A new data fusion method and its application to state estimation of nonlinear dynamic systems

Stochastic Approximation Type Nonlinear Filter with Randomly Varying Truncations

The precipitation oxygen isotopic composition is a useful environmental tracer for climatic and hydrological studies. However, the observed precipitation oxygen is limited at both temporal and spatial scales. Isotope-equipped general circulation models (iGCMs) can compensate for the temporal and spatial discontinuity of observation networks, but they suffer from coarse spatial resolutions and systematic biases. The objective of this study is to build a high-resolution precipitation oxygen isoscape in China for a period of 148 years by integrating observed and iGCMs-simulated precipitation oxygen isotope composition (δ18Op) using data fusion and bias correction methods. The temporal and spatial resolutions are month and 50–60 km for the isoscape, respectively. Prior to building the oxygen isoscape, the performance of two bias correction methods (BCMs) and three data fusion methods (DFMs) is compared after post-processing of eight iGCM simulations. Results show that the outputs of the Convolutional Neural Networks (CNN) fusion method exhibit the strongest correlation with observations with correlation coefficient mostly larger than 0.8, and the smallest bias with root mean square error mostly smaller than 2 ‰. The other two DFMs also perform slightly better than the two BCMs, which show similar performance. Thus, precipitation oxygen isoscape is generated by using the CNN fusion method for the 1969–2007 period in which all iGCMs have output and by using the bias correction methods for the remaining years. Based on the precipitation oxygen isoscape, the spatiotemporal patterns of δ18Op across China are investigated. The generated isoscape shows similar spatial and temporal distribution characteristics to observations. In general, the distribution pattern of δ18Op is consistent with the temperature effect in northern China, and with the precipitation amount effect in southern China, and be more specific in the Qinghai-Tibet Plateau of China. The δ18Op time series mirrors a fluctuating upward trend of the temperature or precipitation in most regions of China. The temporal and spatial distribution characteristics of the generated isoscape are consistent with the characteristics of atmospheric circulation and climate change, indicating successful assimilation and extension of the observed precipitation oxygen isotopes in time and space. Overall, the built isoscape is reliable and useful for providing strong support for tracking atmospheric and hydrological processes. The dataset is available in Zenodo at https://doi.org/10.5281/zenodo.5703811 (Chen et al., 2021).

The precipitation oxygen isotopic composition is a useful environmental tracer for climatic and hydrological studies. However, the observed precipitation oxygen is limited at both temporal and spatial scales. Isotope-equipped general circulation models (iGCMs) can compensate for the temporal and spatial discontinuity of observation networks, but they suffer from coarse spatial resolutions and systematic biases. The objective of this study is to build a high-resolution precipitation oxygen isoscape in China for a period of 148 years by integrating observed and iGCMs-simulated precipitation oxygen isotope composition (δ18Op) using data fusion and bias correction methods. The temporal and spatial resolutions are month and 50–60 km for the isoscape, respectively. Prior to building the oxygen isoscape, the performance of two bias correction methods (BCMs) and three data fusion methods (DFMs) is compared after post-processing of eight iGCM simulations. Results show that the outputs of the Convolutional Neural Networks (CNN) fusion method exhibit the strongest correlation with observations with correlation coefficient mostly larger than 0.8, and the smallest bias with root mean square error mostly smaller than 2 ‰. The other two DFMs also perform slightly better than the two BCMs, which show similar performance. Thus, precipitation oxygen isoscape is generated by using the CNN fusion method for the 1969–2007 period in which all iGCMs have output and by using the bias correction methods for the remaining years. Based on the precipitation oxygen isoscape, the spatiotemporal patterns of δ18Op across China are investigated. The generated isoscape shows similar spatial and temporal distribution characteristics to observations. In general, the distribution pattern of δ18Op is consistent with the temperature effect in northern China, and with the precipitation amount effect in southern China, and be more specific in the Qinghai-Tibet Plateau of China. The δ18Op time series mirrors a fluctuating upward trend of the temperature or precipitation in most regions of China. The temporal and spatial distribution characteristics of the generated isoscape are consistent with the characteristics of atmospheric circulation and climate change, indicating successful assimilation and extension of the observed precipitation oxygen isotopes in time and space. Overall, the built isoscape is reliable and useful for providing strong support for tracking atmospheric and hydrological processes. The dataset is available in Zenodo at https://doi.org/10.5281/zenodo.5703811 (Chen et al., 2021).

Recently, development in intelligent transportation systems (ITS) requires the input of various kinds of data in real-time and from multiple sources, which imposes additional research and application challenges. Ongoing studies on Data Fusion (DF) have produced significant improvement in ITS and manifested an enormous impact on its growth. This paper reviews the implementation of DF methods in ITS to facilitate traffic flow analysis (TFA) and solutions that entail the prediction of various traffic variables such as driving behavior, travel time, speed, density, incident, and traffic flow. It attempts to identify and discuss real-time and multi-sensor data sources that are used for various traffic domains, including road/highway management, traffic states estimation, and traffic controller optimization. Moreover, it attempts to associate abstractions of data level fusion, feature level fusion, and decision level fusion on DF methods to better understand the role of DF in TFA and ITS. Consequently, the main objective of this paper is to review DF methods used for real-time and multi-sensor (heterogeneous) TFA studies. The review outcomes are (i) a guideline of constructing DF methods which involve preprocessing, filtering, decision, and evaluation as core steps, (ii) a description of the recent DF algorithms or methods that adopt real-time and multi-sensor sources data and the impact of these data sources on the improvement of TFA, (iii) an examination of the testing and evaluation methodologies and the popular datasets and (iv) an identification of several research gaps, some current challenges, and new research trends.

Comparison of sixteen methods for fusion of data from impulse-radar sensors and depth sensors applied for monitoring of elderly persons

This work focuses on filters for nonlinear dynamic systems with nonlinear measurements. The Recursive Nonlinear Least Square Error (RNLS) filter has been recently derived for the state estimation of nonlinear dynamic systems. The RNLS is optimal under the LMSE criterion. Performances of RNLS, EKF and SDDRE-based filters are compared on a common basis. The Pareto formalism is used as a tool for such comparison on a common basis. The comparison is performed for a $6^{\mathrm {t}\mathrm {h}}$ order nonlinear system. This system models a tracking target that performs a coordinated turn/barrel-roll maneuver with unknown turning rate, measured by radar in polar coordinates. It is demonstrated by simulations that the RNLS filter is the optimal filter with respect to the quadratic criterion it is designed for. This places the RNLS filter as a vital candidate estimator of nonlinear systems.

An interacting Fuzzy-Fading-Memory-based Augmented Kalman Filtering method for maneuvering target tracking

In this paper, the state estimation for dynamic system with unknown inputs modeled as an autoregressive AR (1) process is considered. We propose an optimal algorithm in mean square error sense by using difference method to eliminate the unknown inputs. Moreover, we consider the state estimation for multisensor dynamic systems with unknown inputs. It is proved that the distributed fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurement; therefore, it achieves the best performance. The computation complexity of the traditional augmented state algorithm increases with the augmented state dimension. While, the new algorithm shows good performance with much less computations compared to that of the traditional augmented state algorithms. Moreover, numerical examples show that the performances of the traditional algorithms greatly depend on the initial value of the unknown inputs, if the estimation of initial value of the unknown input is largely biased, the performances of the traditional algorithms become quite worse. However, the new algorithm still works well because it is independent of the initial value of the unknown input.

This paper presents a Hybrid Particle Filter based RNN method for state estimation of non-linear dynamical system with knowledge of its input and output measurements. Particle filters are sequential Monte Carlo methods based on point mass (or particle) representations of probability densities, which is used to train Recurrent Neural Networks for estimation problems. The performance this method is compared with EKF based estimation and RNN based estimation. An Induction motor is considered as typical non-linear system and is implemented in MATLAB environment.

Robust unscented Kalman filter with adaptation of process and measurement noise covariances

A new framework is presented for understanding how a nonnormal probability density function (pdf) may affect a state estimate and how one might usefully exploit the nonnormal properties of the pdf when constructing a state estimate. A Bayesian framework is constructed that naturally leads to an expansion of the expected forecast error in a polynomial series consisting of powers of the innovation vector. This polynomial expansion in the innovation reveals a new view of the geometric nature of the state estimation problem. It is shown that this expansion in powers of the innovation provides a direct relationship between a nonnormal pdf describing the likely distribution of states and a normal pdf determined by powers of the forecast error. One implication of this perspective is that when state estimation is performed on a nonnormal pdf it leads to state estimates based on the mean to be nonlinear functions of the innovation. A direct relationship is shown between the degree to which the state estimate varies with the innovation and the moments of the distribution. These and other implications of this new view of ensemble state estimation in nonlinear systems are illustrated in simple scalar systems as well as on the Lorenz attractor.

This dissertation explores the intersection of data fusion, federated learning, and Bayesian methods, with a focus on their applications in indoor localization, GNSS, and image processing. Data fusion involves integrating data and knowledge from multiple sources. It becomes essential when data is only available in a distributed fashion or when different sensors are used to infer a quantity of interest. Data fusion typically includes raw data fusion, feature fusion, and decision fusion. In this thesis, we will concentrate on feature fusion. Distributed data fusion involves merging sensor data from different sources to estimate an unknown process. Bayesian framework is often used because it can provide an optimal and explainable feature by preserving the full distribution of the unknown given the data, called posterior, over the estimated process at each agent. This allows for easy and recursive merging of sensor data with prior knowledge without the need for storage. However, there are challenges in data fusion, such as the multiple counting problem, which occurs when data is utilized numerous times without the user's knowledge. In a Bayesian setting, a priori information of the unknown quantities is available and can be present among different distributed estimators. When the local estimates are fused, the prior knowledge used to construct several local posteriors might be overused unless the fusion node accounts for this and corrects it. In this thesis, we analyze the effects of shared priors in Bayesian data fusion contexts. Our analysis helps to understand the performance behavior as a function of the number of collaborative agents and different types of priors, depending on different common fusion rules. To perform this analysis, we use two divergences that are common in Bayesian inference. The generality of the results allows us to analyze very generic distributions. These theoretical results are corroborated through experiments in a variety of estimation and classification problems, including linear and nonlinear models, and federated learning schemes in a Bayesian perspective. Federated Learning is a discipline of Distributed Data Fusion that can be used for model training on local data without exchanging the data itself. This technique is useful in scenarios like image classification, indoor positioning, and jammer signal classification, where privacy concerns make data crowdsourcing difficult. In this thesis, we explore FL in two specific applications: Jammer signal and indoor positioning. Jamming signals can disrupt the operation of GNSS receivers, making jamming mitigation and localization techniques essential. Jammer classification can help with these techniques. For indoor positioning, local data points are collected to create a local fingerprinting database. Data-driven machine learning methods are used to predict the location based on this model learned without data sharing. However, Federated Learning faces several challenges, including the non-IID (non-identically distributed) problem. This problem occurs when the data distribution varies across different clients, which can lead to a decrease in performance. In this thesis, we will discuss various FL frameworks and algorithms that can help address this problem. A FL method from Bayesian perspective are proposed to deal with the problem in indoor positioning problem. Additionally, we will delve into the concepts of personalized and clustered Federated Learning. The personalized approach tailors the learning process to individual clients, which enhances the system's performance by leveraging the unique data and characteristics of each client. We will discuss the application of this approach in indoor positioning and jammer signal classification, highlighting its potential improvements and challenges. Expanding on the personalized approach, we introduce and discuss clustered Federated Learning. This learning method groups clients with similar characteristics or data patterns. Each client is typically associated with one data distribution and participates in training a model for that distribution along with their cluster peers. We propose a Bayesian framework for clustered FL, which associates clients to clusters, along with several practical algorithms for efficient learning, considering the trade-offs between performance and computational complexity. In conclusion, this thesis provides a detailed investigation and evaluation of the integration of data fusion, federated learning, and Bayesian methods. The insights and conversations presented in this study are anticipated to enhance the progress and implementation of these technologies in various domains, particularly in indoor positioning, and GNSS.--Author's abstract

This paper investigated the problem of state and fault estimation for nonlinear discrete time systems in presence of unknown disturbances. A novel unbiased minimum variance filter (UMVF) is derived by reconstructing the non linear version of NUMV filter. In this work we assume that no prior knowledge about the dynamic of the disturbance and the fault are known. In this paper we considers that the fault affects both the system state and measurement equations, but the disturbance affects only the system state. The NUMV filter presented in this paper is an extension of the filter presented in [11]. The efficacy of the proposed filter is demonstrated by two simulation examples.

An extended model-based observer for state estimation in nonlinear hysteretic structural systems

Nonlinear state estimation is a pre-requisite for advanced process control and fault diagnosis tasks. In literature, various recursive nonlinear filtering techniques have been proposed and used for state estimation of nonlinear systems. Over the last few years, Moving Horizon Estimation (MHE) is increasingly being used for state estimation of nonlinear systems. Moving horizon estimation works with a window of data and hence requires additional online computation compared to recursive nonlinear filters. However, MHE performs both smoothing and filtering and thus has the potential to obtain more accurate state estimates as compared to the recursive filters. Most of the available comparisons of MHE with recursive filters are based on simulation case studies where the true states and parameters, as well as noise processes are exactly known. In this work, we apply MHE to a three-tank experimental setup and compare its performance with various nonlinear filters available in literature such as Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Gaussian Sum EKF (GSEKF). We present some of the challenges in experimental implementation of state estimation approaches. These include presence of unknown disturbances, non-whiteness of noise signals as well as lack of accurate measurements. We then discuss the approach followed for obtaining model parameters and noise characterization to make the models amenable for filter implementation. It is found that EKF, GSEKF and UKF perform as well as MHE as far as accuracy is concerned, but require significantly lower computational efforts.