Uncertain Observations Research Articles

Geometric Analysis of Conditional Bias-Informed Kalman Filters

This paper presents a comparative geometric analysis of the conditional bias (CB)-informed Kalman filter (KF) with the Kalman filter (KF) in the Euclidean space. The CB-informed KFs considered include the CB-penalized KF (CBPKF) and its ensemble extension, the CB-penalized Ensemble KF (CBEnKF). The geometric illustration for the CBPKF is given for the bi-state model, composed of an observable state and an unobservable state. The CBPKF co-minimizes the error variance and the variance of the Type-II error. As such, CBPKF-updated state error vectors are larger than the KF-updated, the latter of which is based on minimizing the error variance only. Different error vectors in the Euclidean space imply different eigenvectors and covariance ellipses in the state space. To characterize the differences in geometric attributes between the two filters, numerical experiments were carried out using the Lorenz 63 model. The results show that the CBEnKF yields more accurate confidence regions for encompassing the truth, smaller errors in the ensemble mean, and larger norms for Kalman gain and error covariance matrices than the EnKF, particularly when assimilating highly uncertain observations.

Coupled effects of observation and parameter uncertainty on urban groundwater infrastructure decisions

Abstract. Urban groundwater management requires complex environmental models to represent interactions between hydrogeological processes and infrastructure systems. While the impacts of external uncertainties, such as climate and population growth, have been widely studied, there is limited understanding of how decision support is altered by endogenous uncertainties arising from model parameters and observations used for calibration. This study investigates (1) the importance of observation choice and parameter values on aquifer management objectives when controlling for model error and (2) how the relative performance of management alternatives varies when exposed to endogenous uncertainties, both individually and in combination. We use a spatially distributed groundwater model of the Valley of Mexico, where aquifer management alternatives include demand management, targeted infiltration, and wastewater reuse. The effects of uncertainty are evaluated using global sensitivity analysis, performance ranking of alternatives under a range of human–natural parameters, and identification of behavioral parameter sets filtered with an error metric calculated from varying subsets of observations. Results show that the parameters governing hydraulic conductivity and total water use in the basin have the greatest effect on management objectives. Error metrics (i.e., squared residuals of piezometric head) are not necessarily controlled by the same parameters as the head-based objectives needed for decision-making. Additionally, observational and parameter uncertainty each play a larger role in objective variation than the management alternatives themselves. Finally, coupled endogenous uncertainties have amplifying effects on decision-making, leading to larger variations in the ranking of management alternatives than each on their own. This study highlights how the uncertain parameters of a physically based model and their interactions with uncertain observations can affect water supply planning decisions in densely populated urban areas.

Investigating errors when forecasting processes with uncertain dynamics and observation noise by the self-adjusting brown's zero-order model

This paper reports a study into the errors of process forecasting under the conditions of uncertainty in the dynamics and observation noise using a self-adjusting Brown's zero-order model. The dynamics test models have been built for predicted processes and observation noises, which make it possible to investigate forecasting errors for the self-adjusting and adaptive models. The test process dynamics were determined in the form of a rectangular video pulse with a fixed unit amplitude, a radio pulse of the harmonic process with an amplitude attenuated exponentially, as well as a video pulse with amplitude increasing exponentially. As a model of observation noise, an additive discrete Gaussian process with zero mean and variable value of the mean square deviation was considered. It was established that for small values of the mean square deviation of observation noise, a self-adjusting model under the conditions of dynamics uncertainty produces a smaller error in the process forecast. For the test jump-like dynamics of the process, the variance of the forecast error was less than 1 %. At the same time, for the adaptive model, with an adaptation parameter from the classical and beyond-the-limit sets, the variance of the error was about 20 % and 5 %, respectively. With significant observation noises, the variance of the error in the forecast of the test process dynamics for the self-adjusting and adaptive models with a parameter from the classical set was in the range from 1 % to 20 %. However, for the adaptive model, with a parameter from the beyond-the-limit set, the variance of the prediction error was close to 100 % for all test models. It was established that with an increase in the mean square deviation of observation noise, there is greater masking of the predicted test process dynamics, leading to an increase in the variance of the forecast error when using a self-adjusting model. This is the price for predicting processes with uncertain dynamics and observation noises.

A Novel Factor Graph and Cubature Kalman Filter Integrated Algorithm for Single-Transponder-Aided Cooperative Localization.

Cooperative localization (CL) of underwater multi-AUVs is vital for numerous underwater operations. Single-transponder-aided cooperative localization (STCL) is regarded as a promising scheme for multi-AUVs CL, benefiting from the fact that an accurate reference is adopted. To improve the positioning accuracy and robustness of STCL, a novel Factor Graph and Cubature Kalman Filter (FGCKF)-integrated algorithm is proposed in this paper. In the proposed FGCKF, historical information can be efficiently used in measurement updating to overcome uncertain observation environments, which greatly helps to improve the performance of filtering progress. Furthermore, Adaptive CKF, sum product, and Maximum Correntropy Criterion (MCC) methods are designed to deal with outliers of acoustic transmission delay, sound velocity, and motion velocity, respectively. Simulations and experiments are conducted, and it is verified that the proposed FGCKF algorithm can improve positioning accuracy and robustness greatly than traditional filtering methods.

Integrating Nonlinear Interval Regression Analysis with a Remnant Grey Prediction Model for Energy Demand Forecasting

ABSTRACT Energy demand forecasting is increasingly important for developing national energy policies. This study aims to apply the first order gray model with one variable (GM(1,1)) without following any statistical assumptions to energy demand forecasting. To boost the forecasting accuracy of GM(1,1), a problem arising from collected samples that are often derived from an uncertain assessment should be addressed. One way to deal with these uncertain and imprecise observations is by using nonlinear interval regression analysis with neural networks to generate upper and lower limits for individual samples. As a result, a nonlinear interval gray prediction model is constructed by applying the sequences of upper and lower limits to construct GM(1,1) with residual modification separately. By examining the forecasting performance of a nonlinear interval model by the best non-fuzzy performance values, the empirical results obtained based on real energy demand data show that the proposed models perform well compared with other interval gray prediction models. This study has shown the high applicability of the proposed model to energy demand forecasting.

Value of structural health information in partially observable stochastic environments

Efficient integration of uncertain observations with decision-making optimization is key for prescribing informed intervention actions, able to preserve structural safety of deteriorating engineering systems. To this end, it is necessary that scheduling of inspection and monitoring strategies be objectively performed on the basis of their expected value-based gains that, among others, reflect quantitative metrics such as the Value of Information (VoI) and the Value of Structural Health Monitoring (VoSHM). In this work, we introduce and study the theoretical and computational foundations of the above metrics within the context of Partially Observable Markov Decision Processes (POMDPs), thus alluding to a broad class of decision-making problems of partially observable stochastic deteriorating environments that can be modeled as POMDPs. Step-wise and life-cycle VoI and VoSHM definitions are devised and their bounds are analyzed as per the properties stemming from the Bellman equation and the resulting optimal value function. It is shown that a POMDP policy inherently leverages the notion of VoI to guide observational actions in an optimal way at every decision step, and that the permanent or intermittent information provided by SHM or inspection visits, respectively, can only improve the cost of this policy in the long-term, something that is not necessarily true under locally optimal policies, typically adopted in decision-making of structures and infrastructure. POMDP solutions are derived based on point-based value iteration methods, and the various definitions are quantified in stationary and non-stationary deteriorating environments, with both infinite and finite planning horizons, featuring single- or multi-component engineering systems.

ON THE VISUALIZATION OF POSITIONAL PRECISION

Abstract. Tasks such as image registration or pose estimation require the determination of transformations based on uncertain observations. Hence, the position of any geometric object transformed according to this estimate is also uncertain, at least in terms of precision. Often the knowledge of uncertainty changes the judgment of individuals. Thus, the visualization of this information is crucial whenever a human decision-maker is involved. In the absence of error-free reference data, we consider the estimated precision as the probably most important quantity characterizing the uncertainty. This contribution focuses on the visualization of positional precision as provided by estimated covariance matrices. Basic design principles such as coloration and contouring in 2D and 3D are presented and discussed in the context of practical applications, e.g., the superimposition of distance information as seen nowadays in sports broadcasts. As a novel contribution, we propose quartic plane curves to represent the confidence regions of the loci of conic sections.

A knowledge based system for the management of a time stamped uncertain observation set with application on preserving mobility

The aim of this study is to maintain up-to-date information about the current state of elderly people that are medically followed for risks of fall. Our proposal consists of an individual information database management system that can provide information on-demand on various variables. Such a system has to deal with several sources of uncertainty: lack of information, evolving information and reliability of the information sources. We consider that the features of the person may evolve with time causing uncertainty due to obsolete information. Our context includes new information received bit by bit, with no possibility to collect all required information at once. This paper establishes a first proposal to manage a set of uncertain observations, in order to reduce erroneous and obsolete information while keeping the benefit of previously collected information. We propose an architecture of the system based on a probabilistic knowledge model about the characteristics of interest, a set of decay functions that help to evaluate the confidence degree in previous observations, and a reasoning module to manage new observations, maintain the compatibility and the quality of the observation set. We detail the algorithms of the reasoning module, and the algorithm to update the confidence degree of the observations.

Model‐based diagnosis with uncertain observations

Classical model-based diagnosis uses a model of the system to infer diagnoses—explanations—of a given abnormal observation. In this study we address the case where there is uncertainty over a given observation and explore it. This can happen, for example, when the observation outputs are collected by sensors with some noise, that are known to return incorrect value with some probability. We formally define this problem for abductive and consistency-based forms domains. Furthermore, we propose two complete and sound algorithms for finding and ranking all diagnoses and analyze their complexity. We dive deeper and improve the first algorithm's efficiency even more by exploiting past results. Finally, we propose a third algorithm that returns the most likely diagnosis without finding all possible diagnoses, assuming the uncertainty over the observations and the components behavior modes are independents. Experimental evaluation shows that the last algorithm can be very efficient in cases where the diagnosis cardinality, as well as the uncertainty likelihood over the observation, are expected to be small. If, however, all possible diagnoses are desired, then the choice between the first two algorithms depends on whether the domain's diagnosis form is abductive or consistent.

Bayesian inference with uncertain data of imprecise observations

Bayesian inference is a technique of statistical inference which uses the Bayes’ theorem to update the probability distribution as new observed data are available. Uncertain variables are a tool of modeling imprecisely observed quantities associated with experiential information. By integrating Bayesian inference and uncertain variables, this paper proposes an approach of uncertain Bayesian inference to deal with Bayesian inference problems involving imprecise observations. The posterior distribution is derived which gives the probability distribution of an unknown parameter conditional on uncertain observations. And based on the posterior distribution, some inference problems including the point estimation, the interval estimation and the Bayesian prediction, are investigated.

State estimation for a networked control system with packet delay, packet dropouts, and uncertain observation in S‐E and C‐A channels

SummaryIn this work, a minimum variance estimator is designed for a networked system with inherent network imperfections in both sensor to estimator (S‐E) and controller to actuator (C‐A) channels simultaneously. The channels are affected by packet delays, dropouts, and uncertain observations. These effects are modeled using five Bernoulli distributed random variables. Correlation of noise at neighboring time caused by random delay is avoided by introducing two additional variables in the augmented stochastic model. The developed augmented stochastic model can handle network imperfections in both the S‐E and C‐A channels simultaneously. A minimum variance recursive linear estimator is designed using an innovation approach and projection theorem. Furthermore, sufficient condition is presented for the existence of steady state property of the proposed estimator. Simulation studies are carried out for the proposed estimator using a numerical example and a single link robot arm. Finally, performance comparison with other popular filters shows the effectiveness of the designed estimator.

DELINEATION AND CONSTRUCTION OF 2D GEOMETRIES BY FREEHAND DRAWING AND GEOMETRIC REASONING

Abstract. The creation of accurate and consistent line drawings is the subject of various applications. Prominent examples are the delineation of human-made objects in aerial images and the construction of technical line drawings, flow-charts, or diagrams. Interactive solutions usually restrict the user’s interaction during the design process to enforce geometric relations such as orthogonality or incidence. To avoid the time-consuming selection of operational modes, a freehand approach is desirable using strokes as the only user input. In this case, the construction principles have to be inferred automatically by geometric reasoning with uncertain observations. We present and discuss the corresponding methods in the context of educational technology. By introducing and utilizing a user-friendly software tool, we offer a hands-on approach to explore the feasibility and usability of the procedure. The experiments comprise the polygonal approximation of 2D shapes, theorem proving, and the construction of human-made figures.

A distributed averaging-based evidential Expectation-Maximization algorithm for density estimation in unreliable sensor networks

Abstract In this paper, a novel distributed averaging-based evidential Expectation-Maximization algorithm is presented for data clustering and probability density function estimation in unreliable sensor networks in the presence of uncertain observations. All observations of the sensor network are statistically modelled by a Gaussian mixture model. A generalized likelihood function is maximized in a distributed manner for density estimation. For this purpose, the parameters of the mixture model such as weighting coefficients, mean vectors, and covariance matrices are updated by using a distributed averaging method. The proposed algorithm can be applied to any network with a mesh topology. The convergence of algorithm is also investigated and guaranteed by using a mathematical analysis. In the simulation result section, the proposed algorithm has been applied to a simulated uncertain sensor network with a mesh topology. The simulations confirm the favourable performance of the distributed averaging-based evidential EM algorithm.

A data assimilation approach for groundwater parameter estimation under Bayesian maximum entropy framework

Spatial heterogeneity in groundwater system introduces significant challenges in groundwater modeling and parameter calibration. In order to mitigate the modeling uncertainty, data assiilation methods have been applied in the parameter estimation by assessing the uncertainties from both groundwater model and observations. In practice, the observations from groundwater system can be limited, and furthermore, boundary conditions and hydrogeological parameters, such as hydraulic conductivity, can be uncertain and biased. In order to handle the uncertain observations, this study applied the Bayesian maximum entropy (BME) for a data assimilation approach that integrates groundwater model, MODFLOW, and a variety of observations with uncertainties. In BME, no distributional assumption is imposed in the uncertain observations. We conducted numerical simulation with datasets of hard data of heads and hydrogeological parameters, uncertain head data on boundary, and uncertain hydrogeological parameters, i.e., hydraulic conductivity and storage coefficient. Three numerical scenarios with differerent combinations of datasets were conducted. Results show that the proposed data assimilation approach can gradually improve the modeling performance in the sense of lower mean squared errors over time. Moreover, the inclusion of uncertain observations can further improve the efficiency and accuracy in parameter estimation and hydraulic head prediction.

Development of event‐triggered‐based minimum variance recursive estimator for the NLNS using multi‐model approach

The minimum variance-based recursive estimator is designed to estimate the unmeasurable states of a non-linear networked system (NLNS). The measurable states are transmitted from sensor to the estimator (S–E) through a communication network. An event-triggered mechanism is proposed to limit data transmission in the S–E network to improve channel utilisation. The control input is transmitted from the controller to actuator (C–A) through another communication network. The networks in the S–E and C–A channels are affected by random packet delay, loss, and uncertain observation. These effects are modelled using five Bernoulli distributed random variables. The NLNS is converted to ‘m’ local linear stochastic augmented models by piecewise linearisation technique. The ‘m’ number of local estimators are designed for every local model using projection theorem. Global estimation is obtained by blending local estimators using T–S fuzzy approach. The proposed algorithm is recursive and has the advantage of scalability and flexibility. Finally, estimator performance is demonstrated using a non-linear tunnel diode and compared with the other popular filters. Monte Carlo simulation is performed and accumulated mean-square error values are calculated. From the simulation results, the proposed filter shows satisfactory performance.

Incremental Learning to Personalize Human Activity Recognition Models: The Importance of Human AI Collaboration.

This study presents incremental learning based methods to personalize human activity recognition models. Initially, a user-independent model is used in the recognition process. When a new user starts to use the human activity recognition application, personal streaming data can be gathered. Of course, this data does not have labels. However, there are three different ways to obtain this data: non-supervised, semi-supervised, and supervised. The non-supervised approach relies purely on predicted labels, the supervised approach uses only human intelligence to label the data, and the proposed method for semi-supervised learning is a combination of these two: It uses artificial intelligence (AI) in most cases to label the data but in uncertain cases it relies on human intelligence. After labels are obtained, the personalization process continues by using the streaming data and these labels to update the incremental learning based model, which in this case is Learn++. Learn++ is an ensemble method that can use any classifier as a base classifier, and this study compares three base classifiers: linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), and classification and regression tree (CART). Moreover, three datasets are used in the experiment to show how well the presented method generalizes on different datasets. The results show that personalized models are much more accurate than user-independent models. On average, the recognition rates are: 87.0% using the user-independent model, 89.1% using the non-supervised personalization approach, 94.0% using the semi-supervised personalization approach, and 96.5% using the supervised personalization approach. This means that by relying on predicted labels with high confidence, and asking the user to label only uncertain observations (6.6% of the observations when using LDA, 7.7% when using QDA, and 18.3% using CART), almost as low error rates can be achieved as by using the supervised approach, in which labeling is fully based on human intelligence.

Jeffrey conditionalization: proceed with caution

It has been argued that if the rigidity condition is satisfied, a rational agent operating with uncertain evidence should update her subjective probabilities by Jeffrey conditionalization (JC) or else a series of bets resulting in a sure loss could be made against her (the Dynamic Dutch Book Argument). We show, however, that even if the rigidity condition is satisfied, it is not always safe to update probability distributions by JC because there exist such sequences of non-misleading uncertain observations where it may be foreseen that an agent who updates her subjective probabilities by JC will end up nearly certain that a false hypothesis is true. We analyze the features of JC that lead to this problem, specify the conditions in which it arises and respond to potential objections.

Robust Quadratic Programming for MDPs with uncertain observation noise

The problem of Markov decision processes (MDPs) with uncertain observation noise has rarely been studied. This paper proposes a Robust Quadratic Programming (RQP) approach to approximate Bellman equation solution. Besides efficiency, the proposed algorithm exhibits great robustness against uncertain observation noise, which is essential in real world applications. We further represent the solution into kernel forms, which implicitly expands the state-encoded feature space to higher or even infinite dimensions. Experimental results well justify its efficiency and robustness. The comparison with different kernels demonstrates its flexibility of kernel selection for different application scenarios.

Stochastic output delay identification of discrete-time Gaussian systems

In this paper we propose a solution to the problems of detecting a generally correlated stochastic output delay sequence of a linear system driven by Gaussian noise. This is the model for uncertain observations resulting from losses in the propagation channel due to fading phenomena or packet dropouts that is common in wireless sensor networks, networked control systems, or remote sensing applications. The solution we propose consists of a nonlinear detector which identifies online the stochastic delay sequence. The solution provided is optimal in the sense that minimizes the probability of error of the delay detector. Finally, a filtering stage fed with the information given by the detector can follow to estimate the state of the system. Numerical simulations show good performance of the proposed method.

A SINS/BDS Integrated Navigation Method Based on Classified Weighted Adaptive Filtering

Aiming at the problem that the accuracy and stability of SINS/BDS integrated navigation system decrease due to uncertain model and observation anomalies, a SINS/BDS integrated navigation method based on classified weighted adaptive filtering is proposed. Firstly, the innovation covariance matching technology is used to detect whether there is any abnormality in the system as a whole. Then the types of anomalies are distinguished by hypothesis test. Different types of anomalies have different effects on state estimation. Based on the dynamic changes of innovation, different adaptive weighting methods are adopted to correct navigation information. The simulation results show that this method can effectively improve the fault-tolerant performance of integrated navigation system in complex environment with unknown anomaly types. When both model anomalies and observation anomalies exist, the speed and position accuracy are increased by 42% and 24% compared with the standard KF, 38% and 22% compared with the innovation orthogonal adaptive filtering, which has higher navigation accuracy.