A nonlinear algorithm for traffic estimation with state constraints

The unscented Kalman filter (UKF) has become a popular method for nonlinear state estimation during the last decade. However, the conventional UKF may not be suitable for real-world applications with state constrains that stem from physical definitions, physical laws or model restrictions. A UKF based method with optimized parameters was proposed in this paper to handle state constraints via the projection of sigma points. In the proposed method, the generated sigma points that violate the state constraints were projected onto the constraint boundary first. The three free parameters of the UKF, i.e., α ,β ,κ , were then optimized using a Gaussian process optimization (GPO) method. Simulations indicate that the proposed optimized UKF algorithm with the projection of sigma points can handle constrained state estimation problem effectively and efficiently.

An adaptive freeway traffic state estimator

Traffic state estimation problems must deal with imperfect information. Imperfect information may occur as a result of misalignments between reality and the assumptions or simplifications made when developing the models as well as incomplete or corrupted data. One of the well-known methods of handling imperfect information is the Kalman filter algorithm and its variations, such as the extended Kalman filter and the unscented Kalman filter. While the standard Kalman filter and the extended Kalman filter have been widely applied to the state estimation of linear systems, the unscented Kalman filter has been reported the better choice in the multiclass traffic state estimation. In many applications of Kalman filters to traffic estimation problems, the model and measurement noise covariance matrices are normally estimated. When there is a mismatch between the true and the assumed noise distribution, however, the filter often suffers from performance degradation and even divergence in certain situations. To this end, this paper presents a more efficient and accurate algorithm embedded in the unscented Kalman filter to simultaneously estimate the traffic state and the model noise distribution statistics. The proposed method is facilitated through a simultaneous update of the model noise covariance matrix in the predicted covariance equations of the unscented Kalman filter algorithm. It is found through simulation that the proposed algorithm may improve the model performance over the standard algorithm.

This paper presents a novel data-driven framework for real-time State of Charge (SOC) estimation in lithium-ion battery systems using a data-driven Prognostics and Health Management (PHM) approach. The method leverages an optimized bidirectional Long Short-Term Memory (Bi-LSTM) network, trained with enhanced datasets filtered via exponentially weighted moving averages (EWMAs) and refined through SHAP-based feature attribution. Compared against a Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) across ten diverse drive cycles, the proposed model consistently achieved superior performance, with mean absolute errors (MAEs) as low as 0.40%, outperforming EKF (0.66%) and UKF (1.36%). The Bi-LSTM model also demonstrated higher R2 values (up to 0.9999) and narrower 95% confidence intervals, confirming its precision and robustness. Real-time implementation on embedded platforms yielded inference times of 1.3–2.2 s, validating its deployability for edge applications. The framework’s model-free nature makes it adaptable to other nonlinear, time-dependent systems beyond battery SOC estimation.

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.

Constrained nonlinear state estimation based on the UKF approach

There has been extensive research in traffic state estimation that accounts for the stochastic nature of traffic flow models. However, these studies often exhibit limitations such as an exclusive focus on motorway traffic and a reliance on a single data source. This paper departs from these methods by introducing a stochastic estimation framework that is specifically designed for urban arterial traffic. The framework has the capability to incorporate multiple data sources, which serves to improve its accuracy and robustness. The framework is composed of three components: (i) a stochastic traffic flow model, (ii) a filtering algorithm, and (iii) an algorithm for incorporating multi-source measurements. In terms of the traffic model, we introduce a new stochastic Switching Mode Model that can be applied to arterial roads that have both signalized and unsignalized intersections. This model does not consider uncertainty in the current mode of operation, which substantially reduces the computational complexity because there is only one mode at each time step. Furthermore, we propose three different filtering algorithms for multi-source traffic estimation, including the incremental stochastic Kalman Filter (SKF), the incremental stochastic Unscented Kalman Filter (SUKF), and the hybrid approach. Since the SKF can only deal with linear functions, non-linear measurement equations need to be linearized using first-order Taylor expansions. The SUKF is based on the Unscented Transform (UT), which enables it to work with a wider range of functions regardless of linearity, non-linearity, or non-differentiability. The hybrid algorithm is a combination of the SKF and the SUKF, in which linear equations are treated similarly to the SKF, and non-linear equations are handled with the UT in the same way as in the SUKF. The performances of these algorithms were similar when applied to the synthetic data of an urban arterial in Christchurch CBD, New Zealand. The hybrid algorithm, however, worked slightly better and was more stable than the other two.

Traffic data collection and traffic state estimation are essential for traffic congestion management within smart cities framework. To overcome the inherent shortcomings of single-source data collection techniques, this paper investigates a data fusion method, employing fix and floating (or probe) data types, to estimate traffic states on both freeway and signalized arterial links. The proposed method explores the relationships among the number of probe data, sampling interval of probe vehicles, probe vehicles penetration rate, estimation interval, and traffic density. This paper introduces the definition of generalized penetration rate based on the quotient of travel time of probe vehicles and total travel time. Furthermore, traffic generalized density is estimated with probe data and observed long-term average of actual penetration rate of probe vehicles. Furthermore, real-time penetration rate of probe vehicles is estimated with probe data and density measurements collected by fixed loop detectors. The validity of the proposed method is investigated by extensive tests on NGSIM field data and microsimulation data that reveal accurate performance for real-time traffic state estimation. The proposed methods demonstrate promising extensions for network-wide traffic state estimation.

The ventricular assist device (VAD) provides supports for cardiac function and is used in the long term by many patients on the heart transplant waiting list. Thus, during VAD operation, it is ideal to monitor circulatory status and cardiovascular parameters online to reduce complications, detect abnormal conditions early and control the ventricular assist device. However, wearing additional sensors in the body for monitoring is not ideal, and it is desirable to obtain various types of information about the body using as few and easily measurable sensors as possible. In this study, we propose a method for real-time estimation of the circulatory state [left ventricular pressure (LVP), aortic pressure (AoP), aortic flow (AoF)], and cardiovascular parameters, such as peripheral vascular resistance, and determination of valve opening using the estimated AoF. The proposed method utilizes information generated by the VAD, which is easy to measure. First, the method approximates the heart and circulatory system using an electric circuit model based on the Windkessel model. This model is represented by a state-space model with pump flow rate and pump inlet pressure as inputs and pump outlet pressure as output. In the next step, the model parameters are estimated using an unscented Kalman filter, which can handle nonlinear functions, enabling the estimation of circulatory systems. Validation using data from a hybrid simulated circulatory system and animal studies demonstrate that the normalized root mean square errors (nRMSE) for LVP, AoP, and AoF were within 30%, 13%, and 7%, respectively. Moreover, it was possible to estimate opening of the aortic valve. In particular, data from the animal experiments illustrated that the proposed method can accurately estimate changes in the circulatory state by taking medication, highlighting the effectiveness of the proposed method.

Traffic state estimation is one of the very basic and most important tasks in intelligent transportation systems. Data collected from multiple types of traffic sensors are valuable sources to estimate traffic state. However, those data are always incomplete for the cases such as sensors broken, data missing, etc. The incomplete data can also be used to accurately estimate traffic state by data prediction and data fusion. Firstly, the missing data are predicted based on the data correlations extracted on large amount of historical taxi GPS data. Then, data collected from multiple sensors are fused to get more accurate results. Finally, computing of data fusion is parallelized. The main research focus is placed on learning for extracting the inherent spatio-temporal correlations of traffic data and fusing multimedia traffic data. Accuracy and efficiency experiments are conducted and the experimental results demonstrate that our method can process incomplete data and achieve accurate and real-time traffic state estimation.

In this paper, the Envelope Prediction Algorithm (EPA) is presented based on the Unscented Kalman Filter (UKF) method for the Unmanned Aerial Vehicle (UAV). Firstly, the flight envelope of UAV extended system is calculated by the Attainable Equilibrium Set (AES) algorithm. The discrete Newton iteration method is used to solve the nonlinear algebraic equation of UAV, and then the AES is obtained at the current state. Secondly, the UKF has the characteristics of high accuracy and strong stability, which can effectively to predict the next moment state value of the nonlinear system. Therefore, the UKF in this paper is used to predict the state variables of the UAV system at the next moment. Finally, the AES algorithm is adopted to calculate the next moment flight envelope of the UAV. The simulation results of the UAV indicate that the EPA algorithm can effectively predict the next moment AES of the UAV based on the predict the results.

Traffic congestion and delays at signalized intersections remain a challenge in urban mobility. To minimize congestion, adaptive traffic signal control systems have been adopted across the United States. However, for these systems to function at their best, systems require an accurate estimation of traffic states, such as traffic density and queue length. This paper implements a relatively novel method, Physics-Informed Neural Networks (PINNs), for real-time traffic density estimation to enhance adaptive intersection signal control. The methodology leverages PINNs, which integrate both data-driven learning and physical constraints imposed by the Lighthill-Whitham-Richards (LWR) macroscopic traffic flow model. A simulation of a four-way intersection was used to generate realistic spatio-temporal traffic data to evaluate the performance of the model. Separate PINNs models, one trained for each incoming approach using simulation-based spatio-temporal density data, provide segment-level density predictions. These real-time density estimates are then employed within an adaptive traffic signal control algorithm designed to adjust green light phasing based on detected demand. The proposed PINNs control strategy was evaluated through simulation, comparing its performance against the Webster traffic timing method using key metrics such as average vehicle delay at the intersection and average vehicle travel time. The findings show an approximate 18% decrease in average vehicle delay and more than a 6% reduction in average travel time when utilizing adaptive traffic control based on the PINNs method for determining density values. These findings highlight the potential of leveraging PINNs for accurate, real-time traffic state estimation, which can effectively inform and improve the performance of adaptive traffic signal control systems, leading to reduced congestion and enhanced mobility at intersections.

A novel approach for accelerated and accurate spatial conflation of connected vehicle data on GPUs and its application to real-time statewide traffic state estimation

This paper describes a new nonlinear estimation procedure used to estimate and track the parameters of a nonlinear aircraft. The Unscented Kalman Filter (UKF) is developed and compared to the more traditional Extended Kalman Filter (EKF). State and parameters are estimated on the F-15 for both a complex maneuver and a maneuver with failure. The algorithms have access to the nonlinear dynamic equations, but not the aircraft engine models, aerodynamic models, or atmospheric models. Parameters describing these unknown dynamics are estimated in the EKF and UKF algorithms. Results show the UKF to be more accurate than the EKF, and track all parameters very well at all times, even after a 50% failure of the stabilator. The aerodynamic forces and moments, while difficult to track immediately after the failure because of the discontinuous nonlinearity, did recover quickly and stay within the predicted bounds.

In this paper, based on a novel adaptive time‐varying barrier Lyapunov function (A‐TBLF), we propose an output feedback tracking controller for spacecrafts with adaptive time‐varying state constraints. The adaptive time‐varying barrier is adapted with the real‐time constrained state but not constant or a predefined function. It is guaranteed that the constrained state converges into the predefined domain whenever it starts. Moreover, a barrier update restart scheme is designed in the A‐TBLF method to prevent potential barrier violations. Furthermore, we consider the input explosion of the BLF‐based controller when the state is close to the barrier. A nonlinear margin function is introduced to avoid continuous input saturation, resulting in a smooth and cost‐effective control input. On the other hand, as the accurate angular velocity measurement is assumed to be unavailable, it is proposed an adaptive observer chain with finite‐time estimation to the angular velocity and the lumped disturbance. Therefore, only the attitude angle is used to design the controller and the attitude tracking error can be further eliminated. Simulation results verify the effectiveness of the proposed method, and comparative simulations show the superiorities than other control methods with time‐varying state constraints.