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Real-Time Smoothing Filter Based on Constraints for Backward Filtering

Abstract:

The real-time information of systems has been the subject of extensive studies. Although the state of a system in real time can be estimated using only the Kalman filter, this paper focuses on a method for achieving a more accurate estimation. A smoothing filter (SF) can be utilized to improve the estimation accuracy. To implement this in real time, studies have explored the application of a windowing method to develop a real-time SF (RSF) However, achieving real-time performance remains challenging, as the SF has minimal influence on estimation performance for the current time point at the end of the applied interval. To address these challenges, a real-time constrained SF (RCSF) is proposed in this study, establishing constraints for the backward filter through the definition of prior information. Subsequently, a global positioning system/dead reckoning (GPS/DR) navigation system is implemented. A temporal analysis is conducted to demonstrate the feasibility of real-time implementation of the RCSF. Finally, the RCSF is validated through a comparative analysis with other filters using the KITTI dataset. This study contributes to the advancement of real-time estimation techniques, enhancing the real-time performance and applicability of the conventional RSF, which has limitations in current state estimation.

Joo Han Lee, Yong Hun Kim, Hoang Viet Do, Bo Sung Ko, Jin Woo Song

INS/Multi-Positioning Sensor-Based Fault Tolerant VTOL Navigation System Via 3D Distance Constraints

Abstract:

In recent years, the error-state Kalman filter (ErKF) has been widely employed in various applications, including robotics, aerospace, and localization. However, incorporating state constraints into the ErKF framework using the estimate projection method remains ambiguous. This paper examines this issue in depth, specifically exploring whether constraints should be enforced before or after the ErKF correction step. We adopt a mathematical approach, deriving analytical solutions and analyzing their statistical properties. Our findings prove that, for a linear system with linear constraints, both methods yield statistically equivalent results. However, the filter’s behavior becomes uncertain when dealing with linearized constraints. We further identify a special case of a nonlinear constraint where the results of the linear case remain valid. To support our theoretical analysis and evaluate the filter’s performance under non-ideal conditions, we conduct two Monte Carlo simulations considering increasing initialization errors and constraint incompleteness. The simulation results validate our theoretical insights and suggest that applying constraints to the error state after the correction step may lead to superior performance compared to the alternative approach.

Bo Sung Ko, Joo Han Lee, Hoang Viet Do, Yong Hun Kim, Jin Woo Song

Error-State Kalman Filtering with Linearized State Constraints

Abstract:

This paper presents a fault tolerant navigation algorithm for vertical takeoff and landing advanced aerial mobility platforms. The proposed algorithm incorporates constraints based on the distances between sensors, using the innovation calculated from filter estimation and measurement as a weighting factor. With the proposed sensor configuration, the platform’s attitude is computed and then used for measurement updates, while an adaptive rule is employed to enhance filter robustness. A comprehensive analysis was conducted using Monte Carlo simulations to confirm the algorithm’s robustness, and experimental test verified its feasibility in real-world conditions. The results demonstrated that the proposed algorithm maintained robust performance even in various sensor fault scenarios and achieved significant improvements in attitude estimation accuracy compared to traditional navigation systems. Moreover, the successful experimental validation shows that the algorithm can be effectively implemented using a single inertial measurement unit together with multi-positioning sensors, such as real-time kinematics and ultra- wideband, thereby enhancing reliability and fault tolerance in aerial navigation applications.

Hoang Viet Do, Jin Woo Song

Radar Dead-reckoning Based EKF-SLAM Using Virtual Line Segment

Abstract:

In this paper, we propose a dead reckoning–based radar simultaneous localization and mapping (SLAM) system utilizing constrained virtual line segments. In particular, we utilize Doppler velocity from radar for odometry while constructing a map using 3D radar point-cloud measurements. Unlike the conventional approach where accelerometers are employed, our system integrates radar velocity for pose calculation, thereby preventing double-integration and accelerometer bias and potentially improving the localization accuracy. Additionally, we analyze radar 3D point cloud characteristics and employ a recursive random sample consensus algorithm to eliminate outliers. The resulting set of inlier point clouds is then used to predict virtual line segments. Using virtual lines instead of feature points mitigates the sparse and noisy nature of radar point clouds. Moreover, considering the typical characteristics of indoor environments where walls intersect perpendicularly, we impose constraints on estimates to enhance performance further. We evaluate the performance of the proposed algorithm through experiments conducted in real indoor environments using an unmanned ground vehicle platform. Our results demonstrate significant improvements over traditional odometer-based systems, with reductions of approximately 41% in 2D trajectory error and 49.5% in heading angle error.

Min Ho Lee, Kyeong Wook Seo, Dong Yun Hwang, Jin Woo Song, Hoang Viet Do

Re-estimate the Robot Position by Estimating the Location of Unknown ArUco Markers with Feature Velocity Aid

Abstract:

Indoor navigation stands out as a crucial technology for the smooth performance of robots. This paper proposes an algorithm for position estimation employing a monocular camera and an inertial measurement unit, presenting a system that re-estimates the robot’s position based on the localization of ArUco markers. The algorithm is designed based on the extended Kalman filter, utilizing measurements derived from the calculated position and velocity information obtained from the markers. Experimental validation of the proposed algorithm demonstrates its effectiveness, confirming the ability to estimate the robot’s position by randomly attaching markers in an environment without pre-set configurations.

Kyeong Wook Seo, Dong Yun Hwang, Min Ho Lee, Jin Woo Song, Hoang Viet Do

A dual fault detection algorithm based on the federated Kalman filter to enhance the reliability of the navigation system

Abstract:

In this paper, we propose the dual fault detection (dual FD) algorithm for the enhancement of the navigation system reliability. The dual FD algorithm, which contributes to fast and accurate fault detection results, is constructed by fusing the measurement-based FD algorithm and system-based FD algorithm. The measurement-based algorithm uses the parity space concept and the system-based algorithm employs the federated Kalman filter. To fuse the measurement-based FD algorithm and the system-based FD algorithm, the weighting factors for each FD algorithm are added. In the measurement-based algorithm, the weighting factor related to the failure rate of each sensor is added to the parity vector. In the system-based algorithm, the weighting factor tat limits the covariance weighting is added to enhance the fault detection time. Moreover, the modified threshold for the chi-square test used in the measurement-based FD is employed in the decision-making stage to reduce the fault detection time delay without sacrificing the accuracy of fault detection. The proposed algorithm was verified using simulations for various fault types. The simulation result demonstrated that the proposed dual FD algorithm is as fast as teh measurement-based FD algorithm and as as accurate as the system-based FD algorithm.

Eung Ju Kim, Seong Taek Kim, Yong Hun Kim, Min Jun Choi, Hoang Viet Do, Jin Woo Song

Tracking Control for Electro-Optical System in Vibration Enviroment Based on Self-tuning Fuzzy Sliding Mode Control

Abstract:

In this research, we propose a nonholonomic average speed measurement that newly recombines usable measurement in nonholonomic conditions to improve the heading accuracy of the vehicle Odometer/GPS/INS integrated navigation system. The average speed is less noise and the direction angle can be corrected more accurately because the information comes from data with long baselines. The advantages of this average speed is applied to nonholonomic measurements, which can improve the heading accuracy of the land vehicle navigation system. The proposed algorithm has been verified by Monte Carlo simulation. Verification results show improved heading accuracy and efficient applicability to navigation systems.

Duyen Ha Thi Kim, Tien Ngo Manh, Chien Nguyen Nhu, Viet Do Hoang, Huong Nguyen Thi Thu