Trajectory Estimation Method Research Articles

A Novel Hypersonic Target Trajectory Estimation Method Based on Long Short-Term Memory and a Multi-Head Attention Mechanism.

To address the complex maneuvering characteristics of hypersonic targets in adjacent space, this paper proposes an LSTM trajectory estimation method combined with the attention mechanism and optimizes the model from the information-theoretic perspective. The method captures the target dynamics by using the temporal processing capability of LSTM, and at the same time improves the efficiency of information utilization through the attention mechanism to achieve accurate prediction. First, a target dynamics model is constructed to clarify the motion behavior parameters. Subsequently, an LSTM model incorporating the attention mechanism is designed, which enables the model to automatically focus on key information fragments in the historical trajectory. In model training, information redundancy is reduced, and information validity is improved through feature selection and data preprocessing. Eventually, the model achieves accurate prediction of hypersonic target trajectories with limited computational resources. The experimental results show that the method performs well in complex dynamic environments with improved prediction accuracy and robustness, reflecting the potential of information theory principles in optimizing the trajectory prediction model.

An improved particle filtering projectile trajectory estimation algorithm fusing velocity information

This study proposes an improved particle-filtering projectile trajectory estimation method that fuses velocity information to address the susceptibility to interference and large fluctuations in position and velocity measurements of a single-antenna-two-dimensional trajectory correction fuze. By considering the Doppler effect in satellite velocity measurements and the residuals between the model-derived velocity and velocity derived from the translational Doppler frequency shift, a sliding time window was established to generate velocity weight coefficients that dynamically adjust the weight of the velocity in filtering. By modifying the likelihood function, a particle-filtering algorithm was designed to achieve a fusion estimation of the projectile trajectory. Tests indicate that this method provides more accurate estimates of the position and velocity of the projectile compared to other existing methods, which can reduce the impact of velocity fluctuations to a certain extent. In addition, the computational burden is not increased and can directly replace existing mature algorithms in engineering.

Flight behaviour monitoring and quantification of aedes aegypti using convolution neural network.

Mosquito-borne diseases cause a huge burden on public health worldwide. The viruses that cause these diseases impact the behavioural traits of mosquitoes, including locomotion and feeding. Understanding these traits can help in improving existing epidemiological models and developing effective mosquito traps. However, it is difficult to understand the flight behaviour of mosquitoes due to their small sizes, complicated poses, and seemingly random moving patterns. Currently, no open-source tool is available that can detect and track resting or flying mosquitoes. Our work presented in this paper provides a detection and trajectory estimation method using the Mask RCNN algorithm and spline interpolation, which can efficiently detect mosquitoes and track their trajectories with higher accuracy. The method does not require special equipment and works excellently even with low-resolution videos. Considering the mosquito size, the proposed method's detection performance is validated using a tracker error and a custom metric that considers the mean distance between positions (estimated and ground truth), pooled standard deviation, and average accuracy. The results showed that the proposed method could successfully detect and track the flying (≈ 96% accuracy) as well as resting (100% accuracy) mosquitoes. The performance can be impacted in the case of occlusions and background clutters. Overall, this research serves as an efficient open-source tool to facilitate further examination of mosquito behavioural traits.

Estimation of Foot Trajectory and Stride Length during Level Ground Running Using Foot-Mounted Inertial Measurement Units.

Zero-velocity assumption has been used for estimation of foot trajectory and stride length during running from the data of foot-mounted inertial measurement units (IMUs). Although the assumption provides a reasonable initialization for foot trajectory and stride length estimation, the other source of errors related to the IMU’s orientation still remains. The purpose of this study was to develop an improved foot trajectory and stride length estimation method for the level ground running based on the displacement of the foot. Seventy-nine runners performed running trials at 5 different paces and their running motions were captured using a motion capture system. The accelerations and angular velocities of left and right feet were measured with two IMUs mounted on the dorsum of each foot. In this study, foot trajectory and stride length were estimated using zero-velocity assumption with IMU data, and the orientation of IMU was estimated to calculate the mediolateral and vertical distance of the foot between two consecutive midstance events. Calculated foot trajectory and stride length were compared with motion capture data. The results show that the method used in this study can provide accurate estimation of foot trajectory and stride length for level ground running across a range of running speeds.

GNSS Odometry: Precise Trajectory Estimation Based on Carrier Phase Cycle Slip Estimation

This letter proposes a highly accurate trajectory estimation method for outdoor mobile robots using global navigation satellite system (GNSS) time differences of carrier phase (TDCP) measurements. By using GNSS TDCP, the relative 3D position can be estimated with millimeter precision. However, when a phenomenon called cycle slip occurs, wherein the carrier phase measurement jumps and becomes discontinuous, it is impossible to accurately estimate the relative position using TDCP. Although previous studies have eliminated the effect of cycle slip using a robust optimization technique, it was difficult to completely eliminate the effect of outliers. In this letter, we propose a method to detect GNSS carrier phase cycle slip, estimate the amount of cycle slip, and modify the observed TDCP to calculate the relative position using the factor graph optimization framework. The estimated relative position acts as a loop closure in graph optimization and contributes to the reduction in the integration error of the relative position. Experiments with an unmanned aerial vehicle showed that by modifying the cycle slip using the proposed method, the vehicle trajectory could be estimated with an accuracy of 5-30 cm using only a single GNSS receiver, without using any other external data or sensors.

Magnetic Field-Enhanced Learning-Based Inertial Odometry for Indoor Pedestrian

Pedestrian dead-reckoning (PDR) is a vital technique in pedestrian localization. Compared with traditional PDR, learning-based inertial odometry has the advantages of smaller position drift and is insensitive to pedestrian motion patterns. However, the heading drift of the trajectory is still the dominant error source for the position error drift in these methods. This study focuses on providing a pedestrian trajectory estimation method with low drift by properly fusing learned-based inertial odometry and magnetometer measurements under an indoor scenario containing significant magnetic field disturbance. The proposed method reduces the impact of magnetic field disturbance by adopting a long-term average magnetic vector, which is far more stable than using local magnetic vectors. Meanwhile, the proposed method can estimate the magnetometer bias online rather than depending on precalibrated magnetometer measurements. The test results show that the proposed method can obtain superior positioning performance using uncalibrated raw magnetometer data compared to other methods, even using calibrated magnetometer data. Simultaneously, this method achieves a balance between algorithm accuracy and efficiency.

An android-based field investigation tool to estimate the potential trajectories of perforated AK bullets in 1 mm sheet metal surfaces

This study presents designing of an Android-based software tool to use in AK rifle related shooting investigations. The designed softwear tool; “Bullet Trajectory Plotter” could estimate the potential trajectories of perforated AK bullets in 1 mm sheet metal surfaces. The tool was developed as an Android application to use with a mobile phone or tablet computer. It is based on the results of the authors’ two previous studies, which identified the co-relation between the angles of incidence of standard steel core AK bullets (7.62 × 39 mm) and the length of the bullet hole in 1 mm sheet metal gauges. The software tool proved to be a viable, quickly employable, user-friendly, and fully mobile field investigation tool that can be installed on investigators’ mobile phones to identify the approximate angles of incidence of perforated steel core AK bullets on 1 mm sheet metal surfaces. Additionally, the software tool could be used as a new method of reconfirming findings from the existing trajectory estimation methods.

Target trajectory estimation by unambiguous phase differences from a single fixed passive sensor

In this Letter, considering the configuration of small antenna array aperture used for special usage, the authors proposed a target trajectory estimation method by unambiguous phase differences with prior knowledge on target velocity from a single fixed passive sensor. First, they developed the maximum likelihood estimator of the target trajectory parameters based on unambiguous phase differences and then deduce the corresponding Cramer–Rao lower bound. Furthermore, in terms of the error in prior knowledge on target velocity, the influence of target velocity mismatch on trajectory parameters estimation is analysed. Finally, they evaluated the performance of the proposed method and validated the correctness of their analysis via numerical simulation.

A review of foot pose and trajectory estimation methods using inertial and auxiliary sensors for kinematic gait analysis.

The use of foot mounted inertial and other auxiliary sensors for kinematic gait analysis has been extensively investigated during the last years. Although, these sensors still yield less accurate results than those obtained employing optical motion capture systems, the miniaturization and their low cost have allowed the estimation of kinematic spatiotemporal parameters in laboratory conditions and real life scenarios. The aim of this work was to present a comprehensive approach of this scientific area through a systematic literature research, breaking down the state-of-the-art methods into three main parts: (1) zero velocity interval detection techniques; (2) assumptions and sensors' utilization; (3) foot pose and trajectory estimation methods. Published articles from 1995 until December of 2018 were searched in the PubMed, IEEE Xplore and Google Scholar databases. The research was focused on two categories: (a) zero velocity interval detection methods; and (b) foot pose and trajectory estimation methods. The employed assumptions and the potential use of the sensors have been identified from the retrieved articles. Technical characteristics, categorized methodologies, application conditions, advantages and disadvantages have been provided, while, for the first time, assumptions and sensors' utilization have been identified, categorized and are presented in this review. Considerable progress has been achieved in gait parameters estimation on constrained laboratory environments taking into account assumptions such as a person walking on a flat floor. On the contrary, methods that rely on less constraining assumptions, and are thus applicable in daily life, led to less accurate results. Rule based methods have been mainly used for the detection of the zero velocity intervals, while more complex techniques have been proposed, which may lead to more accurate gait parameters. The review process has shown that presently the best-performing methods for gait parameter estimation make use of inertial sensors combined with auxiliary sensors such as ultrasonic sensors, proximity sensors and cameras. However, the experimental evaluation protocol was much more thorough, when single inertial sensors were used. Finally, it has been highlighted that the accuracy of setups using auxiliary sensors may further be improved by collecting measurements during the whole foot movement and not only partially as is currently the practice. This review has identified the need for research and development of methods and setups that allow for the robust estimation of kinematic gait parameters in unconstrained environments and under various gait profiles.

Body center of mass trajectory and mechanical energy using inertial sensors: a feasible stride?

BackgroundThe description of the three-dimensional (3D) trajectory of the body center of mass (BCoM) provides useful insights on the mechanics of locomotion. The BCoM trajectory can be estimated from ground reaction forces, recorded by force platforms (GRF, gold standard), or from marker trajectories recorded by stereophotogrammetric systems (MKR). However, both instruments do not allow for monitoring locomotion in the real-life environment. In this perspective, magneto-inertial measurement units (MIMUs) are particularly attractive being wearable, thus enabling to collect movement data out of the laboratory. Research questionsTo investigate the feasibility and accuracy of a recent marketed full-body MIMU-based method for the estimation of the 3D BCoM trajectory and energetics during walking. MethodsTwelve subjects walked at self-selected and slow speed along a 12 m long walkway. GRF and MKR were acquired using three force platforms and a stereophotogrammetric system. MIMU data were collected using a full-body MIMU-based motion capture system (Xsens MTw Awinda). The 3D BCoM trajectory, external mechanical work and energy recovery were extracted from the data acquired by the three measurement systems, using state-of-the-art methods. The accuracy of both MKR- and MIMU-based estimates compared with GRF was assessed for the BCoM trajectory (maximum, minimum, range, and RMSD), as well as for mechanical work and energy recovery. ResultsA total number of 108 strides were analyzed. MIMU-based BCoM trajectory displayed larger errors in comparison with GRF (and MKR) for the trajectory ranges: 89 ± 47(93 ± 44)% in antero-posterior, 46 ± 25(40 ± 79)% medio-lateral and -13 ± 23(-5 ± 25)% vertical directions, leading to a 3D RMSD of 17 ± 5(12 ± 5) mm (mean ± SD). These discrepancies largely affected the estimation of both mechanical work and energy recovery (+115 ± 85% and -28 ± 21%, respectively). SignificancePreliminary findings highlighted that the tested MIMU-based method for BCoM trajectory estimation still lacks accuracy and that the quantification of energetics in real-life situations remains an open challenge.

Trajectory estimation method of spinning projectile without velocity input

Abstract It is essential to obtain the position, velocity and attitude of a projectile for course correction, where the velocity of a spinning projectile is the hardest to obtain with merely a GPS (Global Positioning System) receiver. To realize trajectory correction without additional devices except a GPS receiver, a trajectory estimation method without external velocity input is studied. A modified point-mass model of the spinning projectile with fixed canards is established, and its real-time position and velocity is estimated by an extended Kalman filter with input of only position and rotational speed. A trajectory control technology is proposed as well and being verified by the hardware-in-the-loop simulations. The simulation results show that the proposed method can estimate the position and velocity of the trajectory properly and reduce the CEP (Circular Error Probable) of the projectile by about 100 m.

Online State Estimation of a Fin-Actuated Underwater Robot Using Artificial Lateral Line System

A lateral line system is a flow-responsive organ system, with which fish can effectively sense the surrounding flow field, thus serving functions in flow-aided fish behaviors. Inspired by such a biological characteristic, artificial lateral line systems (ALLSs) have been developed for promoting technological innovations of underwater robots. In this article, we focus on investigating state estimation of a freely swimming robotic fish in multiple motions, including rectilinear motion, turning motion, gliding motion, and spiral motion. The state refers to motion parameters, including linear velocity, angular velocity, motion radius, etc., and trajectory of the robotic fish. Specifically, for each motion, a pressure variation (PV) model that links motion parameters to PVs surrounding the robotic fish is first built; then, a linear regression analysis method is used for determining the model parameters. Based on the acquired PV model, motion parameters can be estimated by solving the PV model inversely using the PVs measured by the ALLS. Finally, a trajectory estimation method is proposed for estimating trajectory of the robotic fish based on the ALLS-estimated motion parameters. The experimental results show that the robotic fish is able to estimate its trajectory in the aforementioned multiple motions with the aid of ALLS, with small estimation errors.

A Data-Driven Motion Prior for Continuous-Time Trajectory Estimation on SE(3)

Simultaneous trajectory estimation and mapping (STEAM) is a method for continuous-time trajectory estimation in which the trajectory is represented as a Gaussian Process (GP). Previous formulations of STEAM used a GP prior that assumed either white-noise-on-acceleration (WNOA) or white-noise-on-jerk (WNOJ). However, previous work did not provide a principled way to choose the continuous-time motion prior or its parameters on a real robotic system. This letter derives a novel data-driven motion prior where ground truth trajectories of a moving robot are used to train a motion prior that better represents the robot's motion. In this approach, we use a prior where latent accelerations are represented as a GP with a Matérn covariance function and draw a connection to the Singer acceleration model. We then formulate a variation of STEAM using this new prior. We train the WNOA, WNOJ, and our new latent-force prior and evaluate their performance in the context of both lidar localization and lidar odometry of a car driving along a 20 km route, where we show improved state estimates compared to the two previous formulations.

Advances in the meteor image processing chain using fast algorithms, deep learning, and empirical fitting

The processing pipeline for both video meteor detection and track analysis has evolved to embrace several new algorithms, which have improved the efficiency and performance of various steps in the meteor image processing chain. With the advent of larger pixel count digital sensors, the image processing techniques have needed to keep up with the computational load by not only employing higher end processors, but developing faster thresholding, clustering, and tracking algorithms for detection. In addition, machine learning methods employing both recurrent and convolutional deep neural networks have helped remove the human-in-loop false alarm mitigation step inherent in many meteor collection processing streams. The application of a matched filtering algorithm has helped to refine the measurement positional accuracy of propagating meteor tracks for post-detection analysis. The use of improved multi-site track aggregation has dramatically reduced the occurrence of mis-associating unrelated tracks during the combination into a single trajectory. When coupled with an improved minimization metric in the multi-parameter fitting method for trajectory estimation, this yields better meteor orbital solutions. Finally, proposed concepts in using a convolutional neural network as a meteor detector and performing trajectory fitting with an empirically based propagation model, show promise for more robust meteor image processing and analysis in the near future.

Estimating trajectories of meteors: an observational Monte Carlo approach – I. Theory

ABSTRACTIt has recently been shown by Egal et al. that some types of existing meteor in-atmosphere trajectory estimation methods may be less accurate than others, particularly when applied to high-precision optical measurements. The comparative performance of trajectory solution methods has previously only been examined for a small number of cases. Besides the radiant, orbital accuracy depends on the estimation of pre-atmosphere velocities, which have both random and systematic biases. Thus, it is critical to understand the uncertainty in velocity measurement inherent to each trajectory estimation method. In this first of a series of two papers, we introduce a novel meteor trajectory estimation method that uses the observed dynamics of meteors across stations as a global optimization function and that does not require either a theoretical or an empirical flight model to solve for velocity. We also develop a 3D observational meteor trajectory simulator that uses a meteor ablation model to replicate the dynamics of meteoroid flight, as a means to validate different trajectory solvers. We both test this new method and compare it to other methods, using synthetic meteors from three major showers spanning a wide range of velocities and geometries (Draconids, Geminids, and Perseids). We determine which meteor trajectory solving algorithm performs better for all-sky, moderate field-of-view, and high-precision narrow-field optical meteor detection systems. The results are presented in the second paper in this series. Finally, we give detailed equations for estimating meteor trajectories and analytically computing meteoroid orbits, and provide the python code of the methodology as open-source software.

Vehicle Trajectory Estimation Method by Drive Recorder Images and Point Cloud of Surrounding Environment

The on-the-spot inspections after accident are based on information obtained from the brake marks left on the road and the damage situation of the surroundings. However, this method is affected by the situation before the accident and cannot estimate quantitative guessing. Moreover, technologies such as automatic braking system and lane keeping system, have been developed actively. In developing these technologies, vehicle trajectory is one of the most important data. In this paper, we propose a novel method of estimating vehicle trajectory by using drive recorder images and point cloud which is measured by Mobile Mapping System and LiDAR. In the evaluation experiments, we confirmed the effectiveness of our method by comparing the vehicle poses estimated with RTK-GPS and showing the average errors are within one meter.

A Rapid Estimation for Interplanetary Low-Thrust Trajectories Using Support Vector Regression

During the preliminary phase of space mission planning and design, a large quantity of trajectory optimization problems have to be solved. Obtaining the optimal solutions of low-thrust trajectory is computationally challenging since the optimization problems usually involve an iterative numerical algorithm and the complicated numerical integration of the equations of motion. It is necessary to develop the rapid trajectory estimation methods for low-thrust transfer. In this paper, a new method based on machine learning has been proposed to estimate the optimal interplanetary low-thrust trajectory. The minimum-propellant low-thrust trajectory is optimized by using the hybrid optimization algorithm, which would provide the high-quality training samples for machine learning. Support vector regression is adopted to construct and train the estimation model. Numerical simulations demonstrate that the proposed estimation method and the percentage errors of random test samples are all lower than 5%. This application of machine learning method can accomplish very efficient low-thrust interplanetary trajectory evaluation and it is therefore suitable to extend the design flexibility in the practical exploration mission.

Modelling the measurement accuracy of pre-atmosphere velocities of meteoroids

Many existing optical meteor trajectory estimation methods use the approximation that the velocity of the meteor at the beginning of its luminous phase is equivalent to its velocity before atmospheric entry. Meteoroid kinetic energy loss prior to the luminous phase cannot be measured, but for some masses and entry geometries neglecting this loss may lead to non-negligible deceleration prior to thermal ablation. Using a numerical meteoroid ablation model, we simulate the kinematics of meteoroids beginning at 180 km with initial velocities ranging from 11 km/s to 71 km/s, and compare model velocities at the moment of detection to measurements. We validate the simulations by comparing the simulated luminous beginning heights with observed beginning heights of different populations of meteors detected with different optical systems. We find that most low-velocity meteoroids have a significant velocity difference of 100 m/s to 750 m/s (depending on meteoroid type, mass, and observation system). This systematic underestimate of meteoroid speeds also results in systematically lower semi-major axes for meteoroid orbits.

Image-Based Localization Aided Indoor Pedestrian Trajectory Estimation Using Smartphones.

Accurately determining pedestrian location in indoor environments using consumer smartphones is a significant step in the development of ubiquitous localization services. Many different map-matching methods have been combined with pedestrian dead reckoning (PDR) to achieve low-cost and bias-free pedestrian tracking. However, this works only in areas with dense map constraints and the error accumulates in open areas. In order to achieve reliable localization without map constraints, an improved image-based localization aided pedestrian trajectory estimation method is proposed in this paper. The image-based localization recovers the pose of the camera from the 2D-3D correspondences between the 2D image positions and the 3D points of the scene model, previously reconstructed by a structure-from-motion (SfM) pipeline. This enables us to determine the initial location and eliminate the accumulative error of PDR when an image is successfully registered. However, the image is not always registered since the traditional 2D-to-3D matching rejects more and more correct matches when the scene becomes large. We thus adopt a robust image registration strategy that recovers initially unregistered images by integrating 3D-to-2D search. In the process, the visibility and co-visibility information is adopted to improve the efficiency when searching for the correspondences from both sides. The performance of the proposed method was evaluated through several experiments and the results demonstrate that it can offer highly acceptable pedestrian localization results in long-term tracking, with an error of only 0.56 m, without the need for dedicated infrastructures.

A Rise-Dimensional Modeling and Estimation Method for Flight Trajectory Error in Bistatic Forward-Looking SAR

Bistatic forward-looking synthetic aperture radar (BFSAR) is a kind of bistatic SAR system that can image forward-looking terrain in the flight direction of a moving platform. In BFSAR, compensation of the flight trajectory errors is of great significance to get a well-focused image. To accomplish an accurate motion compensation in image processing, a high-precision navigation system is needed. However, in many cases, due to the accuracy limit of such systems, flight trajectory errors are hard to be compensated correctly, causing mainly the resolution decrease in final images. In order to cope with such a problem, we propose a rise-dimensional modeling and estimation for flight trajectory error based on raw BFSAR data in this paper. To apply this method, we first carry out a preprocessing named azimuth-slowtime decoupling to deal with the spatially variant flight trajectory error before estimation. Then, an optimization model for flight trajectory estimation under the criterion of maximum image intensity is built. The solution to the optimization model is the accurate flight trajectory. Then, block coordinate descent technique is used to solve this optimization model. The processing of BFSAR data shows that the algorithm can obtain a more accurate estimation results, and generate better focused images compared with the existing trajectory estimation method.