Real-time State Estimation Research Articles

Symbolic Representation and Toolkit Development of Iterated Error-State Extended Kalman Filters on Manifolds

Error-state extended Kalman filter (ESEKF) is one of extensively used filtering techniques in robot systems. There are many works that cast ESEKF on manifolds to improve consistency. However, most of these works are designed case by case, which makes it difficult to extend to new manifolds. In this paper, we propose a generic method to formulate the iterated error-state extended Kalman filter (IESEKF) on manifolds, which aims to facilitate the deployment of IESEKF for on-manifold systems (e.g., lidar-inertial and visual-inertial systems). Firstly, a canonical on-manifold representation of the robot system is proposed, based on which, an on-manifold IESEKF framework is formulated and solved by linearization at each estimation point. The proposed framework has two main advantages, one is that an equivalent error-state system is derived from linearization, which is minimally-parameterized without any singularities in practice. And the other is that in each step of IESEKF, the manifold constraints are decoupled from the system behaviors, ultimately leading to a generic and symbolic IESEKF framework that naturally evolving on manifolds. Based on the separation of manifold constraints from the system behaviors, the on-manifold IESEKF is implemented as a toolkit in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C$</tex-math></inline-formula> ++ packages, with which the user needs only to provide the system-specific descriptions, and then call the respective filter steps (e.g., predict, update) without dealing with any manifold constraints. The existing implementation supports full iterated Kalman filtering for versatile systems on manifold <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {M} = \mathbb {R}^{m}\!\times SO(3)\!\times \!\cdots \!\times \! SO(3)\!\times \! SE_{N}(3)\!\times \!\cdots \!\times \! SE_{N}(3)\!\times \mathbb {S}^{2} \times \cdots \times \mathbb {S}^{2}$</tex-math></inline-formula> or any of its sub-manifolds, and is extendable to other types of manifold when necessary. The proposed symbolic IESEKF and the developed toolkit are verified by implementing two filter-based tightly-coupled lidar-inertial navigation systems. Results show that, while greatly facilitating the EKF deployment the developed toolkit leads to estimation performances and computation efficiency comparable to hand-engineered counterparts. Finally, the toolkit is open-sourced at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/hku-mars/IKFoM</uri> . The aimed application is the real-time state estimation of dynamic systems (e.g., robots) whose states are evolving on manifolds.

A study on the implementation of nonlinear Kalman filter applying MMG model

Many technologies need to be established to realize autonomous ships. In particular, accurate state estimation in real time is one of the most important technologies. In the ship and ocean engineering fields, there have been many studies on state estimation using nonlinear Kalman filters. Several methods have been proposed for nonlinear Kalman filters. However, there is insufficient verification on the selection of which filter should be applied among them. Therefore, this study aims to validate the filter selection to provide a guideline for filter selection. The effects of modeling error, observation noise, and type of maneuvers on the estimation accuracy of the unscented Kalman filter (UKF) and ensemble Kalman filter (EnKF) used in this study were investigated. In addition, it was verified whether filtering could be performed in real time. The results show that modeling error significantly impacts the estimation accuracy of the UKF and EnKF. However, the observation noise and types of maneuvers did not have an impact like the modeling error. Thus, we obtained the guideline that UKF and EnKF should be used differently depending on the required computation time. We also obtained that keeping the modeling error sufficiently small is essential to improving the estimation accuracy.

Vehicle State and Road Adhesion Coefficient Joint Estimation Based on High-Order Cubature Kalman Algorithm

With regard to the rear-drive in-wheel motor vehicle, this paper studies the joint estimation method for the vehicle state and road adhesion coefficient. A nonlinear seven degrees of freedom vehicle estimation model and a tire estimation model are established. A vehicle driving state estimator and a road adhesion coefficient estimator based on the generalized high-order cubature Kalman filter (GHCKF) algorithm are designed. The vehicle state estimator combines the vehicle model and the tire model to calculate the vehicle state parameters, provides the state parameters for the road adhesion coefficient estimator, and realizes the real-time estimation of the road adhesion coefficient. The exponential fading memory adaptive algorithm is used to update the measurement noise variance, and we upgrade the GHCKF to the adaptive generalized high-order cubature Kalman filter (AGHCKF), which estimates the vehicle state and road adhesion coefficient. The typical working conditions using the double GHCKF/AGHCKF estimation algorithm were simulated and analyzed. Then, high-and low-speed driving experiments based on typical working conditions were carried out. An integrated navigation system (INS), global positioning system (GPS), and real-time kinematic positioning (RTK) were used to collect the real-time data of the vehicle, and compare them with the estimated values of the joint estimator, to verify the feasibility of the vehicle-state–road-adhesion-coefficient joint estimator. We compared a high-order GHCKF algorithm, high-order improved AGHCKF algorithm, and a cubature Kalman filter (CKF) algorithm, and the simulation and experimental results show that the joint estimator using the CKF, GHCKF, and AGHCKF algorithms can realize the real-time estimation of the vehicle state and the road adhesion coefficient. The AGHCKF algorithm shows the best effectiveness and robustness of the three algorithms.

Optimization methods to solve the set covering problems

Phasor Measurement Unit Placement aims to decrease the cost this phasor equipment while maintaining the observability of the electrical distribution systems. This placement can be modeled as a set covering problem. Synchronized phasor data provides electrical systems’ information with higher quality and frequency than Remote Terminal Units. These data enable the implementation of faster than real-time state estimators. Thus, supervisory control and data acquisition systems can be replaced by automatically monitored systems that add reliability, efficiency, and resilience to smart grid systems. Due to the flexibility and large-scale in the distribution systems, heuristic methods have frequently been applied to this placement problem. Since the use of Chemical Reaction Optimization (CRO) algorithm is not recurrent, we have decided to implement it together with a topological system observability analysis. Initial population creation, parameterization, elementary reactions of CRO, and local search strategies are presented in this study. Computational results were performed in IEEE power system test cases. The optimization method proposed has obtained optimal results at a lower computation time than the literature. To test in large-scale, we have applied another optimization method to Set Covering Problems from Beasley library, with different parameters. However, the results were not satisfactory indicating that the CRO might not be suitable to some large-scale instances of the Set Covering Problems this library. In this case, further studies are required.

Control-oriented cold start modelling and experimental validation of PEM fuel cell stack system

The cold-start of proton exchange membrane fuel cell (PEMFC) has been one of the leading technical challenges for fuel cell vehicle commercialization. During the cold start process, a new control-oriented modelling methodology of a water-cooled PEMFC stack system was present. The voltage and temperature change throughout the stack may be forecast using the model technique. Then the model was validated in a 5 Kw, 20 cells, water-cooled stack at room and subzero temperatures. The result shows that the model accuracy can capture the stationary and transient states of the fuel cell stack well. For the cold start of PEMFCs in automotive applications, the suggested model may be utilized to investigate real-time state estimates and model-based control approaches.

Ensemble Model Based on Hybrid Deep Learning for Intrusion Detection in Smart Grid Networks.

The Smart Grid aims to enhance the electric grid's reliability, safety, and efficiency by utilizing digital information and control technologies. Real-time analysis and state estimation methods are crucial for ensuring proper control implementation. However, the reliance of Smart Grid systems on communication networks makes them vulnerable to cyberattacks, posing a significant risk to grid reliability. To mitigate such threats, efficient intrusion detection and prevention systems are essential. This paper proposes a hybrid deep-learning approach to detect distributed denial-of-service attacks on the Smart Grid's communication infrastructure. Our method combines the convolutional neural network and recurrent gated unit algorithms. Two datasets were employed: The Intrusion Detection System dataset from the Canadian Institute for Cybersecurity and a custom dataset generated using the Omnet++ simulator. We also developed a real-time monitoring Kafka-based dashboard to facilitate attack surveillance and resilience. Experimental and simulation results demonstrate that our proposed approach achieves a high accuracy rate of 99.86%.

Research on Multi-Sensor Simultaneous Localization and Mapping Technology for Complex Environment of Construction Machinery

Simultaneous localization and mapping (SLAM), as a key task of unmanned vehicles for construction machinery, is of great significance for later path planning and control. Construction tasks in the engineering field are mostly carried out in bridges, tunnels, open fields, etc. The prominent features of these environments are high scene similarity, few geometric features, and large-scale repetitive texture information, which is prone to sensor detection degradation. This leads to positioning drift and map building failure. The traditional method of motion estimation and 3D reconstruction uses a single sensor, which lacks enough information, has poor adaptability to the environment, and cannot guarantee good positioning accuracy and robustness in complex environments. Currently, the strategy of multi-sensor fusion is proven to be an effective solution and is widely studied. This paper proposes a SLAM framework that integrates LiDAR, IMU, and camera. It tightly couples the texture information observed by camera, the geometric information scanned by LiDAR, and the measured value of IMU, allowing visual-inertial odometry (VIO) and LiDAR-inertial odometry (LIO) common implementation. The LIO subsystem extracts point cloud features and matches them with the global map. The obtained pose estimation can be used for the initialization of the VIO subsystem. The VIO system uses direct method to minimize the photometric error and IMU measurement error between images to estimate the pose of the robot and the geometric structure of the scene. The two subsystems assist each other to perform pose estimation, and can operate normally even when any subsystem fails. A factor graph is used to combine all constraints to achieve global pose optimization. Keyframe and sliding window strategies are used to ensure real-time performance. Through real-vehicle testing, the system can perform incremental and real-time state estimation and reconstruct a dense 3D point cloud map, which can effectively solve the problems of positioning drift and mapping failure in the lack of geometric features or challenging construction environments.

Battery Charge Curve Prediction via Feature Extraction and Supervised Machine Learning.

Real-time onboard state monitoring and estimation of a battery over its lifetime is indispensable for the safe and durable operation of battery-powered devices. In this study, a methodology to predict the entire constant-current cycling curve with limited input information that can be collected in a short period of time is developed. A total of 10066 charge curves of LiNiO2 -based batteries at a constant C-rate are collected. With the combination of a feature extraction step and a multiple linear regression step, the method can accurately predict an entire battery charge curve with an error of < 2% using only 10% of the charge curve as the input information. The method is further validated across other battery chemistries (LiCoO2 -based) using open-access datasets. The prediction error of the charge curves for the LiCoO2 -based battery is around 2% with only 5% of the charge curve as the input information, indicating the generalization of the developed methodology for predicting battery cycling curves. The developed method paves the way for fast onboard health status monitoring and estimation for batteries during practical applications.

Affective state estimation based on Russell’s model and physiological measurements

Affective states are psycho-physiological constructs connecting mental and physiological processes. They can be represented in terms of arousal and valence according to the Russel’s model and can be extracted from physiological changes in human body. However, a well-established optimal feature set and a classification method effective in terms of accuracy and estimation time are not present in the literature. This paper aims at defining a reliable and efficient approach for real-time affective state estimation. To obtain this, the optimal physiological feature set and the most effective machine learning algorithm, to cope with binary as well as multi-class classification problems, were identified. ReliefF feature selection algorithm was implemented to define a reduced optimal feature set. Supervised learning algorithms, such as K-Nearest Neighbors (KNN), cubic and gaussian Support Vector Machine, and Linear Discriminant Analysis, were implemented to compare their effectiveness in affective state estimation. The developed approach was tested on physiological signals acquired on 20 healthy volunteers during the administration of images, belonging to the International Affective Picture System, conceived for inducing different affective states. ReliefF algorithm reduced the number of physiological features from 23 to 13. The performances of machine learning algorithms were compared and the experimental results showed that both accuracy and estimation time benefited from the optimal feature set use. Furthermore, the KNN algorithm resulted to be the most suitable for affective state estimation. The results of the assessment of arousal and valence states on 20 participants indicate that KNN classifier, adopted with the 13 identified optimal features, is the most effective approach for real-time affective state estimation.

Combining unscented Kalman filter and wavelet neural network for anti-slug

The stability of the subsea oil and gas production system is heavily influenced by slug flow. One successful method of managing slug flow is to use top valve control based on subsea pipeline pressure. However, the complexity of production makes it difficult to measure the pressure of subsea pipelines, and measured values are not always accessible in real-time. The research introduces a technique for integrating Unscented Kalman Filter (UKF) and Wavelet Neural Network (WNN) to estimate the state of subsea pipeline pressure using historical data and a state model. The proposed method treats multiphase flow transport as a nonlinear model, with a dynamic WNN serving as the state observer. To achieve real-time state estimation, the WNN is included into the UKF algorithm to create a WNN-based UKF state equation. Integrate WNN and UKF in a novel way to predict system state accurately. The simulated results show that the approach can efficiently predict the inlet pressure and manage the slug flow in real-time using the riser's top pressure, outlet flow and valve opening. This method of estimate can significantly increase the control effect.

Simultaneous Robust State Estimation, Topology Error Processing, and Outage Detection for Unbalanced Distribution Systems

This paper proposes an efficient algorithmic approach that overcomes the critical challenges in real-time unbalanced distribution system state estimation, topology error processing, and outage identification simultaneously. These challenges include (1) limited locations of measurement devices and unsynchronized measurement data as well as missing and bad data, (2) complicated mixed-phase switch actions and mutual impedances and shunt admittances, and (3) the nonlinear nature of unbalanced distribution system power flow with distributed energy resources (DERs). A single snap-shot mixed-integer quadratic programming (MIQP) optimization framework is proposed to cope with these challenges, which simultaneously identifies real-time network topology, estimates system state, and detects the outages via analytical constraints. An AC optimal power flow (ACOPF) approach is proposed to accurately model unbalanced distribution systems. In the proposed MIQP formulation, nonlinearities due to the complicated mixed-phase switch operations and the ACOPF approach are linearized. The effectiveness of the proposed approach is verified on an actual distribution feeder in Arizona. The results illustrate that the proposed model is robust, accurate, and computationally efficient for implementation in a distribution management system (DMS).

State Vector’s Fusion for Passive Underwater Tracking Using Two Sensor Arrays

The issue of real-time state estimation in passive target tracking using only bearing measurements is addressed in this research. An algorithm has been developed to detect multiple targets and fuse state vectors when a single target is detected. Target detection is carried out considering the state vectors from two different sensor arrays with various noise variances. The algorithm is evaluated against targets having unique and identical parameters such as range, speed and course. The state vectors are determined using three different filtering techniques, namely, extended Kalman filter (EKF), modified gain bearings-only EKF and unscented Kalman filter. Using the MATLAB software environment, Monte-Carlo simulations are conducted to more precisely assess algorithm performance.

A Novel Data Assimilation-Based Real-Time State Estimation Method for Gas Influx Profiling During Riser Gas Events

AbstractRiser gas events during offshore drilling operations are hazardous and challenging to control. Therefore, knowledge of the gas influx sizes and distributions in a marine drilling riser is critical for the selection of riser gas handling methods and the estimation of risks of riser gas unloading. An extended Kalman filter-based data assimilation method is developed and evaluated for the real-time estimation of gas influx rates and void fraction distributions in a riser during riser gas handling. Full-scale experiments were conducted in this study for the evaluation of the proposed data assimilation method. An offshore well, which consists of a marine drilling riser and a wellbore below the subsea blowout preventer, was simulated by a 1572-m-deep experimental well. Real-time measurement data, including surface and downhole pressures, pump rates, and liquid outflow rates, were used to estimate the downhole gas influx rates using the Kalman filter. An online calibrated drift-flux model based on data assimilation is used to estimate the distributions of void fractions in the riser over time. The measurement data from a gas flowmeter and the distributed fiber-optic sensing were used to validate the estimation results, and satisfying performance was seen from the presented method. This study proposed a novel data assimilation-based state estimation method by maximizing the use of measurement data of different types from the available managed pressure drilling systems. This method enables the more accurate estimation and prediction of gas behaviors in a riser and helps to facilitate real-time decision-making during riser gas handling.

MAGNets: Model Reduction and Aggregation of Water Networks

Hydraulic models of large water distribution networks can have thousands of components, and real-time simulation of these systems can be slowed down by their complexity. Several methods have been developed for which the size of the water network models can be reduced while the hydraulic performance of the reduced systems remains very similar to the original model. Model reduction allows users to model only components of interest, thus saving expensive computation time. However, while model reduction has been widely adopted for control and optimization purposes, few tools are available to reduce models on command. This paper introduces MAGNets, an open-source Python package capable of reducing and aggregating EPANET-compatible water models using the variable elimination reduction method. The package allows the user to specify the operating point around which the model will be reduced, the nodes that must remain in the network, and the maximum nodal degree of nodes removed. The reduced model preserves pressure heads of the original model with high accuracy and results in faster running times. The reduction algorithm iteratively removes nodes from the full model and updates the adjacent nodal demands and pipe properties until the final reduced model is achieved. To test the effect of the order of node removal on the size of the reduced model and computational complexity, we tested three different strategies for reduction order. Results suggest that dynamically updating reduction order greatly improves model performance compared to static and random orders. To increase usability, the Python package includes twelve benchmark networks for testing and validation. MAGNets allows for the quick and efficient reduction of hydraulic models as a way to facilitate time-sensitive tasks, such as real-time state estimation and control.

Markovian Transparency Control of an Exoskeleton Robot

In wearable robotics, certain applications require the robot to be transparent, i.e., imperceptible to the user. This is a very difficult cooperative control task due to the inherent coupling between human and robot, unpredictable human movements, and user-dependent behavior. In this letter, we propose a novel transparency controller based on discrete-time Markovian jump linear systems to minimize the human-robot interaction forces of an exoskeleton robot during walking. Our model-based stochastic control approach describes a gait cycle as an event-dependent Markov chain and uses a given transition matrix to switch between them. An IMU-based Kalman filter is used to perform real-time human state estimation and gait phase detection. The robustness and effectiveness of the proposed controller are demonstrated with experiments on a lower-limb exoskeleton driven by series elastic actuators.

FT‐LVIO: Fully Tightly coupled LiDAR‐Visual‐Inertial odometry

AbstractIn this paper, we propose a fully tightly‐coupled multi‐sensor fusion framework termed FT‐LVIO, that fuses measurements from a light detection and ranging (LiDAR), a monocular camera and an inertial measurement unit (IMU) simultaneously to achieve robust and accurate state estimation in real time. FT‐LVIO is built atop the framework of an error‐state‐iterated Kalman filter. To take full advantage of the complimentary characteristics of individual sensors, LiDAR point clouds are undistorted by IMU prediction to the nearest camera exposure time and the filter is updated with measurements from all sensors. In addition, an efficient sampling method for the LiDAR point‐to‐plane measurements is proposed, which can help select the measurements providing sufficient constraints to the pose estimation and facilitate a low‐drift odometry. Extensive experiments are performed on both the public NTU dataset and the private handheld dataset, and the results show that the proposed FT‐LVIO outperforms the state‐of‐the‐art LiDAR‐inertial, visual‐inertial and LiDAR‐visual‐inertial methods in both accuracy and robustness. Furthermore, FT‐LVIO can survive in the challenging staircase environment.

Introduction to the Special Issue on Real-Time Traffic State Estimation

The term traffic state estimation refers to measuring or inferring values of the key traffic state variables, such as density, flow, speed, and delay, by using a combination of observed and derived traffic-related data. Due to recent advances in vehicular networking and sensor technology and by exploiting existing and emerging computer and communications paradigms, the task of estimating traffic state parameters in real-time has become technically feasible but remains a very challenging task.

PMU-based Real-time Distribution System State Estimation Considering Anomaly Detection, Discrimination and Identification

In this paper, a real-time state estimation platform for distribution grids monitored by Phasor Measurement Units (PMUs) is developed, tested, and validated using Real Time Digital Simulator (RTDS). The developed platform serves as a proof-of-concept for potential implementation in an existing 50 kV ring network of the Dutch distribution utility Stedin medium voltage distribution grid located in the southwest (Zeeland area) of the Netherlands. To catch up with the fast sampling rates of PMUs, the platform incorporates computationally efficient techniques for state estimation and detection, discrimination and identification of anomalies like bad data and sudden load changes. Forecasting Aided State Estimation has been utilized to enable measurement innovations needed for fast anomaly detection, discrimination, and identification, whilst the Extended Kalman Filter (EKF) algorithm is selected to provide fast state forecasting and filtering. The platform has been tested under various normal and abnormal operating conditions considering different statistical properties of measurement noise as well as different bad data and sudden load change scenarios. To demonstrate advantages and disadvantages for embedding EKF into the platform, EKF is compared with Unscented Kalman Filter (UKF) in terms of estimation accuracy, computational efficiency, and compatibility with the module for anomaly detection, discrimination, and identification. The results of extensive simulations provide good hints about the feasibility of PMU-based real-time state estimation for the Stedin distribution grid.

Simultaneous seismic input and state estimation with optimal sensor placement for building structures using incomplete acceleration measurements

Simultaneous real-time input and state estimation and optimal sensor placements are investigated in this paper, focusing on systems without direct feedthrough, such as earthquake-excited building structures with absolute floor acceleration measurements. Current studies showed that system properties such as strong observability, strong* detectability (the asterisk distinguishes strong* detectability from strong detectability), and invertibility conditions are crucial to the stability and convergence of unknown input and state estimation, but they can often be violated in practice. Consequently, uncertainties such as modeling errors and measurement noise can greatly degrade the accuracy and stability of the estimations. Estimation in this case has remained challenging due to the above reasons. To fill this gap, this paper develops an optimal sensor placement algorithm (OSPA) for real-time unknown input and state estimation, which ensures the required system conditions are met. The developed OSPA is integrated with two optimal real-time Kalman-based filters, a minimum-variance unbiased input and state estimation filter (MVUIS) and an Augmented State Kalman Filter (ASKF), for simultaneous input and state estimation. In particular, the MVUIS is presented in a recursive three-step structure without using the arbitrary matrix in the gain, which makes no assumptions on the input but requires strong* detectability. To avoid the requirement, ASKF is derived from the MVUIS by incorporating prior knowledge of the input. The developed OSPA along with the MVUIS and ASKF provide the optimal input and state estimation in real-time without incurring low-frequency drift or unstable estimations. Notably, the OSPA improves the performance of MVUIS by reducing amplitude errors and enhances the accuracy of ASKF by reducing phase errors. The developed OSPA integrated with the MVUIS and ASKF are validated through numerical and experimental studies as well as a real-world instrumented building structure under earthquakes using incomplete absolute acceleration measurements.

PASE: An autonomous sequential framework for the state estimation of dynamical systems

Kalman filter (KF) and its variants are commonly used in estimating states of dynamical systems. For accurate estimation of states, researchers have developed intelligent KFs by combining them with machine learning algorithms. The inherent variations in the vehicle dynamics and uncertainties in the environment require the development of an autonomous sequential framework for continuous estimation. Further, the need for real-time estimation of states in certain applications requires low computer memory usage and low computational cost while implementing autonomous-structured learning algorithms. In this paper, a parsimonious autonomous sequential estimator (PASE) is proposed, which combines the KF-based estimator and autonomous-structured recurrent parsimonious learning machine (rPALM) in a sequential manner. The rPALM overcomes the dependency on target variables while point-to-hyperplane distance calculation. The performance of PASE has been evaluated extensively by comparing it with various batch-learning algorithms and single-pass learning-based intelligent estimators. The results clearly indicate that PASE provides better estimation accuracy with a compact architecture for both linear and nonlinear dynamical systems. Finally, the performance of PASE has been evaluated with experimental data for the state estimation of an unmanned ground vehicle while the training of the learning machine is performed with the simulated data. The estimation accuracy in such a scenario is justifying its appropriateness in real-world applications.