Trajectory Estimation Research Articles

Smoother Entropy for Active State Trajectory Estimation and Obfuscation in POMDPs

We study the problem of controlling a partially observed Markov decision process (POMDP) to either aid or hinder the estimation of its state trajectory. We encode the estimation objectives via the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">smoother entropy</i> , which is the conditional entropy of the state trajectory given measurements and controls. Consideration of the smoother entropy contrasts with previous approaches that instead resort to marginal (or instantaneous) state entropies due to tractability concerns. By establishing novel expressions for the smoother entropy in terms of the POMDP belief state, we show that both the problems of minimising and maximising the smoother entropy in POMDPs can surprisingly be reformulated as belief-state Markov decision processes with concave cost and value functions. The significance of these reformulations is that they render the smoother entropy a tractable optimisation objective, with structural properties amenable to the use of standard POMDP solution techniques for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">both</i> active estimation and obfuscation. Simulations illustrate that optimisation of the smoother entropy leads to superior trajectory estimation and obfuscation compared to alternative approaches.

Scheduling Policy for Value-of-Information (VoI) in Trajectory Estimation for Digital Twins

This paper presents an approach to schedule observations from different sensors in an environment to ensure their timely delivery and build a digital twin (DT) model of the system dynamics. At the cloud platform, DT models estimate and predict the system’s state, then compute the optimal scheduling policy and resource allocation strategy to be executed in the physical world. However, given limited network resources, partial state vector information, and measurement errors at the distributed sensing agents, the acquisition of data (i.e., observations) for efficient state estimation of system dynamics is a non-trivial problem. We propose a Value of Information (VoI)-based algorithm that provides a polynomial-time solution for selecting the most informative subset of sensing agents to improve confidence in the state estimation of DT models. Numerical results confirm that the proposed method outperforms other benchmarks, reducing the communication overhead by half while maintaining the required estimation accuracy.

COMPARISON OF TWO MATHEMATICAL MODELS FOR FISHEYE CAMERAS APPLIED IN THE ORB-SLAM

Abstract. Fisheye lens cameras are becoming increasingly popular for vSLAM applications due to their wide field of view (FoV), providing more features to be tracked in a single image shot. However, the complex lens geometry involved in the image formation process still limits their full potential, especially when points in the hyperhemispherical field are unmodeled. In this paper, we compare two adaptations of ORB-SLAM for fisheye lens cameras, considering the use of the rigorous projection model (equisolid-angle) versus the use of the generic projection model (EUCM). The ORB-SLAM versions were adapted for real-time processing on the Nvidia Jetson TX2 board. The experiment was conducted using hyperhemispherical images obtained with a Ricoh Theta S camera. Our results showed that the trajectory estimated with the equisolid-angle ORB-SLAM had smaller discrepancies, compared to the reference trajectory, than the EUCM ORB-SLAM. This suggests that a rigorous photogrammetric model with a suitable treatment of hyperhemispherical points is beneficial for trajectory estimation.

Outcome trajectory estimation for optimal dynamic treatment regimes with repeated measures.

In recent sequential multiple assignment randomized trials, outcomes were assessed multiple times to evaluate longer-term impacts of the dynamic treatment regimes (DTRs). Q-learning requires a scalar response to identify the optimal DTR. Inverse probability weighting may be used to estimate the optimal outcome trajectory, but it is inefficient, susceptible to model mis-specification, and unable to characterize how treatment effects manifest over time. We propose modified Q-learning with generalized estimating equations to address these limitations and apply it to the M-bridge trial, which evaluates adaptive interventions to prevent problematic drinking among college freshmen. Simulation studies demonstrate our proposed method improves efficiency and robustness.

Pragmatic approaches to handling practice effects in longitudinal cognitive aging research.

The challenge of accounting for practice effects (PEs) when modeling cognitive change was amplified by the COVID-19 pandemic, which introduced period and mode effects that may bias the estimation of cognitive trajectory. In three Kaiser Permanente Northern California prospective cohorts, we compared predicted cognitive trajectories and the association of grip strength with cognitive decline using three approaches: (1) no acknowledgment of PE, (2) inclusion of a wave indicator, and (3) constraining PE based on a preliminary model (APM) fit using a subset of the data. APM-based correction for PEs based on balanced, pre-pandemic data, and with current age as the timescale produced the smallest discrepancy between within-person and between-person estimated age effects. Estimated associations between grip strength and cognitive decline were not sensitive to the approach used. Constraining PEs based on a preliminary model is a flexible, pragmatic approach allowing for meaningful interpretation of cognitive change. The magnitude of practice effects (PEs) varied widely by study. When PEs were present, the three PE approaches resulted in divergent estimated age-related cognitive trajectories. Estimated age-related cognitive trajectories were sometimes implausible in models that did not account for PEs. The associations between grip strength and cognitive decline did not differ by the PE approach used. Constraining PEs based on estimates from a preliminary model allows for a meaningful interpretation of cognitive change.

VariFi: Variational Inference for Indoor Pedestrian Localization and Tracking Using IMU and WiFi RSS

Accurate indoor pedestrian localization and tracking are crucial in many practical applications. One efficient yet low-cost sensing scheme is the integration of IMU and WiFi RSS due to the popularity of smart devices and WiFi networks. Many approaches have been proposed to enhance the localization performance. However, they heavily rely on prerequisites including prior knowledge (e.g. map information) and beacon corrections, which degrades the generalization of the approaches and their accuracy in complex environments. To address this issue, in this paper, we propose a novel localization approach named VariFi, which incorporates variational inference techniques to estimate the location of pedestrian. Variational inference is applied in this work, whose inference network can produce accurate estimates as its parameters are optimized in terms of the reconstruction loss and regularization loss in real time. A signal map is constructed to provide a conditional RSS distribution at any given location, which is further applied to generate the reconstruction loss based on the real measurements. Also, a filtering mechanism is designed to reduce local optimum cases in optimization by utilizing the prior estimate and RSS fingerprinting estimate. In addition, VariFi can be further applied to conduct online optimization following the existing localization approaches. We conduct experiments including static localization and trajectory estimation scenarios to validate the performance of our approach. The trajectory estimation results show that our approach outperforms the mainstream approaches in terms of both localization accuracy and robustness, respectively. Furthermore, the combination of existing approaches and VariFi has also been validated effectively in the experiments of two environments, where VariFi has the ability to bring enhanced localization accuracy.

Estimation of Trajectory of High speed Artillery Shell

&#x0D; &#x0D; &#x0D; This paper presents a novel technique that uses the stereoscopic arrangement of multiple cameras to determine the trajectory of a high-speed projectile. It can be used to detect and track artillery shells moving at high speed in the air toward friendly territory. A system with the proposed concept can enhance retaliation success in battlefield countermeasures. There are many state-of-the-art Radar-based systems to detect moving artillery shells and mortars, but the cost and size of those products make them not so easily deployable in all kinds of terrains. A system with multiple cameras is discussed in this paper as an alternative solution. The experimental results, after algorithms were applied to simulated videos of expected scenes showed that the proposed technique is feasible. The proposed technique is fast and accurate and can be converted into deployable hardware. It can lead to realizing a system that has utility in saving precious lives in critical circumstances.&#x0D; &#x0D; &#x0D;

Mapping human brain charts cross-sectionally and longitudinally

Brain scans acquired across large, age-diverse cohorts have facilitated recent progress in establishing normative brain aging charts. Here, we ask the critical question of whether cross-sectional estimates of age-related brain trajectories resemble those directly measured from longitudinal data. We show that age-related brain changes inferred from cross-sectionally mapped brain charts can substantially underestimate actual changes measured longitudinally. We further find that brain aging trajectories vary markedly between individuals and are difficult to predict with population-level age trends estimated cross-sectionally. Prediction errors relate modestly to neuroimaging confounds and lifestyle factors. Our findings provide explicit evidence for the importance of longitudinal measurements in ascertaining brain development and aging trajectories.

Trajectory Estimation of a Flying Robot With a Single Ranging Beacon and Derived Velocity Constraints

The performance of the trajectory estimation with a single beacon highly depends on the observability of the system, which is further determined by the excitation patterns of the robot. Because the desired excitation patterns regarding specific observability conditions cannot always be guaranteed in real-time, the trajectory estimation may casually fail with divergence. To tackle this issue, indirectly derived velocity constraints are first introduced in this work, and their effects on improving the performance of trajectory estimation are comparatively investigated. Considering the geometric evolution equation and using the state augmentation technique, seven different velocity constraints are evaluated. The comparative results indicate that the trajectory estimation divergence can be most effectively avoided with a pure velocity magnitude constraint. On this basis, a velocity-constrained moving horizon estimation algorithm is implemented and verified in an indoor experimental testbed to accurately estimate the trajectory of the flying robot with a single ultra-wideband beacon in a long time interval. The results also quantitatively illustrate that the overall performance of the proposed approach outperforms that of the latest benchmark approach in both estimation precision and computational efficiency. In particular, with approximately the same estimation precision, the computational time cost of the proposed approach is less than 1/10 of that of existing approaches.

Adaptive fuzzy impedance control of exoskeleton robots with electromyography-based convolutional neural networks for human intended trajectory estimation

Adaptive fuzzy impedance control of exoskeleton robots with electromyography-based convolutional neural networks for human intended trajectory estimation

Motor control insights on walking planner and its stability

The application of biomechanics and motor control models in the control of bipedal robots (humanoids and exoskeletons) has revealed limitations of our understanding of human locomotion. A recently proposed model uses the potential energy for bipedal structures to model the bipedal dynamics, allowing us to predict the system dynamics from its kinematics. This work proposes a task-space planner for human-like straight locomotion that targets application in rehabilitation robotics and computational neuroscience. The proposed architecture is based on the potential energy model and employs locomotor strategies from human data. The model generates Centre of Mass (CoM) trajectories, foot swing trajectories and the Base of Support (BoS) over time. The data show that the proposed architecture can generate behaviour in line with human walking strategies for both the CoM and the foot swing. Despite the CoM vertical trajectory not being as smooth as a human trajectory, the proposed model significantly reduces the error in the estimation of the CoM vertical trajectory compared to the inverted pendulum models. The proposed model can also assess stability based on the body kinematics embedding currently used in clinical practice. However, the model also implies a shift in the interpretation of the spatiotemporal parameters of the gait, which are now determined by the conditions for the equilibrium and not vice versa. In other words, locomotion is a dynamic reaching where the motor primitives are also determined by gravity.

Spatially Aware Transformer Networks for Contextual Prediction of Diabetic Nephropathy Progression from Whole Slide Images.

Diabetic nephropathy (DN) in the context of type 2 diabetes is the leading cause of end-stage renal disease (ESRD) in the United States. DN is graded based on glomerular morphology and has a spatially heterogeneous presentation in kidney biopsies that complicates pathologists' predictions of disease progression. Artificial intelligence and deep learning methods for pathology have shown promise for quantitative pathological evaluation and clinical trajectory estimation; but, they often fail to capture large-scale spatial anatomy and relationships found in whole slide images (WSIs). In this study, we present a transformer-based, multi-stage ESRD prediction framework built upon nonlinear dimensionality reduction, relative Euclidean pixel distance embeddings between every pair of observable glomeruli, and a corresponding spatial self-attention mechanism for a robust contextual representation. We developed a deep transformer network for encoding WSI and predicting future ESRD using a dataset of 56 kidney biopsy WSIs from DN patients at Seoul National University Hospital. Using a leave-one-out cross-validation scheme, our modified transformer framework outperformed RNNs, XGBoost, and logistic regression baseline models, and resulted in an area under the receiver operating characteristic curve (AUC) of 0.97 (95% CI: 0.90-1.00) for predicting two-year ESRD, compared with an AUC of 0.86 (95% CI: 0.66-0.99) without our relative distance embedding, and an AUC of 0.76 (95% CI: 0.59-0.92) without a denoising autoencoder module. While the variability and generalizability induced by smaller sample sizes are challenging, our distance-based embedding approach and overfitting mitigation techniques yielded results that suggest opportunities for future spatially aware WSI research using limited pathology datasets.

RUL Estimation for Rolling Bearings Using Augmented Quaternion-Based Least Mean P-Power With Correntropy Induced Metric Under Framework of Sparsity

Accurate remaining useful life (RUL) estimation of rolling bearings can significantly improve the safety, availability, reliability and productivity of a rotating machinery system. In this article, a new approach of RUL estimation for rolling bearings based upon the fractional-order spatiotemporal sparse low-rank matrix (FST-SLRM) and augmented quaternion least mean p-power with correntropy induced metric (AQLMP-CIM) is originally proposed. Specifically, the proposed approach includes three modules: the construction of the fused health indicator, which fuses the classical features and spectral kurtosis derived indices; the decomposition of the static and dynamic components, the fused health indicator time series (FHITS) is decomposed by the FST-SLRM algorithm, thus low- and high- frequency trend components (i.e., LFCs, HFCs) are obtained, respectively; and the prognostics of degradation trajectory and RUL estimation, the degradation trajectories are obtained by the AQLMP-CIM algorithm via integrating the predicted LFC and HFC, and the RUL is eventually acquired. Two experimental cases are conducted on run-to-failure fatigue test of rolling bearings, the results demonstrate that the proposed approach is able to achieve better performance compared with state-of-the-art benchmarks.

Bounded Consensus Tracking of Heterogeneous Multiagent Systems Under Digraphs With Diverse Communication and Input Delays.

We study the bounded consensus tracking problem for the heterogeneous multiagent system composed of single- and double-integrator agents in the presence of diverse communication and input delays. The objective is to ensure bounded tracking when only a portion of agents has access to the desired trajectory while agents interact with each other through a directed communication network. To achieve this goal, we propose a protocol consisting of a consensus-based trajectory estimator followed by a controller tracking the estimated trajectory for each agent. Though the agents involved in the mission are heterogeneous, the estimators of all the agents are designed as coupled single integrators to provide estimates of the acceleration, velocity, and position along the desired trajectory. The coupled single-integrator estimator followed by the tracking controller strategy leads to a decoupling whereby the allowable estimator gains for an agent depend only on its communication delays and its controller gains depend only on its input delay. The tracking errors remain bounded even if the desired acceleration is unknown to all the agents. Simulation results are carried out to validate the proposed consensus tracking algorithm.

Tightly Coupled 3D Lidar Inertial SLAM for Ground Robot

This paper proposes a robotic state estimation and map construction method. The traditional lidar SLAM methods are affected by sensor measurement noise, which causes the estimated trajectory to drift, especially along the altitude direction caused by lidar noise. In this paper, ground parameters in the environment are extracted to construct the ground factors to compress the trajectory estimation drifting along the altitude direction using the characteristics of constant robot pose relative to the ground. Our method uses tightly coupled lidar and inertial to obtain low-drift lidar odometry factors by factor graph optimization. The optimized lidar odometry factors are then added to a global factor graph, together with ground, loop closure, and GPS factors to obtain accurate robot state estimation and mapping after factor graph optimization. The experimental results show that our method has comparable results with advanced lidar SLAM methods, and even performs better in some complex and large-scale environments.

Building cluster demand flexibility: An innovative characterization framework and applications at the planning and operational levels

Flexible loads in building clusters are a sizable source of demand flexibility that can be tapped to provide grid services. Even with extensive research on demand flexibility characterization, it is not well studied how characterizing demand flexibility can facilitate energy aggregators bidding into wholesale electricity markets. In this paper, we propose an innovative framework that characterizes demand flexibility from a building cluster in a bottom-up manner and generates detailed information that can be used for bidding into the ancillary services market. Our framework allows system operators to perform a comprehensive evaluation of grid service bids submitted by energy aggregators. Different characterization parameters have been suggested depending on temperature setpoint and dead-band schedules. As a computationally efficient representation of a building cluster, we introduce a novel, scalable virtual storage model capable of accounting for temporal changes in temperature setpoints and/or dead-bands. Unlike its existing counterparts, our model is applicable to any building cluster regardless of the level of heterogeneity in building properties. The proposed framework is tested on a cluster consisting of 1000 single-family houses, each equipped with a heat pump as the heating system, controlled by a three-layer hierarchical controller. The results demonstrate that detailed flexibility characterization allows system operators to procure demand-side grid services without thermal comfort being jeopardized or power systems being adversely affected. For the introduced bidding scheme to be viable, the system operator needs to have an accurate estimate of the baseline power trajectory of each aggregator. This is important for compensating aggregators and preventing a malicious one from submitting fraudulent bids.

OSM-SLAM: Aiding SLAM with OpenStreetMaps priors.

In the last decades, Simultaneous Localization and Mapping (SLAM) proved to be a fundamental topic in the field of robotics, due to the many applications, ranging from autonomous driving to 3D reconstruction. Many systems have been proposed in literature exploiting a heterogeneous variety of sensors. State-of-the-art methods build their own map from scratch, using only data coming from the equipment of the robot, and not exploiting possible reconstructions of the environment. Moreover, temporary loss of data proves to be a challenge for SLAM systems, as it demands efficient re-localization to continue the localization process. In this paper, we present a SLAM system that exploits additional information coming from mapping services like OpenStreetMaps, hence the name OSM-SLAM, to face these issues. We extend an existing LiDAR-based Graph SLAM system, ART-SLAM, making it able to integrate the 2D geometry of buildings in the trajectory estimation process, by matching a prior OpenStreetMaps map with a single LiDAR scan. Each estimated pose of the robot is then associated with all buildings surrounding it. This association allows to improve localization accuracy, but also to adjust possible mistakes in the prior map. The pose estimates coming from SLAM are then jointly optimized with the constraints associated with the various OSM buildings, which can assume one of the following types: Buildings are always fixed (Prior SLAM); buildings surrounding a robot are movable in chunks, for every scan (Rigid SLAM); and every single building is free to move independently from the others (Non-rigid SLAM). Lastly, OSM maps can also be used to re-localize the robot when sensor data is lost. We compare the accuracy of the proposed system with existing methods for LiDAR-based SLAM, including the baseline, also providing a visual inspection of the results. The comparison is made by evaluating the estimated trajectory displacement using the KITTI odometry dataset. Moreover, the experimental campaign, along with an ablation study on the re-localization capabilities of the proposed system and its accuracy in loop detection-denied scenarios, allow a discussion about how the quality of prior maps influences the SLAM procedure, which may lead to worse estimates than the baseline.

Hybrid Motion Model for Multiple Object Tracking in Mobile Devices

For an intelligent transportation system, multiple object tracking (MOT) is more challenging from the traditional static surveillance camera to mobile devices of the Internet of Things (IoT). To cope with this problem, previous works always rely on additional information from multivision, various sensors, or precalibration. Only based on a monocular camera, we propose a hybrid motion model to improve the tracking accuracy in mobile devices. First, the model evaluates camera motion hypotheses by measuring optical flow similarity and transition smoothness to perform robust camera trajectory estimation. Second, along the camera trajectory, smooth dynamic projection is used to map objects from image to world coordinate. Third, to deal with trajectory motion inconsistency, which is caused by occlusion and interaction of long time interval, tracklet motion is described by the multimode motion filter for adaptive modeling. Fourth, in tracklets association, we propose a spatiotemporal evaluation mechanism, which achieves higher discriminability in motion measurement. Experiments on MOT15, MOT17, and KITTI benchmarks show that our proposed method improves the trajectory accuracy, especially in mobile devices and our method achieves competitive results over other state-of-the-art methods.

LSTM-Based Projectile Trajectory Estimation in a GNSS-Denied Environment.

This paper presents a deep learning approach to estimate a projectile trajectory in a GNSS-denied environment. For this purpose, Long-Short-Term-Memories (LSTMs) are trained on projectile fire simulations. The network inputs are the embedded Inertial Measurement Unit (IMU) data, the magnetic field reference, flight parameters specific to the projectile and a time vector. This paper focuses on the influence of LSTM input data pre-processing, i.e., normalization and navigation frame rotation, leading to rescale 3D projectile data over similar variation ranges. In addition, the effect of the sensor error model on the estimation accuracy is analyzed. LSTM estimates are compared to a classical Dead-Reckoning algorithm, and the estimation accuracy is evaluated via multiple error criteria and the position errors at the impact point. Results, presented for a finned projectile, clearly show the Artificial Intelligence (AI) contribution, especially for the projectile position and velocity estimations. Indeed, the LSTM estimation errors are reduced compared to a classical navigation algorithm as well as to GNSS-guided finned projectiles.

Compressed sensing using a trajectory-based model for ultrasonic tomography in a wooden medium with cylindrical symmetry

Stress wave propagation induced by embedded waveguides in circular cross-sections produces radial AW1a, reflected mode (AW1b), and Rayleigh propagations (AW2). Prior studies in this area have developed optimal filtering techniques to extract the characteristics of different arrival components from the time-series waveform. This study exploits the information uncovered in the time-series signal to reduce the sensing requirements for stress wave tomographic inversion. This work employs the algebraic reconstruction technique (ART) and the trajectory estimation from the transient finite element model (FEM) to perform the tomographic inversion. The proposed methodology consists of the following steps: (1) Estimate the arrival trajectories using the time-dependent energy flux propagation vector from the existing FEM-based propagation model. (2) Formulate the pixel contribution matrix based on the estimated trajectories from step 1. (3) Based on a known priori, perform tomographic inversion based on the optimal relaxation and additive iterative techniques. This presentation will discuss the technique and the associated algorithm and present the results of the proposed reconstruction technique with numerical validations. Its broader impact will drastically reduce the traditional through-transmission tomography from 28 measurements around the circular cross-sectional region to 6, providing rapid data collection with comparable efficacy.