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13 pages, 4401 KiB

Open AccessTechnical Note

An Adaptive Constant Acceleration Model for Maneuvering Target Tracking

by Jieyu Huang, Junwei Xie, Haolong Zhai, Zhengjie Li and Weike Feng

Remote Sens. 2025, 17(5), 850; https://doi.org/10.3390/rs17050850 - 28 Feb 2025

Viewed by 965

An adaptive constant acceleration (ACA) model is proposed for the maneuvering target tracking problem. Based on the Taylor series expansion of acceleration, we establish the relationship between the Jerk and the velocity as well as the acceleration so that the maneuvering acceleration variance [...] Read more.

An adaptive constant acceleration (ACA) model is proposed for the maneuvering target tracking problem. Based on the Taylor series expansion of acceleration, we establish the relationship between the Jerk and the velocity as well as the acceleration so that the maneuvering acceleration variance is approximated by the components in the state error covariance matrix. Then, the latter one is connected with the process noise, and the adaptive adjustment of the ACA model is realized. Combining with the strong tracking square-root cubature filter (ST-SCKF) in our previous work, an ACA-ST-SCKF is developed. The simulation results show that the proposed filter possesses better adaptability, tracking accuracy and lower computational complexity compared with the adaptive current statistical (ACS) model-based ST-SCKF, the modified CS (MCS) model-based ST-SCKF, and the IMM-based STF-SCKF. Full article

(This article belongs to the Special Issue Array and Signal Processing for Radar)

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20 pages, 6607 KiB

Open AccessArticle

A Nonlinear Suspension Road Roughness Recognition Method Based on NARX-PASCKF

by Jiahao Qian, Yinong Li, Ling Zheng, Huan Wu, Yanlin Jin and Linhong Yu

Sensors 2024, 24(21), 6938; https://doi.org/10.3390/s24216938 - 29 Oct 2024

Cited by 1 | Viewed by 1078

Abstract

Road roughness significantly impacts vehicle safety and dynamic responses. For nonlinear suspension systems, the nonlinear characteristics often make it challenging for estimators to identify the actual road roughness accurately. This paper proposes a hybrid road roughness identification algorithm based on nonlinear auto-regressive with [...] Read more.

Road roughness significantly impacts vehicle safety and dynamic responses. For nonlinear suspension systems, the nonlinear characteristics often make it challenging for estimators to identify the actual road roughness accurately. This paper proposes a hybrid road roughness identification algorithm based on nonlinear auto-regressive with exogenous inputs (NARX) and a process noise adaptive square root cubature Kalman filter (PASCKF) to address this issue. Driven by vehicle acceleration data, an NARX-based road roughness identification system is constructed to mitigate the model uncertainties. Furthermore, a hybrid strategy is proposed. On the one hand, the accurate road roughness estimated by the NARX is converted into process noise covariance, enhancing the estimator’s accuracy and convergence rate. Another switching strategy is proposed to optimize the non-convergence issues of the PASCKF. Finally, simulation and actual vehicle experiment data demonstrate that this approach offers superior identification accuracy and adaptability compared to the standalone SCKF algorithm. Full article

(This article belongs to the Section Vehicular Sensing)

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19 pages, 2355 KiB

Open AccessArticle

The Square-Root Unscented and the Square-Root Cubature Kalman Filters on Manifolds

by Joachim Clemens and Constantin Wellhausen

Sensors 2024, 24(20), 6622; https://doi.org/10.3390/s24206622 - 14 Oct 2024

Cited by 1 | Viewed by 1266

Abstract

Estimating the state of a system by fusing sensor data is a major prerequisite in many applications. When the state is time-variant, derivatives of the Kalman filter are a popular choice for solving that task. Two variants are the square-root unscented Kalman filter [...] Read more.

Estimating the state of a system by fusing sensor data is a major prerequisite in many applications. When the state is time-variant, derivatives of the Kalman filter are a popular choice for solving that task. Two variants are the square-root unscented Kalman filter (SRUKF) and the square-root cubature Kalman filter (SCKF). In contrast to the unscented Kalman filter (UKF) and the cubature Kalman filter (CKF), they do not operate on the covariance matrix but on its square root. In this work, we modify the SRUKF and the SCKF for use on manifolds. This is particularly relevant for many state estimation problems when, for example, an orientation is part of a state or a measurement. In contrast to other approaches, our solution is both generic and mathematically coherent. It has the same theoretical complexity as the UKF and CKF on manifolds, but we show that the practical implementation can be faster. Furthermore, it gains the improved numerical properties of the classical SRUKF and SCKF. We compare the SRUKF and the SCKF on manifolds to the UKF and the CKF on manifolds, using the example of odometry estimation for an autonomous car. It is demonstrated that all algorithms have the same localization performance, but our SRUKF and SCKF have lower computational demands. Full article

(This article belongs to the Section Vehicular Sensing)

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21 pages, 4079 KiB

Open AccessArticle

Maximum Correntropy Square-Root Cubature Kalman Filter with State Estimation for Distributed Drive Electric Vehicles

by Pingshu Ge, Ce Zhang, Tao Zhang, Lie Guo and Qingyang Xiang

Appl. Sci. 2023, 13(15), 8762; https://doi.org/10.3390/app13158762 - 29 Jul 2023

Cited by 6 | Viewed by 2133

Abstract

For nonlinear systems, both the cubature Kalman filter (CKF) and square-root cubature Kalman filter (SCKF) can get good estimation performance under Gaussian noise. However, the actual driving environment noise mostly has non-Gaussian properties, leading to a significant reduction in robustness and accuracy for [...] Read more.

For nonlinear systems, both the cubature Kalman filter (CKF) and square-root cubature Kalman filter (SCKF) can get good estimation performance under Gaussian noise. However, the actual driving environment noise mostly has non-Gaussian properties, leading to a significant reduction in robustness and accuracy for distributed vehicle state estimation. To address such problems, this paper uses the square-root cubature Kalman filter with the maximum correlation entropy criterion (MCSRCKF), establishing a seven degrees of freedom (7-DOF) nonlinear distributed vehicle dynamics model for accurately estimating longitudinal vehicle speed, lateral vehicle speed, yaw rate, and wheel rotation angular velocity using low-cost sensor signals. The co-simulation verification is verified by the CarSim/Simulink platform under double-lane change and serpentine conditions. Experimental results show that the MCSRCKF has high accuracy and enhanced robustness for distributed drive vehicle state estimation problems in real non-Gaussian noise environments. Full article

(This article belongs to the Special Issue Intelligent Vehicles and Autonomous Driving)

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25 pages, 6362 KiB

Open AccessArticle

Three-Dimensional Multi-Target Tracking Using Dual-Orthogonal Baseline Interferometric Radar

by Saima Ishtiaq, Xiangrong Wang, Shahid Hassan, Alsharef Mohammad, Ahmad Aziz Alahmadi and Nasim Ullah

Sensors 2022, 22(19), 7549; https://doi.org/10.3390/s22197549 - 5 Oct 2022

Cited by 3 | Viewed by 2372

Abstract

Multi-target tracking (MTT) generally needs either a Doppler radar network with spatially separated receivers or a single radar equipped with costly phased array antennas. However, Doppler radar networks have high computational complexity, attributed to the multiple receivers in the network. Moreover, array signal [...] Read more.

Multi-target tracking (MTT) generally needs either a Doppler radar network with spatially separated receivers or a single radar equipped with costly phased array antennas. However, Doppler radar networks have high computational complexity, attributed to the multiple receivers in the network. Moreover, array signal processing techniques for phased array radar also increase the computational burden on the processing unit. To resolve this issue, this paper investigates the problem of the detection and tracking of multiple targets in a three-dimensional (3D) Cartesian space based on range and 3D velocity measurements extracted from dual-orthogonal baseline interferometric radar. The contribution of this paper is twofold. First, a nonlinear 3D velocity measurement function, defining the relationship between the state of the target and 3D velocity measurements, is derived. Based on this measurement function, the design of the proposed algorithm includes the global nearest neighbor (GNN) technique for data association, an interacting multiple model estimator with a square-root cubature Kalman filter (IMM-SCKF) for state estimation, and a rule-based M/N logic for track management. Second, Monte Carlo simulation results for different multi-target scenarios are presented to demonstrate the performance of the algorithm in terms of track accuracy, computational complexity, and IMM mean model probabilities. Full article

(This article belongs to the Section Radar Sensors)

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25 pages, 33558 KiB

Open AccessArticle

Estimation of Longitudinal Force, Sideslip Angle and Yaw Rate for Four-Wheel Independent Actuated Autonomous Vehicles Based on PWA Tire Model

by Xiaoqiang Sun, Yulin Wang and Weiwei Hu

Sensors 2022, 22(9), 3403; https://doi.org/10.3390/s22093403 - 29 Apr 2022

Cited by 4 | Viewed by 3870

Abstract

This article introduces an efficient and high-precision estimation framework for four-wheel independently actuated (FWIA) autonomous vehicles based on a novel tire model and adaptive square-root cubature Kalman filter (SCKF) estimation strategy. Firstly, a reliable and concise tire model that considers the tire’s nonlinear [...] Read more.

This article introduces an efficient and high-precision estimation framework for four-wheel independently actuated (FWIA) autonomous vehicles based on a novel tire model and adaptive square-root cubature Kalman filter (SCKF) estimation strategy. Firstly, a reliable and concise tire model that considers the tire’s nonlinear mechanics characteristics under combined conditions through the piecewise affine (PWA) identification method is established to improve the accuracy of the lateral dynamics model of FWIA autonomous vehicles. On this basis, the longitudinal relaxation length of each tire is integrated into the lateral dynamics modeling of FWIA autonomous vehicle. A novel nonlinear state function, including the PWA tire model, is proposed in this paper. To reduce the impact of the uncertainty of noise statistics on the estimation accuracy, an adaptive SCKF estimation algorithm based on the maximum a posteriori (MAP) criterion is proposed in the estimation framework. Finally, the estimation accuracy and stability of the adaptive SCKF algorithm are verified by the co-simulation of CarSim and Simulink. The simulation results show that when the statistical characteristics of noise are unknown and the target state changes suddenly under critical maneuvers, the estimation framework proposed in this paper still maintains high accuracy and stability. Full article

(This article belongs to the Special Issue Sensor Fusion and Advanced Controller for Connected and Automated Vehicles)

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17 pages, 4769 KiB

Open AccessArticle

Vehicle State Estimation Using Interacting Multiple Model Based on Square Root Cubature Kalman Filter

by Wan Wenkang, Feng Jingan, Song Bao and Li Xinxin

Appl. Sci. 2021, 11(22), 10772; https://doi.org/10.3390/app112210772 - 15 Nov 2021

Cited by 20 | Viewed by 3091

Abstract

The distributed drive arrangement form has better potential for cooperative control of dynamics, but this drive arrangement form increases the parameter acquisition workload of the control system and increases the difficulty of vehicle control accordingly. In order to observe the vehicle motion state [...] Read more.

The distributed drive arrangement form has better potential for cooperative control of dynamics, but this drive arrangement form increases the parameter acquisition workload of the control system and increases the difficulty of vehicle control accordingly. In order to observe the vehicle motion state accurately and in real-time, while reducing the effect of uncertainty in noise statistical information, the vehicle state observer is designed based on interacting multiple model theory with square root cubature Kalman filter (IMM-SCKF). The IMM-SCKF algorithm sub-model considers different state noise and measurement noise, and the introduction of the square root filter reduces the complexity of the algorithm while ensuring accuracy and real-time performance. To estimate the vehicle longitudinal, lateral, and yaw motion states, the algorithm uses a three degree of freedom (3-DOF) vehicle dynamics model and a nonlinear brush tire model, which is then validated in a Carsim-Simulink co-simulation platform for multiple operating conditions. The results show that the IMM-SCKF algorithm’s fusion output results can effectively follow the sub-model with smaller output errors, and that the IMM-SCKF algorithm’s results are superior to the traditional SCKF algorithm’s results. Full article

(This article belongs to the Special Issue Intelligent Vehicles: Overcoming Challenges)

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24 pages, 6476 KiB

Open AccessArticle

Multi-Target Tracking Algorithm Based on 2-D Velocity Measurements Using Dual-Frequency Interferometric Radar

by Saima Ishtiaq, Xiangrong Wang and Shahid Hassan

Electronics 2021, 10(16), 1969; https://doi.org/10.3390/electronics10161969 - 16 Aug 2021

Cited by 6 | Viewed by 4300

Abstract

Multi-target tracking (MTT) generally requires either a network of Doppler radar receivers distributed at different locations or a phased array radar. The targets moving with small/no radial velocity or angular velocity only cannot be detected and localized completely by deploying Doppler radar without [...] Read more.

Multi-target tracking (MTT) generally requires either a network of Doppler radar receivers distributed at different locations or a phased array radar. The targets moving with small/no radial velocity or angular velocity only cannot be detected and localized completely by deploying Doppler radar without antenna arrays or multiple receivers. To resolve this issue, we present a new MTT algorithm based on 2-D velocity measurements, namely, radial and angular velocities, using dual-frequency interferometric radar. The contributions of the proposed research are twofold: First, we introduce the mathematical model and implementation of the proposed algorithm by explicitly establishing the relationship between 2-D velocity measurements and kinematic state of the target in terms of Cartesian coordinates. Based on 2-D velocity measurement function, the proposed MTT algorithm comprises the following steps: (i) data association using global nearest neighbor (GNN) method (ii) target state estimation using interacting multiple model (IMM) estimator combined with square-root cubature Kalman filter (SCKF) (iii) track management using rule-based M/N logic. Second, performance of the proposed algorithm is evaluated in terms of tracking accuracy, computational complexity and IMM mean model probabilities. Simulation results for different scenarios with multiple targets moving in different tracks have been presented to verify the effectiveness of the proposed algorithm. Full article

(This article belongs to the Special Issue Modern Techniques in Radar Systems)

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18 pages, 1661 KiB

Open AccessArticle

Machine Learning for Modeling the Singular Multi-Pantograph Equations

by Amirhosein Mosavi, Manouchehr Shokri, Zulkefli Mansor, Sultan Noman Qasem, Shahab S. Band and Ardashir Mohammadzadeh

Entropy 2020, 22(9), 1041; https://doi.org/10.3390/e22091041 - 18 Sep 2020

Cited by 18 | Viewed by 3546

Abstract

In this study, a new approach to basis of intelligent systems and machine learning algorithms is introduced for solving singular multi-pantograph differential equations (SMDEs). For the first time, a type-2 fuzzy logic based approach is formulated to find an approximated solution. The rules [...] Read more.

In this study, a new approach to basis of intelligent systems and machine learning algorithms is introduced for solving singular multi-pantograph differential equations (SMDEs). For the first time, a type-2 fuzzy logic based approach is formulated to find an approximated solution. The rules of the suggested type-2 fuzzy logic system (T2-FLS) are optimized by the square root cubature Kalman filter (SCKF) such that the proposed fineness function to be minimized. Furthermore, the stability and boundedness of the estimation error is proved by novel approach on basis of Lyapunov theorem. The accuracy and robustness of the suggested algorithm is verified by several statistical examinations. It is shown that the suggested method results in an accurate solution with rapid convergence and a lower computational cost. Full article

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