions is also estimated and compared. The results show that the proposed joint algorithm has higher estimation accuracy, faster convergence speed and more extensive applicability.

This paper proposes a new move toward to assess the performance of sensorless control of interior permanent magnet synchronous motor (IPMSM) drive along with electromagnetic noise effect by using EKF. Normally in rotary condition, rotor position and speed estimation of IPMSM drive are drawn through an Extended Kalman Filter (EKF) algorithm by measuring its voltages and currents of the stator. The main drawback in developing EKF is it may not proficient to consider the effect of electromagnetic noise which is mainly produced during the time of different speed ranges. Owing to this reason this may cause to vary the motor flux linkages which are significant to find the rotor position and speed by EKF method will give approximate results. To carry on this process, we present the simulation results for sensorless speed control of IPMSM drive by using EKF algorithm with the incorporation of a noise signal which is corresponding to the frequency of electromagnetic noise signal using MATLAB/Simulink software. The armature current, rotor position, and speed estimation are analyzed under this noise signal effect and the effectiveness of the EKF for sensorless control of IPMSM drive is observed.

BeiDou Navigation Satellite System (BDS) is composed of satellites in geostationary Earth orbit (GEO), medium Earth orbit (MEO) and inclined geosynchronous orbit (IGSO). However, the orbit determination of geostationary Earth orbits and of geosynchronous orbits (GSO) with small inclination angle and small eccentricity is a challenging task that is addressed in this paper using Extended Kalman Filter (EKF). The satellite positions were predicted in Earth-centred inertial (ECI) reference frame when propagated through Keplerian model and perturbation force model for different values of right ascension of ascending node (RAAN). Root mean square (RMS) errors of 9.61 cm, 6.73 cm and 11.46 cm were observed in ECI X, Y and Z satellite position coordinates of GSO respectively, whereas, the RMS errors for GEO satellite were 8.89 cm, 7.92 cm, and 0.93 cm respectively in ECI X, Y and Z coordinates; for perturbation force model with maximum value of RAAN when compared with dynamic orbit determination model. Kolmogorov-Smirnov test for EKF reported a p-value > 0.05, indicating a good fit of perturbation force model for orbit propagation. Orbit determination using EKF with perturbation force model were compared with that using EKF with Kepler's model. Wilcoxon Rank Sum test was used to compare the residuals from EKF algorithm through Kepler's model and perturbation force model. EKF with Perturbation force model showed improvement in predicting the satellite positions as compared to Kepler's model. EKF with Perturbation force model was further applied to International GNSS Service (IGS) station data and kilometre level accuracy was achieved. RMS errors of 0.75 km, 2.53 km and 1.91 km were observed in ECI X, Y and Z satellite position coordinates of GSO, respectively, whereas, the RMS errors for GEO satellite were 3.89 km, 4.20 km and 6.66 km respectively in ECI X, Y and Z coordinates for perturbation force model.

The discrimination of inrush currents and internal fault currents in transformers is an important feature of a transformer protection scheme. The harmonic current restrained feature is used in conventional differential relay protection of transformers. A literature survey shows that the discrimination between the inrush currents and internal fault currents is still an area that is open to research. In this paper, the classification of internal fault currents and magnetic inrush currents in the transformer is performed by using an extended Kalman filter (EKF) algorithm. When a transformer is energized under normal conditions, the EKF estimates the primary side winding current and, hence, the absolute residual signal (ARS) value is zero. The ARS value will not be equal to zero for internal fault and inrush phenomena conditions; hence, the EKF algorithm will be used for discriminating the internal faults and inrush faults by keeping the threshold level to the ARS value. The simulation results are compared with the theoretical analysis under various conditions. It is also observed that the detection time of internal faults decreases with the severity of the fault. The results of various test cases using the EKF algorithm are presented. This scheme provides fast protection of the transformer for severe faults.

The Extended Kalman Filter (EKF) is both the historical algorithm for\nmulti-sensor fusion and still state of the art in numerous industrial\napplications. However, it may prove inconsistent in the presence of\nunobservability under a group of transformations. In this paper we first build\nan alternative EKF based on an alternative nonlinear state error. This EKF is\nintimately related to the theory of the Invariant EKF (IEKF). Then, under a\nsimple compatibility assumption between the error and the transformation group,\nwe prove the linearized model of the alternative EKF automatically captures the\nunobservable directions, and many desirable properties of the linear case then\ndirectly follow. This provides a novel fundamental result in filtering theory.\nWe apply the theory to multi-sensor fusion for navigation, when all the sensors\nare attached to the vehicle and do not have access to absolute information, as\ntypically occurs in GPS-denied environments. In the context of Simultaneous\nLocalization And Mapping (SLAM), Monte-Carlo runs and comparisons to OC-EKF,\nrobocentric EKF, and optimization-based smoothing algorithms (iSAM) illustrate\nthe results. The proposed EKF is also proved to outperform standard EKF and to\nachieve comparable performance to iSAM on a publicly available real dataset for\nmulti-robot SLAM.\n

In this paper, according to the characteristics of underwater target tracking, extended Kalman filter (EKF) algorithm was applied to address underwater bearing-only non-maneuverable target tracking problem. To ensure the observability in bearing-only passive target tracking, we use two sensor arrays in uniform rectilinear motion to track the single target. EKF is recursive Bayesian filter algorithm based on the linearization of the nonlinearities in the state and the measurement system. And the simulation experiment shows that, to the constant velocity single target, the bearings-only EKF algorithm with dual-array has good results, also the EKF has lower computation complexity than unscented Kalman filter and particle filter. It confirms the effectiveness of the EKF algorithm in solving the underwater bearing-only target tracking problem.

Purpose of reseach. The article deals with the study of the operation of the extended Kalman filter (EKF), supplemented with an adaptive digital filter in order to compensate for the error in the operation of the EKF when performing data integration of the mobile robot control system.Methods. The adaptive digital filter (ADF) is a self-tuning filter that iteratively changes its variable parameters to achieve the optimal desired values of the output data. The EKF supplemented with the ADF with the NLMS adaptation algorithm will be called the EKF–ADF system or the EKF+NLMS digital filter. An important task is the selection of the number of frames and ADF weighting coefficients at which the optimum quality of noise suppression and the convergence rate of the adaptation algorithm are achieved.Results. With various options of organizing the operation of the ADF buffer memory, the adjusted values for assessing the state of the ‘mobile robot–environment’ system may differ. When the number of input data frames and ADF weighting coefficients are small, low quality noise suppression will be observed. With an increase in the number of frames and weighting coefficients, the quality of noise suppression is improved, and the convergence rate of the adaptation algorithm decreases.Conclusion. The EKF+NLMS digital filter algorithm takes an intermediate place between the EKF algorithm and the serial filtering of the EKF and ADF signals with the NLMS algorithm according to the criteria for estimating the mean square error, mean absolute error, signal-to-noise ratio, and convergence rate.

In this paper, a Self-organizing Fuzzy Neural Network employing an Extended Kalman Filter (EKF), termed Self-organizing Fuzzy Neural Networks with Extended Kalman Filter (SOFNNEKF) is designed and developed. The learning algorithm based on an EKF is simple and effective and is able to generate a fuzzy neural network with a high accuracy and compact structure. The structure learning of the SOFNNEKF, based on adding and pruning techniques is proposed. The EKF algorithm is used to adjust free parameters of the SOFNNEKF. Simulation and comparative studies with other methods demonstrate that a more compact structure with high performance can be achieved by the proposed algorithm.

The development of a backpropagation (BP) algorithm for neuron training has made it possible to use the layered neural network for simulating the nonlinear system. On the other hand, the neuron training algorithm based on the extended Kalman filter algorithm (KNT) has been developed. It is already shown that KNT has high performance compared with the BP. In this report, we show a technique to accelerate the training speed of the KNT. We call this technique the VC (variable covariance) technique. By applying the KNT with the VC technique to an exclusive OR problem, we clarify the performance of the present acceleration technique.

The extended Kalman filter (EKF)used in radar tracking applications is computationally intensive leading to difficulties in broadband real-time applications. Hence, it is necessary to resort to parallel processing techniques. With the advent of very large scale integration (VLSI) technology, different types of architectures such as systolic arrays and wavefront arrays have been developed for this purpose. The transputer is one such architecture that can be used as a processing node in a parallel processing network. Therefore, two configurations, namely, pipe configuration and mesh configuration are developed for transputer implementation of radar tracking extended Kalman filtering. The EKF algorithm is analyzed in detail for reduction of number of computations. The transputer implementations are written using ANSI-C language with the proposed reduction of matrix operations and run using a mother board with 4 TRAMS each containing one T800 transputer. A typical maneuvering trajectory is simulated and used to compare the computation time per iteration of single and four transputer implementations of the tracking Kalman filter. Further, the speed-up comparison of sequential implementation of EKF, both with and without the proposed reduction of computations, is reported.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Diffuse optical tomography (DOT) is a non-invasive imaging modality that uses near-infrared light to probe the optical properties of tissue. In conventionally used deterministic methods for DOT inversion, the measurement errors were not taken into account, resulting in unsatisfactory noise robustness and, consequently, affecting the DOT image reconstruction quality. In order to overcome this defect, an extended Kalman filter (EKF)-based DOT reconstruction algorithm was introduced first, which improved the reconstruction results by incorporating a priori information and measurement errors to the model. Further, to mitigate the instability caused by the ill-condition of the observation matrix in the tomographic imaging problem, a new, to the best of our knowledge, estimation algorithm was derived by incorporating Tikhonov regularization to the EKF method. To verify the effectiveness of the EKF algorithm and Tikhonov regularization-based EKF algorithm for DOT imaging, a series of numerical simulations and phantom experiments were conducted, and the experimental results were quantitatively evaluated and compared with two conventionally used deterministic methods involving the algebraic reconstruction technique and Levenberg-Marquardt algorithm. The results show that the two EKF-based algorithms can accurately estimate the location and size of the target, and the imaging accuracy and noise robustness are obviously improved. Furthermore, the Tikhonov regularization-based EKF obtained optimal parameter estimations, especially under the circumstance of low absorption contrast (1.2) and high noise level (10%).

This paper proposes a simple extended Kalman filter (EKF) loss model controller (LMC) for efficiency improvement of a six-phase induction machine in all speed ranges. The proposed method is fast and can be operated online. If the machine parameters are changed during the operation, the EKF algorithm is activated to find the parameters to ensure optimal efficiency operation. Not only is the motor speed measurement difficult at low speeds but it is also difficult to calculate the machine efficiency at the same speeds. Thus, the EKF model can estimate speed, load, and motor efficiency at low speed ranges so that optimization can be done in all loads and speed ranges. Unlike the conventional LMC method, the proposed method is independent of parameter variations. Because of the independency of this method against the parameter variations, it works similarly to the search based efficiency control methods. Two DSP boards including estimator and controller are used to achieve high accuracy and speed in estimating and controlling machines. The simulation and experimental results verify the robustness of the sensorless method against parameter variations.