Search Results (16)

The use of inertial measurement units (IMUs) as an alternative to optical marker-based systems has the potential to make gait analysis part of the clinical standard of care. Previously, an IMU-based system leveraging Rauch–Tung–Striebel smoothing to estimate knee angles was assessed using a six-degrees-of-freedom joint simulator. In a clinical setting, however, accurately measuring abduction/adduction and external/internal rotation of the knee joint is particularly challenging, especially in the presence of soft tissue artefacts. In this study, the in vivo IMU-based joint angles of 40 asymptomatic knees were assessed during level walking, under two distinct sensor placement configurations: (1) IMUs fixed to a rigid harness, and (2) IMUs mounted on the skin using elastic hook-and-loop bands (from here on referred to as “skin-mounted IMUs”). Estimates were compared against values obtained from a harness-mounted optical marker-based system. The comparison of these three sets of kinematic signals (IMUs on harness, IMUs on skin, and optical markers on harness) was performed before and after implementation of a REference FRame Alignment MEthod (REFRAME) to account for the effects of differences in coordinate system orientations. Prior to the implementation of REFRAME, in comparison to optical estimates, skin-mounted IMU-based angles displayed mean root-mean-square errors (RMSEs) up to 6.5°, while mean RMSEs for angles based on harness-mounted IMUs peaked at 5.1°. After REFRAME implementation, peak mean RMSEs were reduced to 4.1°, and 1.5°, respectively. The negligible differences between harness-mounted IMUs and the optical system after REFRAME revealed that the IMU-based system was capable of capturing the same underlying motion pattern as the optical reference. In contrast, obvious differences between the skin-mounted IMUs and the optical reference indicated that the use of a harness led to fundamentally different joint motion being measured, even after accounting for reference frame misalignments. Fluctuations in the kinematic signals associated with harness use suggested the rigid device oscillated upon heel strike, likely due to inertial effects from its additional mass. Our study proposes that optical systems can be successfully replaced by more cost-effective IMUs with similar accuracy, but further investigation (especially in vivo and upon heel strike) against moving videofluoroscopy is recommended. Full article

High-precision navigation systems are crucial for unmanned autonomous vessels. However, commonly used Global Navigation Satellite System (GNSS) signals are often severely affected by environmental obstruction, leading to reduced positioning accuracy or even the inability to locate. To address the issues caused by signal obstruction in high-precision navigation systems, the research presented in this paper proposes a vector-tracking loop (VTL) structure based on the forward Kalman Filter (KF) and the backward Rauch Tung Striebel (RTS) smoothing algorithm. The introduction of loop filters in the signal-tracking loop improves the tracking accuracy of the carrier and code, thereby enhancing the stability and robustness of the navigation system. The traditional scalar-tracking loop (STL), traditional VTL, and Kalman Filter (KF)-based VTL were compared through shipborne motion experiments, and the proposed method demonstrated superior signal-tracking capability and navigation accuracy. In the experiment, there were three blocking areas along the experimental path. The experimental results show that, when there are signal blockages of 12 s, 18 s, and 40 s, compared to the traditional VTL method, the proposed method can reduce the horizontal position error by 93.9%, 95.8%, and 94.5%, respectively, as well as the horizontal velocity error by 71.1%, 95.8%, and 97.6%, respectively. Full article

High−precision and robust localization is critical for intelligent vehicle and transportation systems, while the sensor signal loss or variance could dramatically affect the localization performance. The vehicle localization problem in an environment with Global Navigation Satellite System (GNSS) signal errors is investigated in this study. The error state Kalman filtering (ESKF) and Rauch–Tung–Striebel (RTS) smoother are integrated using the data from Inertial Measurement Unit (IMU) and GNSS sensors. A segmented RTS smoothing algorithm is proposed in order to estimate the error state, which is typically close to zero and mostly linear, which allows more accurate linearization and improved state estimation accuracy. The proposed algorithm is evaluated using simulated GNSS signals with and without signal errors. The simulation results demonstrate its superior accuracy and stability for state estimation. The designed ESKF algorithm yielded an approximate 3% improvement in long straight line and turning scenarios compared to classical EKF algorithm. Additionally, the ESKF−RTS algorithm exhibited a 10% increase in the localization accuracy compared to the ESKF algorithm. In the double turning scenarios, the ESKF algorithm resulted in an improvement of about 50% in comparison to the EKF algorithm, while the ESKF−RTS algorithm improved by about 50% compared to the ESKF algorithm. These results indicated that the proposed ESKF−RTS algorithm is more robust and provides more accurate localization. Full article

Traditional precise engineering surveys adopt manual static, discrete observation, which cannot meet the dynamic, continuous, high-precision and holographic fine measurements required for large-scale infrastructure construction, operation and maintenance, where mobile laser scanning technology is becoming popular. However, in environments without GNSS signals, it is difficult to use mobile laser scanning technology to obtain 3D data. We fused a scanner with an inertial navigation system, odometer and inclinometer to establish and track mobile laser measurement systems. The control point constraints and Rauch-Tung-Striebel filter smoothing were fused, and a 3D point cloud generation method based on multi-sensor fusion was proposed. We verified the method based on the experimental data; the average deviation of positioning errors in the horizontal and elevation directions were 0.04 m and 0.037 m, respectively. Compared with the stop-and-go mode of the Amberg GRP series trolley, this method greatly improved scanning efficiency; compared with the method of generating a point cloud in an absolute coordinate system based on tunnel design data conversion, this method improved data accuracy. It effectively avoided the deformation of the tunnel, the sharp increase of errors and more accurately and quickly processed the tunnel point cloud data. This method provided better data support for subsequent tunnel analysis such as 3D display, as-built surveying and disease system management of rail transit tunnels. Full article

This paper proposes novel unbiased minimum-variance receding-horizon fixed-lag (UMVRHF) smoothers in batch and recursive forms for linear discrete time-varying state space models in order to improve the computational efficiency and the estimation performance of receding-horizon fixed-lag (RHF) smoothers. First, an UMVRHF smoother in batch form is proposed by combining independent receding-horizon local estimators for two separated sub-horizons. The local estimates and their error covariance matrices are obtained based on an optimal receding horizon filter and the smoother in terms of the unbiased minimum variance; they are then optimally combined using Millman’s theorem. Next, the recursive form of the proposed UMVRHF smoother is derived to improve its computational efficiency and extendibility. Additionally, we introduce a method for extending the proposed recursive smoothing algorithm to a posteriori state estimations and propose the Rauch–Tung–Striebel receding-horizon fixed-lag smoother in recursive form. Furthermore, a computational complexity reduction technique that periodically switches the two proposed recursive smoothing algorithms is proposed. The performance and effectiveness of the proposed smoothers are demonstrated by comparing their estimation results with those of previous algorithms for Kalman and receding-horizon fixed-lag smoothers via numerical experiments. Full article

In this paper, an adaptive fading-memory receding-horizon (AFMRH) filter is proposed by combining the receding-horizon structure and the adaptive fading-memory method. In the recent finite horizon, state error covariance is adapted with an adaptive fading factor; then the process noise covariance matrix adaption is realized by adjusting the properties of systems. An AFMRH fixed-lag smoother is also proposed by combining the proposed AFMRH filtering algorithm and a Rauch–Tung–Striebel smoothing algorithm to improve the estimation accuracy. Because the proposed AFMRH filter and smoother are reduced to the optimal receding-horizon (RH) filter and smoother when all measurements have the same weight, the proposed adaptive RH estimators could provide a more general solution than the optimal RH filter and smoother. To reduce the complexity and improve the estimation performance of the proposed RH estimators, an adaptive horizon adjustment method and a switching filtering algorithm based on an adaptive fading factor are also proposed. In particular, the proposed adaptive horizon adjustment method is designed to be computationally efficient, which makes it suitable for online and real-time applications. Through computer simulation, the performance and adaptiveness of the proposed approaches were verified by comparing them with existing fading-memory approaches. Full article

The weigh-in-motion (WIM) system weighs the entire vehicle by identifying the dynamic forces of each axle of the vehicle on the road. The load of each axle is very important to detect the total weight of the vehicle. Different drivers have different driving behaviors, and when large trucks pass through the weighing detection area, the driving state of the trucks may affect the weighing accuracy of the system. This paper proposes YOLOv3 network model as the basis for this algorithm, which uses the feature pyramid network (FPN) idea to achieve multi-scale prediction and the deep residual network (ResNet) idea to extract image features, so as to achieve a balance between detection speed and detection accuracy. In the paper, spatial pyramid pooling (SPP) network and cross stage partial (CSP) network are added to the original network model to improve the learning ability of the convolutional neural network and make the original network more lightweight. Then the detection-based target tracking method with Kalman filtering + RTS (rauch–tung–striebel) smoothing is used to extract the truck driving status information (vehicle trajectory and speed). Finally, the effective size of the vehicle in different driving states on the weighing accuracy is statistically analyzed. The experimental results show that the method has high accuracy and real-time performance in truck driving state extraction, can be used to analyze the influence of weighing accuracy, and provides theoretical support for personalized accuracy correction of WIM system. At the same time, it is beneficial for WIM system to assist the existing traffic system more accurately and provide a highway health management and effective decision making by providing reliable monitoring data. Full article

The state of charge (SOC) of a lithium battery system is critical since it indicates the remaining operating hours, full charge time, and peak power of the battery. This paper recommends an extended Rauch–Tung–Striebel smoother (ERTSS) for estimating SOC. It is implemented based on an improved equivalent circuit model with hysteresis voltage. The smoothing step of ERTSS will reduce the estimation error further. Additionally, the genetic algorithm (GA) is employed for searching the optimal ERTSS’s smoothing time interval. Various dynamic cell tests are conducted to verify the model’s accuracy and error estimation deviation. The test results demonstrate that ERTSS’s SOC estimation error is limited to $4\%$ with an initial error between −25 ${}^{\circ }$C and 45 ${}^{\circ }$C and that the root mean square error (RMSE) of ERTSS’s SOC estimation is approximately 5% lower than that of extended Kalman filter (EKF). The ERTSS improves the SOC estimation accuracy at all operating temperatures of batteries. Full article

Hybrid systems are subject to multiple dynamic models, or so-called modes. To estimate the state, the sequence of modes has to be estimated, which results in an exponential growth of possible sequences. The most prominent solution to handle this is the interacting multiple model filter, which can be extended to smoothing. In this paper, we derive a novel generalization of the interacting multiple filter and smoother to manifold state spaces, e.g., quaternions, based on the boxplus-method. As part thereof, we propose a linear approximation to the mixing of Gaussians and a Rauch–Tung–Striebel smoother for single models on boxplus-manifolds. The derivation of the smoother equations is based on a generalized definition of Gaussians on boxplus-manifolds. The three, novel algorithms are evaluated in a simulation and perform comparable to specialized solutions for quaternions. So far, the benefit of the more principled approach is the generality towards manifold state spaces. The evaluation and generic implementations are published open source. Full article

The occlusion of buildings in urban environments leads to the intermittent reception of satellite signals, which limits the utilization of observations. This subsequently results in a decline of the positioning and attitude accuracy of Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS) integrated system (GNSS/INS). This study implements a smooth post-processing strategy based on a tightly coupled differential GNSS/INS. Specifically, this strategy used the INS-estimated position to reinitialize integer ambiguity. The GNSS raw observations were input into the Kalman filter to update the measurement. The Rauch–Tung–Striebel smoothing (RTSS) algorithm was used to process the observations of the entire period. This study analyzed the performance of loosely coupled and tightly coupled systems in an urban environment and the improvement of the RTSS algorithm on the navigation solution from the perspective of fully mining the observations. The experimental results of the simulation data and real data show that, compared with the traditional tightly coupled processing strategy which does not use INS-aided integer ambiguity resolution and RTSS algorithm, the strategy in this study sufficiently utilized INS observations and GNSS observations to effectively improve the accuracy of positioning and attitude and ensure the continuity of navigation results in an obstructed environment. Full article

An accurate motion model and reliable measurements are required for autonomous underwater vehicle localization and navigation in underwater environments. However, without a propeller, underwater gliders have limited maneuverability and carrying capacity, which brings difficulties for modeling and measuring. In this paper, an extended Kalman filter (EKF)-based method, combining a modified kinematic model of underwater gliders with the travel-time differences between signals received from a single beacon, is proposed for estimating the glider positions in a predict-update cycle. First, to accurately establish a motion model for underwater gliders moving in the ocean, we introduce two modification parameters, the attack and drift angles, into a kinematic model of underwater gliders, along with depth-averaged current velocities. The attack and drift angles are calculated based on the coefficients of hydrodynamic forces and the sensor-measured angle variation over time. Then, instead of satisfying synchronization requirements, the travel-time differences between signals received from a single beacon, multiplied by the sound speed, are taken as the measurements. To further reduce the EKF estimation error, the Rauch-Tung-Striebel (RTS) smoothing method is merged into the EKF system. The proposed method is tested in a virtual spatiotemporal environment from an ocean model. The experimental results show that the performance of the RTS-EKF estimate is improved when compared with the motion model estimate, especially by 46% at the inflection point, at least in the particular study developed in this article. Full article

Global navigation satellite systems (GNSSs) are commonly used for navigation and mapping applications. However, in GNSS-hostile environments, where the GNSS signal is noisy or blocked, the navigation information provided by a GNSS is inaccurate or unavailable. To overcome these issues, this study proposed a real-time visual odometry (VO)/GNSS integrated navigation system. An on-line smoothing method based on the extended Kalman filter (EKF) and the Rauch-Tung-Striebel (RTS) smoother was proposed. VO error modelling was also proposed to estimate the VO error and compensate the incoming measurements. Field tests were performed in various GNSS-hostile environments, including under a tree canopy and an urban area. An analysis of the test results indicates that with the EKF used for data fusion, the root-mean-square error (RMSE) of the three-dimensional position is about 80 times lower than that of the VO-only solution. The on-line smoothing and error modelling made the results more accurate, allowing seamless on-line navigation information. The efficiency of the proposed methods in terms of cost and accuracy compared to the conventional inertial navigation system (INS)/GNSS integrated system was demonstrated. Full article

In this paper, an application of spherical radial cubature Bayesian filtering and smoothing algorithms is presented to solve a typical underwater bearings only passive target tracking problem effectively. Generally, passive target tracking problems in the ocean environment are represented with the state-space model having linear system dynamics merged with nonlinear passive measurements, and the system is analyzed with nonlinear filtering algorithms. In the present scheme, an application of spherical radial cubature Bayesian filtering and smoothing is efficiently investigated for accurate state estimation of a far-field moving target in complex ocean environments. The nonlinear model of a Kalman filter based on a Spherical Radial Cubature Kalman Filter (SRCKF) and discrete-time Kalman smoother known as a Spherical Radial Cubature Rauch–Tung–Striebel (SRCRTS) smoother are applied for tracking the semi-curved and curved trajectory of a moving object. The worth of spherical radial cubature Bayesian filtering and smoothing algorithms is validated by comparing with a conventional Unscented Kalman Filter (UKF) and an Unscented Rauch–Tung–Striebel (URTS) smoother. Performance analysis of these techniques is performed for white Gaussian measured noise variations, which is a significant factor in passive target tracking, while the Bearings Only Tracking (BOT) technology is used for modeling of a passive target tracking framework. Simulations based experiments are executed for obtaining least Root Mean Square Error (RMSE) among a true and estimated position of a moving target at every time instant in Cartesian coordinates. Numerical results endorsed the validation of SRCKF and SRCRTS smoothers with better convergence and accuracy rates than that of UKF and URTS for each scenario of passive target tracking problem. Full article

In this paper, we introduce a tracking algorithm based on labeled Random Finite Sets (RFS) and Rauch–Tung–Striebel (RTS) smoother via a Generalized Labeled Multi-Bernoulli (GLMB) multi-scan estimator to track multiple objects in a wide range of tracking scenarios. In the forward filtering stage, we use the GLMB filter to generate a set of labels and the association history between labels and the measurements. In the trajectory-estimating stage, we apply a track management strategy to eliminate tracks with short lifespan compared to a threshold value. Subsequently, we apply the information of trajectories captured from the forward GLMB filtering stage to carry out standard forward filtering and RTS backward smoothing on each estimated trajectory. For the experiment, we implement the tracker with standard GLMB filter, the hybrid track-before-detect (TBD) GLMB filter, and the GLMB filter with objects spawning. The results show improvements in tracking performance for all implemented trackers given negligible extra computational effort compared to standard GLMB filters. Full article

A localization and tracking algorithm for an early-warning tracking system based on the information fusion of Infrared (IR) sensor and Laser Detection and Ranging (LADAR) is proposed. The proposed Kalman filter scheme incorporates Out-of-Sequence Measurements (OOSMs) to address long-range, high-speed incoming targets to be tracked by networked Remote Observation Sites (ROS) in cluttered environments. The Rauch–Tung–Striebel (RTS) fixed lag smoothing algorithm is employed in the proposed technique to further improve tracking accuracy, which, in turn, is used for target profiling and efficient filter initialization at the targeted platform. This efficient initialization increases the probability of target engagement by increasing the distance at which it can be effectively engaged. The increased target engagement range also reduces risk of any damage from debris of the engaged target. Performance of the proposed target localization algorithm with OOSM and RTS smoothing is evaluated in terms of root mean square error (RMSE) for both position and velocity, which accurately depicts the improved performance of the proposed algorithm in comparison with existing retrodiction-based OOSM filtering algorithms. The effects of assisted target state initialization at the targeted platform are also evaluated in terms of Time to Impact (TTI) and true track retention, which also depict the advantage of the proposed strategy. Full article