Uncertain Measurements Research Articles

Extended Object Tracking Using Spatially Resolved Micro-Doppler Signatures

Recent progress in radar development enable high-resolution radar sensors to resolve multiple detections for an extended object. One of the main challenges in radar-based object detection and tracking is the handling of an uncertain measurement model problem dealing with wandering dominant scatter points on the extended object surface depending on the relative orientation and motion. This phenomenon needs to be considered for near extended object tracking in critical driving situations, e.g., for safety applications, which require fast and accurate target state estimation in high dynamic scenarios. This paper presents a method to detect rotating wheels of approaching targets. Using the position and velocity of detected wheels as input for a tracking procedure, instead of target detections, relaxes the uncertain measurement model problem. A generic radar signal processing method to detect the position and bulk velocities of rotating wheels for approaching target vehicles is presented. The method evaluates the micro-Doppler signals, generated by rotating wheels, of close targets. These wheel hypotheses serve as input for a subsequent sequential Monte Carlo tracking framework. The presented methods are evaluated on real experimental data where a target vehicle is used to reconstruct safety-critical dynamic evading maneuvers.

An adaptive variational Bayesian filter for nonlinear multi-sensor systems with unknown noise statistics

An improved adaptive variational Bayesian cubature information fusion algorithm for nonlinear multi-sensor systems with uncertain noise statistics is proposed in this paper. Aiming to estimate uncertain process and measurement noise covariances in nonlinear systems, the variational Bayesian theory is combined with the inverse Wishart distribution. System states and uncertain noise covariances are jointly estimated for nonlinear systems by means of cubature sampling, deriving the variational Bayesian cubature Kalman filter (VBCKF-QR). In addition, a variational Bayesian Cubature Information filter (VBCIF-QR) is proposed, and a distributed information feedback fusion algorithm is also derived for multi-sensor systems with unknown noise statistics. Simulation results demonstrate that the proposed VBCKF-QR/VBCIF-QR outperform conventional cubature Kalman/information filters.

State of Charge Estimation for Lithium-Ion Power Battery Based on H-Infinity Filter Algorithm

To accurately estimate the state of charge (SOC) of lithium-ion power batteries in the event of errors in the battery model or unknown external noise, an SOC estimation method based on the H-infinity filter (HIF) algorithm is proposed in this paper. Firstly, a fractional-order battery model based on a dual polarization equivalent circuit model is established. Then, the parameters of the fractional-order battery model are identified by the hybrid particle swarm optimization (HPSO) algorithm, based on a genetic crossover factor. Finally, the accuracy of the SOC estimation results of the lithium-ion batteries, using the HIF algorithm and extended Kalman filter (EKF) algorithm, are verified and compared under three conditions: uncertain measurement accuracy, uncertain SOC initial value, and uncertain application conditions. The simulation results show that the SOC estimation method based on HIF can ensure that the SOC estimation error value fluctuates within ±0.02 in any case, and is slightly affected by environmental and other factors. It provides a way to improve the accuracy of SOC estimation in a battery management system.

Quantifying the uncertainty in nitrogen application and groundwater nitrate leaching in manure based cropping systems

Uncertainty in application rates of nitrogen (N) limits the effectiveness of nutrient management plans that aim to realize yield goals while minimizing environmental N losses. Measuring N application rates accurately is especially difficult in manure dependent cropping systems. California dairies use both solid manure and process wastewater (PWW) to fertilize forage crop fields. California dairy farmers measure the ratio of N applied to N removed from each crop field, the N Ratio, based on many uncertain measurements of the quantity and concentration of applied N sources. In this study, a Monte Carlo based model was used to propagate the uncertainty of each application measurement to the overall N application rate. Then the Monte Carlo model was used to stochastically vary the N application rate around farmer measured values for two forage fields (A: silty clay soil, B: sandy loam soil) over a 5 year period. The N Ratios and groundwater nitrate concentrations were simulated for 1000 stochastic N application scenarios using the HYDRUS-1D water and solute transport model and the results were compared to monitoring well measurements. Results showed that uncertainty in measurements of N applied in PWW were the dominant source of uncertainty in total N application rates, contributing 64 to 94% of overall uncertainty. N Ratio uncertainty varied widely between harvests. The average upper and lower limits of the 95% confidence interval deviated from the median simulated N Ratio by 0.25 (range: 0.13 to 0.48) and 0.27 (range: 0.12 to 0.55), respectively, among all harvested crops. Simulated groundwater nitrate concentrations were lower than monitoring well measurements by an average of 20 and 2 mg L−1 for Fields A and B, respectively. All simulated and observed nitrate concentrations in groundwater recharge from both fields were three to eight times the federal maximum contaminant level for nitrate as N of 10 mg L−1. Determining and reducing uncertainty in measurements of N applied in PWW is likely the most impactful way to improve accuracy of overall N application rates. Within current measurement and management systems, measurements of N application in manure dependent cropping systems are not accurate enough to identify application rates that will both support yield goals and reduce environmental N losses.

Nonlinear Stochastic Estimators on the Special Euclidean Group SE(3) Using Uncertain IMU and Vision Measurements

Two novel robust nonlinear stochastic full pose (i.e, attitude and position) estimators on the Special Euclidean Group SE(3) are proposed using the available uncertain measurements. The resulting estimators utilize the basic structure of the deterministic pose estimators adopting it to the stochastic sense. The proposed estimators for six degrees of freedom (DOF) pose estimations consider the group velocity vectors to be contaminated with constant bias and Gaussian random noise, unlike nonlinear deterministic pose estimators which disregard the noise component in the estimator derivations. The proposed estimators ensure that the closed loop error signals are semi-globally uniformly ultimately bounded in mean square. The efficiency and robustness of the proposed estimators are demonstrated by the numerical results which test the estimators against high levels of noise and bias associated with the group velocity and body-frame measurements and large initialization error. Keywords: Nonlinear stochastic pose filter, pose observer, position, attitude, Ito, stochastic differential equations, Brownian motion process, adaptive estimate, feature, inertial measurement unit, inertial vision system, 6 DOF, IMU, SE(3), SO(3), orientation, landmark, Gaussian, noise.

Constraining the Milky Way Mass Profile with Phase-space Distribution of Satellite Galaxies

Abstract We estimate the Milky Way (MW) halo properties using satellite kinematic data including the latest measurements from Gaia DR2. With a simulation-based 6D phase-space distribution function (DF) of satellite kinematics, we can infer halo properties efficiently and without bias, and handle the selection function and measurement errors rigorously in the Bayesian framework. Applying our DF from the EAGLE simulation to 28 satellites, we obtain an MW halo mass of and a concentration of with the prior based on the M–c relation. The inferred mass profile is consistent with previous measurements but with better precision and reliability due to the improved methodology and data. Potential improvement is illustrated by combining satellite data and stellar rotation curves. Using our EAGLE DF and best-fit MW potential, we provide much more precise estimates of the kinematics for those satellites with uncertain measurements. Compared to the EAGLE DF, which matches the observed satellite kinematics very well, the DF from the semi-analytical model based on the dark-matter-only simulation Millennium II (SAM-MII) over-represents satellites with small radii and velocities. We attribute this difference to less disruption of satellites with small pericenter distances in the SAM-MII simulation. By varying the disruption rate of such satellites in this simulation, we estimate a ∼5% scatter in the inferred MW halo mass among hydrodynamics-based simulations.

Optimizing Sets of Solutions for Controlling Constrained Nonlinear Systems

In this article, we present a novel control approach for formally solving reach-avoid problems for constrained and disturbed nonlinear systems by optimizing over reachable sets. Reach-avoid problems arise in many modern control applications of safety-critical systems, such as autonomous driving and human-robot collaboration. They require us to control all states from a set of initial states in finite time into a final set while guaranteeing the satisfaction of state and input constraints despite the presence of disturbances and uncertain measurements. We optimize over reachable sets, thereby, simultaneously improving the control performance and guaranteeing constraint satisfaction for all solutions. Moreover, our new approach involves a novel combination of state-dependent feedforward and feedback control, which leads to better control performance compared to the existing approaches as demonstrated in several numerical examples. Our algorithm is particularly suited for computing motion primitives used in maneuver automata, which realizes fast and efficient online planning. The online applicability is supported by the simple structure of the resulting controller, which is a time-varying linear tracking controller.

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

SummaryThis paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.

Vibrational processing of a dynamic structural flight system: A multichannel spectral estimation approach.

Dynamic testing of large flight vehicles (rockets) is not only complex, but also can be very costly. These flights are infrequent and can lead to disastrous effects if something were to fail during the flight. The development of sensors coupled to internal components offers a great challenge in reducing their size, yet still maintaining their precision. Sounding rockets provide both a viable and convenient alternative to the more costly vehicular flights. Some of the major objectives are to test various types of sensors for monitoring components of high interest as well as investigating real-time processing techniques. Signal processing presents an extreme challenge in this noisy multichannel environment. The estimation and tracking of modal frequencies from vibrating structures is an important set of features that can provide information about the components under test; therefore, high resolution multichannel spectral processing is required. The application of both single channel and multichannel techniques capable of producing reliable modal frequency estimates of a vibrating structure from uncertain accelerometer measurements is discussed.

Fusion estimation under binary sensors

Binary sensors compress the measurement information into two possible values as output and have found applications in many fields such as medical monitoring, environment monitoring and localization. This paper is concerned with the fusion estimation problem for a class of binary sensor systems with bounded noises, where the monitored physical process is described by time-varying state-space models. Since binary sensors only provide the valid information at the switching instant, a novel uncertain measurement model is proposed to characterize this feature. Then, by constructing an upper bound of fusion/estimation error at each time, convex optimization problems are established in terms of linear matrix inequalities to design stable centralized and distributed fusion estimators. An illustrative example is given to show the effectiveness of the proposed methods.

Uncertainty propagation in complex networks: From noisy links to critical properties.

Many complex networks are built up from empirical data prone to experimental error. Thus, the determination of the specific weights of the links is a noisy measure. Noise propagates to those macroscopic variables researchers are interested in, such as the critical threshold for synchronization of coupled oscillators or for the spreading of a disease. Here, we apply error propagation to estimate the macroscopic uncertainty in the critical threshold for some dynamical processes in networks with noisy links. We obtain closed form expressions for the mean and standard deviation of the critical threshold depending on the properties of the noise and the moments of the degree distribution of the network. The analysis provides confidence intervals for critical predictions when dealing with uncertain measurements or intrinsic fluctuations in empirical networked systems. Furthermore, our results unveil a nonmonotonous behavior of the uncertainty of the critical threshold that depends on the specific network structure.

Bayesian Update and Method of Distributions: Application to Leak Detection in Transmission Mains

AbstractWater‐hammer equations are used to describe transient flow in pipe networks. Uncertainty in model parameters, initial and boundary conditions, and location and strength of a possible leak renders deterministic predictions of this system untenable. When deployed in conjunction with pressure measurements, probabilistic solutions of the water‐hammer equations serve as a tool for detecting leaks in pipes. We use the method of distributions to obtain a probability density function (PDF) for pressure head, whose dynamics are described by the stochastic water‐hammer equations. This PDF provides a prior distribution for subsequent Bayesian data assimilation, in which data collected by pressure sensors are combined with this prior to obtain a posterior PDF of the leak location and size. We conduct a series of numerical experiments with uncertain initial velocity and measurement noise to ascertain the robustness and accuracy of the proposed approach. The results show the method's ability to identify the leak location and strength in a water transmission main.

Decision Tree Learning for Uncertain Clinical Measurements

Clinical decision requires reasoning in the presence of imperfect data. DTs are a well-known decision support tool, owing to their interpretability, fundamental in safety-critical contexts such as medical diagnosis. However, learning DTs from uncertain data leads to poor generalization, and generating predictions for uncertain data hinders prediction accuracy. Several methods have suggested the potential of probabilistic decisions at the internal nodes in making DTs robust to uncertainty. Some approaches only employ probabilistic thresholds during evaluation. Others also consider the uncertainty in the learning phase, at the expense of increased computational complexity or reduced interpretability. The existing methods have not clarified the merit of a probabilistic approach in the distinct phases of DT learning, nor when the uncertainty is present in the training or the test data. We present a probabilistic DT approach that models measurement uncertainty as a noise distribution, independently realized: (1) when searching for the split thresholds, (2) when splitting the training instances, and (3) when generating predictions for unseen data. The soft training approaches (1, 2) achieved a regularizing effect, leading to significant reductions in DT size, while maintaining accuracy, for increased noise. Soft evaluation (3) showed no benefit in handling noise.

Data-driven Metabolic Network Reduction for Multiple Modes Considering Uncertain Measurements

Dynamic models of biotechnological processes form the basis of process optimization, control, and estimation. Metabolic network models are often at the core of such models. Since metabolic network models can be very large, and consequently computationally expensive, model reduction techniques can be applied. The derivation of a suitable reduced metabolic network that captures the essential metabolism is still a challenging problem. State-of-the-art network reduction algorithms utilize a priori defined phenotypes that reflect the expected behavior of the biological system. However, most bioprocesses undergo changes in the metabolism, hence, a switch in the cellular phenotype. If these phenotypes are unknown a priori, the reduced network fails to represent all observed metabolic behaviors. Contrary to these approaches, we propose a method that reduces genome-scale metabolic networks models using data from real experiments instead of relying on predefined phenotypes. Doing so, we circumvent the use of a priori information and guarantee that the network is capable to describe all observed phenotypes and can be reliably used for estimation, prediction, and optimization.

An improved iterative stochastic multi-objective acceptability analysis method for robust alternative selection in new product development

Alternative selection in new product development (NPD) is a multi-criteria decision-making (MCDM) problem. It usually starts with incomplete, imprecise or even partially missing information. Currently, most existing methods in dealing with this problem cannot work well if required information is incomplete or missing. It is acknowledged that stochastic multi-objective acceptability analysis (SMAA) can be applied to address MCDM problem with incomplete preference information and uncertain criteria measurements. In SMAA, alternatives are evaluated based on SMAA measurements (acceptability index, central weight vector and confidence factor). The discriminability of SMAA for the optimum alternative heavily depends on differences of SMAA measurements among different alternatives. Usually, a large number of alternatives and high level of uncertainty are involved in alternative selection in NPD. In this situation, the differences among SMAA measurements are not obvious, and therefore SMAA cannot deal with such problem very well. To this end, this paper proposes an improved SMAA method called Iterative-SMAA (I-SMAA) for alternative selection in NPD. In the I-SMAA, an iterative multi-step decision-making process is suggested to improve differences of SMAA measurements among different alternatives, and thus assist decision makers (DMs) to positively discern from the most preferred alternative. To enhance the decision-making efficiency, sensitive criteria are acquired in each iteration by ranking sensitivity analysis. DMs are guided to provide partial preference information and give more accurate criteria measurements for sensitive criteria rather than all criteria. Eventually, to verify the proposed method, a numerical example of the existing literature is solved with the method, and the results are compared. And then, a practical example of a preparation equipment for coal samples is further employed to verify the practicability of the proposed I-SMAA.

Baseline anthropometric measurements and obesity of people working in Isale-Oko, Sagamu, Ogun State, Southwest, Nigeria

Objectives: It is uncertain anthropometric measurements are affected by the type of job an individual is doing in an environment. Therefore, this study was designed to assess the baseline anthropometric measurements with relation to obesity of people working at a motor park in Sagamu. Design: This is a cross-sectional study of 139 individuals working in the motor park of Isale-Oko, Sagamu, aged 20–70 years. Passengers were exempted. The weight in kg and height in meters of each participant were measured. The waist circumference (cm) (WC), hip circumference (cm) (HC), and thigh circumference (cm) of each participant were measured using a flexible tape. The waist-to-hip ratio (WHR) was calculated. The body mass indexes (BMI) (kg/m2) and the waist-to-thigh ratio were calculated. Data were analyzed using descriptive statistic and ANOVA. Results: The occupational distributions include the drivers, conductors, traders, and garage staff. Young participants contribute to 60.4% of the study populations. There were 64.3% young participants among the conductors, 63.2% of the drivers, 64.8% of the traders, and 40% of the garage staff. The mean BMI of the drivers showed that they tend to be obese (30.85 ± 0.66 kg/m2). Conductors tend to be overweight with BMI of 26.57 ± 0.60 kg/m2. The WC of drivers was significantly highest among the occupational groups 98.82 ± 1.75 cm, while the conductors had the least WC 94.38 ± 2.87 cm. The traders had the highest HC 106.31 ± 1.88 cm. The drivers and conductors had the highest WHR of 0.96 ± 0.03 and 0.92 ± 0.01, respectively. Conclusions: The anthropometric parameter measurements of individual participants obtained from this study can be used as baseline for the future study. The high BMI and WC in drivers and high HC in traders increase the risk of developing diabetes mellitus.

Extended State based Kalman Filter for Uncertain Systems with Bias

This paper addresses the state estimation for a class of stochastic systems with both uncertain dynamics and measurement bias. By using the idea of uncertainty/disturbance estimation, an extended state based Kalman filter algorithm is developed to estimate the original state, the uncertain dynamics and the measurement bias. Furthermore, a necessary and sufficient condition for the observability of augmented system is presented. Also, the stability of the proposed algorithm is analyzed. It is shown that the proposed filter can achieve unbiased estimation of measurement bias, such that the influence of measurement bias is eliminated. Finally, a simulation study is provided to illustrate the effectiveness of proposed method.

Configuration Optimization and Channel Estimation in Hybrid Beamforming mmWave Systems With Channel Support Side Information

Hybrid beamforming (HBF) is a promising technique in millimeter-wave (mmWave) systems with a limited number of radio frequency (RF) chains. Acquiring channel state information is essential for HBF design. Various compressive-sensing-based channel estimation (CE) schemes that exploit the sparse nature of mmWave channels have been proposed. The design of an analog beamforming matrix plays a key role in providing high CE quality with low pilot overhead. In this paper, a novel and flexible HBF architecture called adaptive sum product network (ASPN) is proposed, which can realize more flexible analog beamforming with less hardwares. Based on the ASPN architecture, a novel variational-Bayesian-inference-based compressive CE algorithm is proposed, which can fully exploit the channel support side information (CSSI) at the base station under a general uncertain measurement matrix induced by the off-grid parameters for power leakage elimination. To optimally configure the degrees of freedom in the ASPN according to the CSSI, a dynamic configuration optimization algorithm is proposed by formulating the CE performance metric in terms of the configuration parameters of ASPN. The importance and effectiveness of the flexibility introduced in ASPN HBF architecture, the compressive CE algorithm as well as the configuration algorithm are illustrated by the superb performance of the proposed scheme compared to the representative state-of-the-art techniques through extensive simulation results.

Global control for a class of feedforward nonlinear systems with uncertain measurement functions

Based on the nested-saturation technique, this paper investigates the global stabilization problem for a class of upper-triangular nonlinear systems with uncertain measurement functions. By imposing certain assumptions on the uncertain powers, a state-feedback controller, only involving the known parameters, is designed to locally stabilize the nonlinear system. Then, a saturated controller is constructed by combining the nested function and the local stabilizer. With appropriate saturation level, it can be proved that the saturated controller is able to make the closed-loop system globally asymptotically stable. Finally, a simulation example is presented to demonstrate the effectiveness and robustness of the proposed control scheme.

Real-Time Faulted Line Localization and PMU Placement in Power Systems Through Convolutional Neural Networks

Diverse fault types, fast reclosures, and complicated transient states after a fault event make real-time fault location in power grids challenging. Existing localization techniques in this area rely on simplistic assumptions, such as static loads, or require much higher sampling rates or total measurement availability. This paper proposes a faulted line localization method based on a convolutional neural network (CNN) classifier using bus voltages. Unlike prior data-driven methods, the proposed classifier is based on features with physical interpretations that improve the robustness of the location performance. The accuracy of our CNN-based localization tool is demonstrably superior to other machine learning classifiers in the literature. To further improve the location performance, a joint phasor measurement units placement strategy are proposed and validated against other methods. A significant aspect of our methodology is that under very low observability ( ${7\%}$ of buses), the algorithm is still able to localize the faulted line to a small neighborhood with high probability. The performance of our scheme is validated through simulations of faults of various types in the IEEE 39-bus and 68-bus power systems under varying uncertain conditions, system observability, and measurement quality.