Kalman Filtering Process Research Articles

Spatio-Temporal Correlation-Based False Data Injection Attack Detection Using Deep Convolutional Neural Network

There are lots of cyber-attack, especially false data injection attacks, in modern power systems. This attack can circumvent traditional residual-based detection methods, and destroy the integrity of control information, thus hindering the stability of the power system. In this paper, a novel Spatio-temporal detection mechanism is proposed to evaluate and locate false data injection attacks. In the proposed method, temporal correlation and spatial correlation are analyzed by cubature Kalman filter and Gaussian process regression, respectively, to capture the dynamic features of state vectors. Then, a deep convolutional neural network is trained to depict the functional relationship between Spatio-temporal correlation functions and the output, which is set as the detection indicator to access whether the power system under attack or not. Furthermore, the performance of the proposed mechanism is evaluated with comprehensive numerical simulation on IEEE 39-bus test system. The results of the case studies showed that the proposed method can achieve 99.84%-100% accuracy.

Coupling theK-nearest neighbors and locally weighted linear regression with ensemble Kalman filter for data-driven data assimilation

AbstractMachine learning-based data-driven methods are increasingly being used to extract structures and essences from the ever-increasing pool of geoscience-related big data, which are often used in relation to the atmosphere, oceans, and land surfaces. This study focuses on applying a data-driven forecast model to the classical ensemble Kalman filter process to reconstruct, analyze, and elucidate the model. In this study, a nonparametric sampler from a catalog of historical datasets, namely, a nearest neighbor or analog sampler, is given by numerical simulations. Based on this catalog (sampler), the dynamics physics model is reconstructed using theK-nearest neighbors algorithm. The optimal values of the surrogate model are found, and the forecast step is performed using locally weighted linear regression. Several numerical experiments carried out using the Lorenz-63 and Lorenz-96 models demonstrate that the proposed approach performs as good as the ensemble Kalman filter for larger catalog sizes. This approach is restricted to the ensemble Kalman filter form. However, the basic strategy is not restricted to any particular version of the Kalman filter. It is found that this combined approach can outperform the generally used sequential data assimilation approach when the size of the catalog is substantially large.

Tracking a Low-Angle Isolated Target via an Elevation-Angle Estimation Algorithm Based on Extended Kalman Filter with an Array Antenna

In a low-angle tracking situation, estimating the elevation angle is challenging due to the entrance of the multipath signals in the antenna’s main lobe. In this article, we propose two methods based on the extended Kalman filter (EKF) and frequency diversity (FD) process to estimate the elevation angle of a low-angle isolated target. In the first case, a simple weighting of the per-frequency estimates is obtained (termed WFD). Differently, in the second case, a matrix-based elaboration of the per-frequency estimates is proposed (termed MFD). The proposed methods are completely independent of prior knowledge of geometrical information and the physical parameters. The simulation results show that both methods have excellent performance and guarantee accurate elevation angle estimation in different multipath environments and even in very-low SNR conditions. Hence, they are both suitable for low-peak-power radars.

Improved Attitude and Heading Accuracy with Double Quaternion Parameters Estimation and Magnetic Disturbance Rejection.

The use of unmanned aerial vehicle (UAV) applications has grown rapidly over the past decade with the introduction of low-cost microelectromechanical system (MEMS)-based sensors that measure angular velocity, gravity, and magnetic field, which are important for an object orientation determination. However, the use of low-cost sensors has also been limited because their readings are easily distorted by unwanted internal and/or external noise signals such as environmental magnetic disturbance, which lead to errors in attitude and heading estimation results. In an extended Kalman filter (EKF) process, this study proposes a method for mitigating the effect of magnetic disturbance on attitude determination by using a double quaternion parameters for representation of orientation states, which decouples the magnetometer from attitude computation. Additionally, an online measurement error covariance matrix tuning system was implemented to reject the impact of magnetic disturbance on the heading estimation. Simulation and experimental tests were conducted to verify the performance of the proposed methods in resolving the magnetic noise effect on attitude and heading. The results showed that the proposed method performed better than complimentary, gradient descent, and single quaternion-based EKF.

Research on Kalman Filter for One-dimensional Discrete Data

Kalman filter processes the input and observation signals with noise on the basis of linear state space representation to obtain the system state or real signal. In the one-dimensional model, due to the lack of multi-dimensional description of the target, the prior estimate of the state is often the measured value of the previous moment. When the target state changes, the divergence phenomenon will occur. Aiming at the problem that the one-dimensional traditional Kalman filter lacks the target observation dimension, which leads to the divergence or imprecision of the filter, this paper focuses on improving the estimation method of the target state, and proposes a real-time prediction model based on the cascade structure. This model can improve the response of Kalman filter to the change of target state and dynamically adjust the Kalman iterative domain to improve the measurement accuracy. The digital signal filtering simulation is carried out and the performance of the filter is verified based on LabVIEW. Experimental results show that the algorithm can maintain the accuracy and real-time performance of filtering when only one dimension observation results are obtained.

A deep Kalman filter network for hand kinematics estimation using sEMG

In human-machine interfaces (HMI), deep learning (DL) techniques such as convolutional neural networks (CNN), long-short term memory networks (LSTM) and the hybrid CNN-LSTM framework have been exploited for hand kinematics estimation using surface electromyography (sEMG). However, these DL techniques only capture the relationship between sEMG and hand kinematics, but ignores the prior knowledge of the system. By contrast, Kalman filter (KF) can apply Kalman gain to combine the internal transition model and the observation model effectively. To this end, we propose a novel architecture named deep Kalman filter network (DKFN), in which we utilize CNN to extract high-level features from sEMG and employ a LSTM-based Kalman filter process (LSTM-KF) to conduct sequential regression. In particular, LSTM-KF adopts the computational graph of KF but estimates parameters of the transition/observation model and the Kalman gain from data using LSTM modules. With this process, the advantages of KF and LSTM can be exploited jointly. Experimental results demonstrate that the proposed DKFN can outperform CNN and CNN-LSTM in the sequential regression for wrist/fingers kinematics estimation.

State estimation based on improved cubature Kalman filter algorithm

During the recursive calculate process of the cubature Kalman filter (CKF), the covariance matrix tends to lose positive definiteness and noise statistical characteristics are inaccurate, which results in inaccurate filtering or even filter divergence. This study presents an improved algorithm based on the CKF. The algorithm combines the square root filter algorithm and the Sage–Husa maximum a posterior noise estimator, which can ensure the non-negative determination and symmetry of the covariance matrix and has the ability to deal with unknown and time-varying noise statistical characteristics in the filtering process adaptively. In the multi-dimension system, the noise covariance matrix may dissatisfy non-negative definiteness and result in filter divergence, and then the noise covariance matrix estimator is improved. The analysis is verified by state estimation example of the non-linear system, compared with the standard CKF, the accuracy of the adaptive square root CKF (ASRCKF) state estimation is increased by 63.13, 63.88, and 42.71%, respectively. Finally, the effectiveness of the ASRCKF is verified by the state estimation of the permanent magnet linear synchronous motor.

DSP Implementation of Neutron Radiation Detection Based on Kalman Filter

Aiming at the situation of nuclear neutron pulse count distortion and low measurement accuracy, a digital processing chip and Kalman filter are designed to replace the traditional hardware filtering method. The system uses TMS320F28335 as the main control chip, and takes advantage of the DSP-specific digital signal processing chip. After using the extended Kalman filter to reduce the noise and filter the pulse neutron count, the experiment proves that the nuclear pulse neutron count measurement after the extended Kalman filter process is stable, and the measurement accuracy has been significantly improved. The overall structure and working principle of the system are introduced, and specific hardware and software design schemes are given.

Adaptive Kalman filtering-based pedestrian navigation algorithm for smartphones

Pedestrian navigation with daily smart devices has become a vital issue over the past few years and the accurate heading estimation plays an essential role in it. Compared to the pedestrian dead reckoning (PDR) based solutions, this article constructs a scalable error model based on the inertial navigation system and proposes an adaptive heading estimation algorithm with a novel method of relative static magnetic field detection. To mitigate the impact of magnetic fluctuation, the proposed algorithm applies a two-way Kalman filter process. Firstly, it achieves the historical states with the optimal smoothing algorithm. Secondly, it adjusts the noise parameters adaptively to reestimate current attitudes. Different from the pedestrian dead reckoning-based solution, the error model system in this article contains more state information, which means it is more sensitive and scalable. Moreover, several experiments were conducted, and the experimental results demonstrate that the proposed heading estimation algorithm obtains better performance than previous approaches and our system outperforms the PDR system in terms of flexibility and accuracy.

Improved GOES-R ABI image navigation and registration using maximum likelihood parameter estimation

Image navigation and registration (INR) for the GOES-R series advanced baseline imager (ABI) is performed in ground processing of the raw image data. A Kalman filter processes ABI star measurements to compute time-varying optical misalignment parameters that allow real-time alignment of image samples to the GOES-R Fixed Grid. For the system to meet INR requirements, the filter measurements noise covariance (R) and process noise covariance (Q) matrices must closely approximate behavior of the true system. Prelaunch estimates of the Q and R parameters did not match actual GOES-16 performance. Several attempts to manually determine improved Q&R parameters were not completely successful. Instead, the Kalman filter was calibrated (tuned) using maximum likelihood (ML) estimation of the parameters: computed utilizing partial derivatives of the Kalman equations, Gauss–Newton iteration, and nonlinear optimization logic. The updated parameters significantly improved performance and are currently operational for GOES-16 and 17. ML estimation of Kalman filter parameters has been used successfully for other systems but has not widely been documented. Greater use is encouraged. We also include a review of ABI INR theory and implementation.

Line Spectrum Enhancement of Underwater Acoustic Signals Using Kalman Filter

To detect weak underwater acoustic signals radiated by submarines and other underwater equipment, an effective line spectrum enhancement algorithm based on Kalman filter and FFT processing is proposed. The proposed algorithm first determines the frequency components of the weak underwater signal and then filters the signal to enhance the line spectrum, thereby improving the signal-to-noise ratio (SNR). This paper discussed two cases: one is a simulated signal consisting of a dual-frequency sinusoidal periodic signal and Gaussian white noise, and the signal is received after passing through a Rayleigh fading channel; the other is a ship signal recorded from the South China Sea. The results show that the line spectrum of the underwater acoustic signal could be effectively enhanced in both cases, and the filtered waveform is smoother. The analysis of simulated signals and ship signal reflects the effectiveness of the proposed algorithm.

On detection of observation faults in the observation and position domains for positioning of intelligent transport systems

Intelligent transportation systems (ITS) depend on global navigation satellite systems (GNSS) as a major positioning sensor, where the sensor should be able to detect and exclude faulty observations to support its reliability. In this article, two fault detection and exclusion (FDE) approaches are discussed. The first is its application in the observation domain using Chi-square test in Kalman filter processing. The second approach discusses FDE testing in the positioning domain using the solution separation (SS) method, where new FDE forms are presented that are tailored for ITS. In the first form, the test is parameterized along the direction of motion of the vehicle and in the cross-direction, which are relevant to applications that require lane identification and collision alert. A combined test is next established. Another form of the test is presented considering the maximum possible positioning error, and finally a direction-independent test. A new test that can be implemented in the urban environment is presented, which takes into account multipath effects that could disrupt the zero-mean normal distribution assumption of the positioning errors. Additionally, a test is presented to check that the position error resulting from the remaining measurements lies within acceptable limits. The proposed methods are demonstrated through a kinematic test run in various environments that may be experienced in ITS.

A Fusion Localization Method based on a Robust Extended Kalman Filter and Track-Quality for Wireless Sensor Networks.

As one of the most essential technologies, wireless sensor networks (WSNs) integrate sensor technology, embedded computing technology, and modern network and communication technology, which have become research hotspots in recent years. The localization technique, one of the key techniques for WSN research, determines the application prospects of WSNs to a great extent. The positioning errors of wireless sensor networks are mainly caused by the non-line of sight (NLOS) propagation, occurring in complicated channel environments such as the indoor conditions. Traditional techniques such as the extended Kalman filter (EKF) perform unsatisfactorily in the case of NLOS. In contrast, the robust extended Kalman filter (REKF) acquires accurate position estimates by applying the robust techniques to the EKF in NLOS environments while losing efficiency in LOS. Therefore it is very hard to achieve high performance with a single filter in both LOS and NLOS environments. In this paper, a localization method using a robust extended Kalman filter and track-quality-based (REKF-TQ) fusion algorithm is proposed to mitigate the effect of NLOS errors. Firstly, the EKF and REKF are used in parallel to obtain the location estimates of mobile nodes. After that, we regard the position estimates as observation vectors, which can be implemented to calculate the residuals in the Kalman filter (KF) process. Then two KFs with a new observation vector and equation are used to further filter the estimates, respectively. At last, the acquired position estimates are combined by the fusion algorithm based on the track quality to get the final position vector of mobile node, which will serve as the state vector of both KFs at the next time step. Simulation results illustrate that the TQ-REKF algorithm yields better positioning accuracy than the EKF and REKF in the NLOS environment. Moreover, the proposed algorithm achieves higher accuracy than interacting multiple model algorithm (IMM) with EKF and REKF.

A Kalman filter application for rainfall estimation using radar reflectivity measurements

The rainfall amount observed at a given location mostly depend on the cloud density, which can be quantified with the reflectivity values observed by meteorology weather radars. In this study, we aim to estimate the rainfall amount using a Kalman filter with radar reflectivity measurements. We first assume that the amount of rainfall observed at automatic weather observation stations (AWOSs) are elements of an unknown state vector and consider the Kalman filter process model as the true rainfall amounts observed at these AWOSs over time. For the measurement model of the Kalman filter, we use the radar reflectivity values observed at each AWOS location. For the execution of the Kalman filter, a number of rainfall amount and radar reflectivity value pairs are first required to learn the process and measurement models of the Kalman filter. The estimation performance of the proposed Kalman filter is then compared with empirical reflectivity (Z) - rainfall (R) relationships. Numerical results show that when the Kalman filter is executed with radar reflectivity measurements observed around a large number of AWOS locations, the mean squared errors of the Kalman filter rainfall estimates are smaller than the ones obtained with empirical ZR relationships.

Real-time implementation of Kalman filter to improve accuracy in the measurement of time of flight in an ultrasonic pulse-echo setup.

In this paper, we demonstrate a hardware implementation of Kalman filter to enhance accuracy in the measurements of time-of-flight in an ultrasonic pulse echo technique (operated at 10 MHz). Pulser-receivers and other respective circuit units are designed using off-the-shelf electronic components. The advanced reduced instruction-set computing machine processor based Raspberry Pi single board computer is used to implement the Kalman filter and control various processes. Additionally, a graphical user interface is designed using Qt software, under the Debian open source operating system. The software has capability to measure and display the time-of-flight and ultrasonic propagation velocity in a liquid under test. The designed system with the Kalman filter exhibited an extremely small error of about 0.01% in the time-of-flight measurements compared with other systems. The functionality of the developed approach to measure time of flight and thereby ultrasonic velocity with significant improvement has been discussed in this article. It was experimentally verified that by improving other parameters such as the separation between the transducer and the reflector and cell structure, significant improvement in the accuracy of ultrasonic velocity in the liquid under test is achieved.

Polarization de-multiplexing using a modified Kalman filter in CO-OFDM transmissions

We propose the modified Kalman filter (MKF) using the received signal for observation and constructing an inverse process of the conventional Kalman filter (CKF) for polarization de-multiplexing in coherent optical (CO) orthogonal frequency-division multiplexing (OFDM) transmissions. The MKF can avoid the convergence error problem in CKF without matrix inverse operation and has a faster converging speed and a much larger tolerance to the process and measurement noise covariance, about two orders of magnitude more than those of CKF. We experimentally demonstrate the 12 Gbaud OFDM signal transmission over 480 km standard single-mode fiber. The performance of MKF and CKF outperforms pilot-aided polarization de-multiplexing with better accuracy and nonlinearity tolerance.

A Kalman Filter Process for Energy Optimization in WSNs

Wireless Sensor Networks (WSNs) consist of a large number of small interconnected devices. The aim of such networks is the monitoring of some types of area. This work is done by collaboration between these devices. All of them must sense and send information to the sink. These devices are characterized by limited memory, limited computing resource and they are usually powered by an irreplaceable battery, which limits their lifetime. Therefore it is essential to design an effective and energy aware protocols in order to extend the network lifetime by reducing the energy consumption. In this article, a new communication mechanism for IEEE 802.15.4 based WSNs called Kalman based MAC (K-MAC) protocol is proposed. K-MAC is designed to maximize the efficiency of the energy consumption. Therefore, the network nodes lifetime will extend through a predicting filter. The objectif of this filter is to optimize the sleep interval time of nodes between consecutive wake-ups. The network node be awake only if it have to receive or to send data. In other words, there will be an adaptation between the activation of the transceivers and the node traffic load. The simulation results show that K-MAC obtains better performance in terms of energy efficiency, Packet Delivery Ratio (PDR), the whole without affecting negatively the latency.

A hybrid FCW-EMD and KF-BA-SVM based model for short-term load forecasting

This paper proposes a hybrid short-term load forecasting method, which is based on the fuzzy combination weights as well as the empirical mode decomposition process (FCW-EMD), and support vector machine optimized via the Bat algorithm as well as the Kalman filtering process (KF-BA-SVM). The subjective weight is presented as a new theory and is applied to capture the inherent correlation effectively among hourly loads. Based on the proposed objective weights and subjective weights, the fuzzy combination weights theory (FCW)-a new similar day selection theory is presented, which improves the accuracy of the similar day selection, and correspondingly, makes the original data for EMD processing decrease dramatically. BA is introduced to optimize parameters of the SVM model for further improving the forecasting accuracy. Using the decomposed load series via empirical model decomposition (EMD) as inputs to SVM and further correcting the output of SVM via KF, a hybrid FCW-EMD and KF-BA-SVM short-term load forecasting method is established. Numerical case studies on the load forecasting of a transformer substation in south China show that the proposed hybrid forecasting model outperforms other forecasting methods and effectively improves the prediction accuracy.

Using external tropospheric corrections to improve GNSS positioning of hot-air balloon

High accurate global navigation satellite systems (GNSS) require to correct a signal delay caused by the troposphere. The delay can be estimated along with other unknowns or introduced from external models. We assess the impact of the recently developed augmentation tropospheric model on real-time kinematic precise point positioning (PPP). The model is based on numerical weather forecast and thus reflects the actual state of weather conditions. Using the G-Nut/Geb software, we processed GNSS and meteorological data collected during the experiment using a hot-air balloon flying up to an altitude of 2000 m. We studied the impacts of random walk noise setting of zenith total delay (ZTD) on estimated parameters and the mutual correlations, the use of external tropospheric corrections, the use of data from a single or dual GNSS constellation and the use of Kalman filter and backward smoothing processing methods. We observed a significant negative correlation of the estimated rover height and ZTD which depends on constraining ZTD estimates. Such correlation caused a degraded performance of both parameters when estimated simultaneously, in particular for a single GNSS constellation. The impact of ZTD constraining reached up to 50-cm differences in the rover height. Introducing external tropospheric corrections improved the PPP solution regarding: (1) shortened convergence, (2) better overall robustness, particularly, in case of degraded satellite geometry, (3) less adjusted parameters with lower correlations. The numerical weather model-driven PPP resulted in 9–12- and 5–6-cm uncertainties in the rover altitude using the Kalman filter and the backward smoothing, respectively. Compared to standard PPP, it indicates better performance by a factor of 1–2 depending on the availability of GNSS constellations, the troposphere constraining and the processing strategy.

Cylindrical coordinate rocket trajectory profiles and line‐of‐sight projective coordinates for tracking ballistic missiles from satellite infrared sensor line‐of‐sight observations

In this paper the authors apply the concept of cylindrical coordinate trajectory profiles to the accurate and efficient estimation of the launch parameter state of an intercontinental ballistic missiles from line-of sight observations that are assembled by a pair of geo-stationary satellite infrared sensors. To estimate the four-parameter launch state (geodetic latitude, longitude, direction, time) they introduce the notion of a two-coordinate projective coordinate representation of line-of-sight from observing sensor to observed target instead of the usual two angular coordinates such as local azimuth and elevation. They also introduce the notion of optimally combining launch parameter states, each state estimated from the observations of one of the pair. Finally, they investigate the performance of a nine-component inertial state (position vector, velocity vector, mass, mass rate, drag coefficient) extended Kalman filter that is primed by the optimal state estimate. The extended Kalman filter processes interleaved line-of-sight projective coordinate observations. A numerical experiment is presented with the simulated fly-out of a notional three stage North Korean intercontinental Ballistic Missile as observed by a dual viewing pair of geo-stationary satellite infrared sensors separated by approximately 90 degrees in longitude.