Showing papers on "Kalman filter published in 2019"

Power System Dynamic State Estimation: Motivations, Definitions, Methodologies, and Future Work

Abstract: This paper summarizes the technical activities of the Task Force on Power System Dynamic State and Parameter Estimation. This Task Force was established by the IEEE Working Group on State Estimation Algorithms to investigate the added benefits of dynamic state and parameter estimation for the enhancement of the reliability, security, and resilience of electric power systems. The motivations and engineering values of dynamic state estimation (DSE) are discussed in detail. Then, a set of potential applications that will rely on DSE is presented and discussed. Furthermore, a unified framework is proposed to clarify the important concepts related to DSE, forecasting-aided state estimation, tracking state estimation, and static state estimation. An overview of the current progress in DSE and dynamic parameter estimation is provided. The paper also provides future research needs and directions for the power engineering community.

A Dynamic Event-Triggered Transmission Scheme for Distributed Set-Membership Estimation Over Wireless Sensor Networks

Abstract: This paper is concerned with the distributed set-membership estimation for a discrete-time linear time-varying system over a resource-constrained wireless sensor network under the influence of unknown-but-bounded (UBB) process and measurement noise. Sensors collaborate among themselves by exchanging local measurements with only neighboring sensors in their sensing ranges. First, a new dynamic event-triggered transmission scheme (ETS) is developed to schedule the transmission of each sensor’s local measurement. In contrast with the majority of existing static ETSs, the newly proposed dynamic ETS can result in larger average interevent times and thus less totally released data packets. Second, a criterion for designing desired event-triggered set-membership estimators is derived such that the system’s true state always resides in each sensor’s bounding ellipsoidal estimation set regardless of the simultaneous presence of UBB process and measurement noise. Third, a recursive convex optimization algorithm is presented to determine optimal ellipsoids as well as the estimator gain parameters and the event triggering weighting matrix parameter. Furthermore, the proposed dynamic ETS is applied to address the distributed set-membership estimation problem for a discrete-time linear time-varying system with a nonlinearity satisfying a sector constraint. Finally, an illustrative example is given to show the effectiveness and advantage of the developed approach.

State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

Abstract: This paper considers the state estimation problem of bilinear systems in the presence of disturbances. The standard Kalman filter is recognized as the best state estimator for linear systems, but it is not applicable for bilinear systems. It is well known that the extended Kalman filter (EKF) is proposed based on the Taylor expansion to linearize the nonlinear model. In this paper, we show that the EKF method is not suitable for bilinear systems because the linearization method for bilinear systems cannot describe the behavior of the considered system. Therefore, this paper proposes a state filtering method for the single-input–single-output bilinear systems by minimizing the covariance matrix of the state estimation errors. Moreover, the state estimation algorithm is extended to multiple-input–multiple-output bilinear systems. The performance analysis indicates that the state estimates can track the true states. Finally, the numerical examples illustrate the specific performance of the proposed method.

A Novel Fractional Order Model for State of Charge Estimation in Lithium Ion Batteries

Abstract: Battery models are the cornerstone to battery state of charge (SOC) estimation and battery management systems in electric vehicles. This paper proposes a novel fractional-order model for a battery, which considers both Butler–Volmer equation and fractional calculus of constant phase element. The structure characteristics of the proposed model are then analyzed, and a novel identification method, which combines least squares and nonlinear optimization algorithm, is proposed. The method is proven to be efficient and accurate. Based on the proposed model, a fractional-order unscented Kalman filter is developed to estimate SOC, while singular value decomposition is applied to tackle the nonlinearity of Butler–Volmer equation and fractional calculus of constant phase element. The systematic comparison between the proposed model and traditional fractional order model is carried out on two LiNiMnCo lithium-ion batteries at different temperatures, ageing levels, and electric vehicle current profiles. The comparison results show that the proposed model has higher estimation accuracy in battery terminal voltage and SOC than the traditional model over wide range of temperature and ageing level under electric vehicle operation conditions. Furthermore, the hardware-in-the-loop test validates that the proposed SOC estimation method is suitable for SOC estimation in electric vehicles.

Robust Unscented Kalman Filter for Power System Dynamic State Estimation With Unknown Noise Statistics

Abstract: Due to the communication channel noises, GPS synchronization process, changing environment temperature and different operating conditions of the system, the statistics of the system process and measurement noises may be unknown and they may not follow Gaussian distributions. As a result, the traditional Kalman filter-based dynamic state estimators may provide strongly biased state estimates. To address these issues, this paper develops a robust generalized maximum-likelihood unscented Kalman filter (GM-UKF). The statistical linearization approach is presented to derive a compact batch-mode regression form by processing the predicted state vector and the received measurements simultaneously. This regression form enhances the data redundancy and allows us to detect bad phasor measurement unit measurements and incorrect state predictions, and filter out unknown Gaussian and non-Gaussian noises through the generalized maximum likelihood-estimator. The latter minimizes a convex Huber function with weights calculated via the projection statistics (PS). Particularly, the PS is applied to a proposed 2-dimensional matrix that consists of temporally correlated innovation vectors and predicted states. Finally, the total influence function is used to derive the error covariance matrix of the GM-UKF state estimates, yielding the robust state prediction at the next time instant. Extensive simulations carried out on the IEEE 39-bus test system demonstrate the effectiveness and robustness of the proposed method.

Sparse Bayesian Learning for the Time-Varying Massive MIMO Channels: Acquisition and Tracking

Abstract: The low-rank property of the channel covariances can be adopted to reduce the overhead of the channel training in massive MIMO systems. In this paper, with the help of the virtual channel representation, we apply such property to both time-division duplex and frequency-division duplex systems, where the time-varying channel scenarios are considered. First, we formulate the dynamic massive MIMO channel as one sparse signal model. Then, an expectation maximization-based sparse Bayesian learning framework is developed to learn the model parameters of the sparse virtual channel. Specifically, the Kalman filter (KF) and the Rauch–Tung–Striebel smoother are utilized to track the model parameters of the uplink (UL) spatial sparse channel in the expectation step. During the maximization step, a fixed-point theorem-based algorithm and a low-complex searching method are constructed to recover the temporal varying characteristics and the spatial signatures, respectively. With the angle reciprocity, we recover the downlink (DL) model parameters from the UL ones. After that, the KF with the reduced dimension is adopt to fully exploit the channel temporal correlations to enhance the DL/UL virtual channel tracking accuracy. A monitoring scheme is also designed to detect the change of model parameters and trigger the relearning process. Finally, we demonstrate the efficacy of the proposed schemes through the numerical simulations.

A Novel Robust Gaussian–Student's t Mixture Distribution Based Kalman Filter

Abstract: In this paper, a novel Gaussian–Student's t mixture (GSTM) distribution is proposed to model non-stationary heavy-tailed noises. The proposed GSTM distribution can be formulated as a hierarchical Gaussian form by introducing a Bernoulli random variable, based on which a new hierarchical linear Gaussian state-space model is constructed. A novel robust GSTM distribution based Kalman filter is proposed based on the constructed hierarchical linear Gaussian state-space model using the variational Bayesian approach. The Kalman filter and robust Student's t based Kalman filter (RSTKF) with fixed distribution parameters are two existing special cases of the proposed filter. The novel GSTM distributed Kalman filter has the important advantage over the RSTKF that the adaptation of the mixing parameter is much more straightforward than learning the degrees of freedom parameter. Simulation results illustrate that the proposed filter has better estimation accuracy than those of the Kalman filter and RSTKF for a linear state-space model with non-stationary heavy-tailed noises.

Highly computationally efficient state filter based on the delta operator

Abstract: The Kalman filter is not suitable for the state estimation of linear systems with multistate delays, and the extended state vector Kalman filtering algorithm results in heavy computational burden because of the large dimension of the state estimation covariance matrix. Thus, in this paper, we develop a novel state estimation algorithm for enhancing the computational efficiency based on the delta operator. The computation analysis and the simulation example show the performance of the proposed algorithm.

A Simplified Model-Based State-of-Charge Estimation Approach for Lithium-Ion Battery With Dynamic Linear Model

Abstract: The performance of model-based state-of-charge (SOC) estimation method relies on an accurate battery model. Nonlinear models are thus proposed to accurately describe the external characteristics of the lithium-ion battery. The nonlinear estimation algorithms and online parameter identification methods are needed to guarantee the accuracy of the model-based SOC estimation with nonlinear battery models. A new approach forming a dynamic linear battery model is proposed in this paper, which enables the application of the linear Kalman filter for SOC estimation and also avoids the usage of online parameter identification methods. With a moving window technology, partial least squares regression is able to establish a series of piecewise linear battery models automatically. One element state-space equation is then obtained to estimate the SOC from the linear Kalman filter. The experiments on a LiFePO4 battery prove the effectiveness of the proposed method compared with the extended Kalman filter with two resistance and capacitance equivalent circuit model and the adaptive unscented Kalman filter with least squares support vector machines.

Robust Kalman Filters Based on Gaussian Scale Mixture Distributions With Application to Target Tracking

Abstract: In this paper, a new robust Kalman filtering framework for a linear system with non-Gaussian heavy-tailed and/or skewed state and measurement noises is proposed through modeling one-step prediction and likelihood probability density functions as Gaussian scale mixture (GSM) distributions. The state vector, mixing parameters, scale matrices, and shape parameters are simultaneously inferred utilizing standard variational Bayesian approach. As the implementations of the proposed method, several solutions corresponding to some special GSM distributions are derived. The proposed robust Kalman filters are tested in a manoeuvring target tracking example. Simulation results show that the proposed robust Kalman filters have a better estimation accuracy and smaller biases compared to the existing state-of-the-art Kalman filters.

Adaptive Consensus-Based Distributed Target Tracking With Dynamic Cluster in Sensor Networks

Abstract: This paper is concerned with the target tracking problem over a filtering network with dynamic cluster and data fusion. A novel distributed consensus-based adaptive Kalman estimation is developed to track a linear moving target. Both optimal filtering gain and average disagreement of the estimates are considered in the filter design. In order to estimate the states of the target more precisely, an optimal Kalman gain is obtained by minimizing the mean-squared estimation error. An adaptive consensus factor is employed to adjust the optimal gain as well as to acquire a better filtering performance. In the filter’s information exchange, dynamic cluster selection and two-stage hierarchical fusion structure are employed to get more accurate estimation. At the first stage, every sensor collects information from its neighbors and runs the Kalman estimation algorithm to obtain a local estimate of system states. At the second stage, each local sensor sends its estimate to the cluster head to get a fused estimation. Finally, an illustrative example is presented to validate the effectiveness of the proposed scheme.

Deep Neural Network Compression for Aircraft Collision Avoidance Systems

Abstract: One approach to designing decision-making logic for an aircraft collision avoidance system frames the problem as a Markov decision process and optimizes the system using dynamic programming. The re...

Finite Sample Analysis of Stochastic System Identification

Abstract: In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without external inputs. The objective is to recover the system parameters as well as the Kalman filter gain, given a single trajectory of output measurements over a finite horizon of length N. Based on a subspace identification algorithm and a finite number of N output samples, we provide non-asymptotic high-probability upper bounds for the system parameter estimation errors. Our analysis uses recent results from random matrix theory, self-normalized martingales and SVD robustness, in order to show that with high probability the estimation errors decrease with a rate of $1/\sqrt N$ up to logarithmic terms. Our non-asymptotic bounds not only agree with classical asymptotic results, but are also valid even when the system is marginally stable.

MME-EKF-Based Path-Tracking Control of Autonomous Vehicles Considering Input Saturation

Abstract: This paper investigates the path-tracking control issue for autonomous ground vehicles with the integral sliding mode control (ISMC) considering the transient performance improvement. The path-tracking control is converted into the yaw stabilization problem, where the sideslip-angle compensation is adopted to reduce the steady-state errors, and then the yaw-rate reference is generated for the path-tracking purpose. The lateral velocity and roll angle are estimated with the measurement of the yaw rate and roll rate. Three contributions have been made in this paper: first, to enhance the estimation accuracy for the vehicle states in the presence of the parametric uncertainties caused by the lateral and roll dynamics, a robust extended Kalman filter is proposed based on the minimum model error algorithm; second, an improved adaptive radial basis function neural network (RBFNN) considering the approximation error adaptation is developed to compensate for the uncertainties caused by the vertical motion; third, the RBFNN and composite nonlinear feedback (CNF) based ISMC is developed to achieve the yaw stabilization and enhance the transient tracking performance considering the input saturation of the front steering angle. The overall stability is proved with Lyapunov function. Finally, the superiority of the developed control strategy is verified by comparing with the traditional CNF with high-fidelity CarSim-MATLAB simulations.

State-of-Charge Estimation of Lithium-Ion Batteries via Long Short-Term Memory Network

Abstract: Accurate state-of-charge (SOC) estimation is critical for driving range prediction of electric vehicles and optimal charge control of batteries. In this paper, a stacked long short-term memory network is proposed to model the complex dynamics of lithium iron phosphate batteries and infer battery SOC from current, voltage, and temperature measurements. The proposed network is trained and tested using data collected from the dynamic stress test, US06 test, and federal urban driving schedule. The performance on SOC estimation is evaluated regarding tracking accuracy, computation time, robustness against unknown initial states, and compared with results from the model-based filtering approach (unscented Kalman filter). Moreover, different training and testing data sets are constructed to test its robustness against varying loading profiles. The experimental results show that the proposed network well captures the nonlinear correlation between SOC and measurable signals and provides better tracking performance than the unscented Kalman filter. In case of inaccurate initial SOCs, the proposed network presents quick convergence to the true SOC, with root mean square errors within 2% and mean average errors within 1%. Moreover, the estimation time at each time step is sub-millisecond, making it appropriate for real-time applications.

Kalman Filtering Framework-Based Real Time Target Tracking in Wireless Sensor Networks Using Generalized Regression Neural Networks

Abstract: Traditional received signal strength indicators (RSSI’s)-based moving target localization and tracking using wireless sensor networks (WSN’s) generally employs lateration/angulation techniques. Although this method is a very simple technique but it creates significant errors in localization estimations due to nonlinear relationship between RSSI and distance. The generalized regression neural network (GRNN) being a one-pass learning algorithm is well known for its ability to train quickly on sparse data sets. This paper proposes an implementation of GRNN as an alternative to this traditional RSSI-based approach, to obtain first location estimates of single target moving in 2-D in WSN, which are then further refined using Kalman filtering (KF) framework. Two algorithms namely, GRNN + KF and GRNN + unscented KF (UKF) are proposed in this paper. The GRNN is trained with the simulated RSSI values received at moving target from beacon nodes and the corresponding actual target 2-D locations. The precision of the proposed algorithms are compared against traditional RSSI-based, GRNN-based approach as well as other models in the literature such as traditional RSSI + KF and traditional RSSI + UKF algorithms. The proposed algorithms demonstrate superior tracking performance (tracking accuracy in the scale of few centimeters) irrespective of nonlinear system dynamics as well as environmental dynamicity.

Distributed Kalman Filtering and Control Through Embedded Average Consensus Information Fusion

Abstract: This paper presents a unified framework for distributed filtering and control of state-space processes. To this end, a distributed Kalman filtering algorithm is developed via decomposition of the optimal centralized Kalman filtering operations. This decomposition is orchestrated in a fashion so that each agent retains a Kalman style filtering operation and an estimate of the state vector. In this setting, the agents mirror the operations of the centralized Kalman filter in a distributed fashion through embedded average consensus fusion of local state vector estimates and their associated covariance information. For rigor, closed-form expressions for the mean and mean square error performance of the developed distributed Kalman filter are derived. More importantly, in contrast to current approaches, due to the comprehensive framework for fusion of the covariance information, a duality between the developed distributed Kalman filter and decentralized control is established. Thus, resulting in an effective and all inclusive distributed framework for filtering and control of state-space processes over a network of agents. The introduced theoretical concepts are validated using the simulations that indicate a precise match between simulation results and the theoretical analysis. In addition, simulations indicate that performance levels comparable to that of the optimal centralized approaches are attainable.

Forecasting Time Series With VARMA Recursions on Graphs

Abstract: Graph-based techniques emerged as a choice to deal with the dimensionality issues in modeling multivariate time series. However, there is yet no complete understanding of how the underlying structure could be exploited to ease this task. This paper provides contributions in this direction by considering the forecasting of a process evolving over a graph. We make use of the (approximate) time-vertex stationarity assumption, i.e., time-varying graph signals whose first- and second-order statistical moments are invariant over time and correlated to a known graph topology. The latter is combined with vector autoregressive and vector autoregressive moving average models to tackle the dimensionality issues present in predicting the temporal evolution of multivariate time series. We find out that by projecting the data to the graph spectral domain the multivariate model estimation reduces to that of fitting a number of uncorrelated univariate autoregressive–moving-average models and an optimal low-rank data representation can be exploited so as to further reduce the estimation costs. In the case that the multivariate process can be observed at a subset of nodes, the proposed models extend naturally to Kalman filtering on graphs allowing for optimal tracking. Numerical experiments with both synthetic and real data validate the proposed approach and highlight its benefits over state-of-the-art alternatives.

Kalman Filter-Based Large-Scale Wildfire Monitoring With a System of UAVs

Abstract: Wildfires play an important role in forest management, while an accurate assessment of current wildfire status is imperative for fire management. In this paper, a Kalman filter-based methodology is proposed to estimate the wildfire progress with online measurements that are collected by a system of unmanned aerial vehicles. The method is developed to estimate the wildfire propagation behavior as well as fire front contour. It is enabled by developing a scalar field wildfire model and utilizing the Kalman filter to estimate the parameters of the model. In addition, an uncertainty function is developed to describe the performance of the estimation results. The effectiveness of the algorithm is demonstrated in an independent fire simulation environment.

Event-Triggered Fuzzy Filtering for Nonlinear Dynamic Systems via Reduced-Order Approach

Abstract: This paper is concerned with the problem of generalized $\mathcal {H}_{2}$ reduced-order filter design for continuous Takagi–Sugeno fuzzy systems using an event-triggered scheme. For a continuous Takagi–Sugeno fuzzy dynamic system, a reduced-order filter is designed to transform the original model into a linear lower order one. This filter can also approximate the original system with $\mathcal {H}_{2}$ performance, with a new type of event-triggered scheme used to decrease the communication loads and computation resources within the network. By transforming the filtering problem to a convex optimization one, conditions are presented to design the fuzzy reduced-order filter. Finally, two illustrative examples are used to verify the feasibility and applicability of the proposed design scheme.

Tight Fusion of a Monocular Camera, MEMS-IMU, and Single-Frequency Multi-GNSS RTK for Precise Navigation in GNSS-Challenged Environments

Abstract: Precise position, velocity, and attitude is essential for self-driving cars and unmanned aerial vehicles (UAVs). The integration of global navigation satellite system (GNSS) real-time kinematics (RTK) and inertial measurement units (IMUs) is able to provide high-accuracy navigation solutions in open-sky conditions, but the accuracy will be degraded severely in GNSS-challenged environments, especially integrated with the low-cost microelectromechanical system (MEMS) IMUs. In order to navigate in GNSS-denied environments, the visual–inertial system has been widely adopted due to its complementary characteristics, but it suffers from error accumulation. In this contribution, we tightly integrate the raw measurements from the single-frequency multi-GNSS RTK, MEMS-IMU, and monocular camera through the extended Kalman filter (EKF) to enhance the navigation performance in terms of accuracy, continuity, and availability. The visual measurement model from the well-known multistate constraint Kalman filter (MSCKF) is combined with the double-differenced GNSS measurement model to update the integration filter. A field vehicular experiment was carried out in GNSS-challenged environments to evaluate the performance of the proposed algorithm. Results indicate that both multi-GNSS and vision contribute significantly to the centimeter-level positioning availability in GNSS-challenged environments. Meanwhile, the velocity and attitude accuracy can be greatly improved by using the tightly-coupled multi-GNSS RTK/INS/Vision integration, especially for the yaw angle.

Literature review and fundamental approaches for vehicle and tire state estimation

Abstract: Most modern day automotive chassis control systems employ a feedback control structure. Therefore, real-time estimates of the vehicle dynamic states and tire-road contact parameters are invaluable ...