Quadrature filters for one-step randomly delayed measurements

In this paper, two existing quadrature filters, viz., the Gauss–Hermite filter (GHF) and the sparse-grid Gauss–Hermite filter (SGHF) are extended to solve nonlinear filtering problems with one step randomly delayed measurements. The developed filters are applied to solve a maneuvering target tracking problem with one step randomly delayed measurements. Simulation results demonstrate the enhanced accuracy of the proposed delayed filters compared to the delayed cubature Kalman filter and delayed unscented Kalman filter

A new algorithm for continuous-discrete filtering with randomly delayed measurements

This paper is a postprint of a paper submitted to and accepted for publication in IET Control Theory & Applications and is subject to Institution of Engineering and Technology Copyright. The copy of record is available at IET Digital Library.The filtering of nonlinear continuous-discrete systems is widely applicable in real-life and extensive literature is available to deal with such problems. However, all of these approaches are constrained with the assumption that the current measurement is available at every time step, although delay in measurement is natural in real-life applications. To deal with this problem, we re-derive the conventional Bayesian approximation framework for solving the continuous-discrete filtering problems. In practice, the delay is often smaller than one sampling time, which is the main case considered here. During the filtering of such systems, the actual time of correspondence should be known for a measurement received at the kth time instant. In this paper, a simple and intuitively justified cost function is used to decide the time to which the measurement at kth time instant actually corresponds. The performance of the proposed filter is compared with a conventional filter based on numerical integration which ignores random delays for a continuousdiscrete tracking problem. We show that the conventional filter fails to track the target while the modification proposed in this paper successfully deals with random delays. The proposed method may be seen as a valuable addition to the tools available for continuous-discrete filtering in nonlinear systems

Gaussian Filtering for Simultaneously Occurring Delayed and Missing Measurements

Data Access Statement: This research did not use any experimentally generated data or data from any publicly available dataset. Model definitions (including the specified probability distributions) and parameter values (including the initialization parameters) provided in the paper are adequate for reproducing the exact qualitative behavior of the algorithms illustrated in the paper.© Copyright 2022 The Authors. Approximate filtering algorithms in nonlinear systems assume Gaussian prior and predictive density and remain popular due to ease of implementation as well as acceptable performance. However, these algorithms are restricted by two major assumptions: they assume no missing or delayed measurements. However, practical measurements are frequently delayed and intermittently missing. In this paper, we introduce a new extension of the Gaussian filtering to handle the simultaneous occurrence of the delay in measurements and intermittently missing measurements. Our proposed algorithm uses a novel modified measurement model to incorporate the possibility of the delayed and intermittently missing measurements. Subsequently, it redesigns the traditional Gaussian filtering for the modified measurement model. Our algorithm is a generalized extension of the Gaussian filtering, which applies to any of the traditional Gaussian filters, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF). A further contribution of this paper is that we study the stochastic stability of the proposed method for its EKF-based formulation. We compared the performance of the proposed filtering method with the traditional Gaussian filtering (particularly the CKF) and three extensions of the traditional Gaussian filtering that are designed to handle the delayed and missing measurements individually or simultaneously.10.13039/501100001409-Department of Science and Technology (DST), Government of India, through Innovation in Science Pursuit for Inspired Research (INSPIRE) Faculty Award (Grant Number: DST/INSPIRE/04/2018/000089

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Uncertainty-aware variational inference for target tracking

In the low Earth orbit, target tracking with ground based assets in the context of situational awareness is particularly difficult. Because of the nonlinear state propagation between the moments of measurement arrivals, the inevitably accumulated errors will make the target state prediction and the measurement likelihood inaccurate and uncertain. In this paper, optimizable models with learned parameters are constructed to model the state and measurement prediction uncertainties. A closed-loop variational iterative framework is proposed to jointly achieve parameter inference and state estimation, which comprises an uncertainty-aware variational filter (UnAVF). The theoretical expression of the evidence lower bound and the maximization of the variational lower bound are derived without the need for the true states, which reflect the awareness and reduction of uncertainties. The evidence lower bound can also evaluate the estimation performance of other Gaussian density filters, not only the UnAVF. Moreover, two rules, estimation consistency and lower bound consistency, are proposed to conduct the initialization of hyperparameters. Finally, the superior performance of UnAVF is demonstrated over an orbit state estimation problem

Real Time Dynamic State Estimation: Development and Application to Power System

Since the state estimation algorithm has been firstly proposed, considerable research interest has been shown in adapting and applying the different versions of this algorithm to the power transmission systems. Those applications include power system state estimation (PSSE) and short-term operational planning. In the transmission level, state estimation offers various applications including, process monitoring and security monitoring. Recently, distribution systems experience a much higher level of variability and complexity due to the large increase in the penetration level of distributed energy resources (DER), such as distributed generation (DG), demand-responsive loads, and storage devices. The first step, for better situational awareness at the distribution level, is to adapt the most developed real time state estimation algorithm to distribution systems, including distribution system state estimation (DSSE). DSSE has an important role in the operation of the distribution systems. Motivated by the increasing need for robust and accurate real time state estimators, capable of capturing the dynamics of system states and suitable for large-scale distribution networks with a lack of sensors, this thesis introduces a three state estimators based on a distributed approach. The first proposed estimator technique is the square root cubature Kalman filter (SCKF), which is the improved version of cubature Kalman filter (CKF). The second one is based on a combination of the particle filter (PF) and the SCKF, which yields a square root cubature particle filter (SCPF). This technique employs a PF with the proposal distribution provided by the SCKF. Additionally, a combination of PF and CKF, which yields a cubature particle filter (CPF) is proposed. Unlike the other types of filters, the PF is a non-Gaussian algorithm from which a true posterior distribution of the estimated states can be obtained. This permits the replacement of real measurements with pseudo-measurements and allows the calculation to be applied to large-scale networks with a high degree of nonlinearity. This research also provides a comparison study between the above mentioned algorithms and the latest algorithms available in the literature. To validate their robustness and accuracy, the proposed methods were tested and verified using a large range of customer loads with 50 % uncertainty on a connected IEEE 123-bus system. Next, a developed foretasted aided state estimator is proposed. The foretasted aided state estimator is needed to increase the immunization of the state estimator against the delay and loss of the real measurements, due to the sensors malfunction or communication failure. Moreover, due to the lack of measurements in the electrical distribution system, the pseudo-measurements are needed to insure the observability of the state estimator. Therefore, the very short term load forecasting algorithm that insures the observability and provides reliable backup data in case of sensor malfunction or communication failure is proposed. The proposed very short term load forecasting is based on the wavelet recurrent neural network (WRNN). The historical data used to train the RNN are decomposed into low-frequency, low-high frequency and high frequency components. The neural networks are trained using an extended Kalman filter (EKF) for the low frequency component and using a square root cubature Kalman filter (SCKF) for both low-high frequency and high frequency components. To estimate the system states, state estimation algorithm based SCKF is used. The results demonstrate the theoretical and practical advantages of the proposed methodology. Finally, in recent years several cyber-attacks have been recorded against sensitive monitoring systems. Among them is the automatic generation control (AGC) system, a fundamental control system used in all power networks to keep the network frequency at its desired value and for maintaining tie line power exchanges at their scheduled values. Motivated by the increasing need for robust and safe operation of AGCs, this thesis introduces an attack resilient control scheme for the AGC system based on attack detection using real time state estimation. The proposed approach requires redundancy of sensors available at the transmission level in the power network and leverages recent results on attack detection using mixed integer linear programming (MILP). The proposed algorithm detects and identifies the sensors under attack in the presence of noise. The non-attacked sensors are then averaged and made available to the feedback controller. No assumptions about the nature of the attack signal are made. The proposed method is simulated using a large range of attack signals and uncertain sensors measurements. All the proposed algorithms were implemented in MATLAB to verify their theoretical expectations

An Information Theory Model for Optimizing Quantitative Magnetic Resonance Imaging Acquisitions

Quantitative magnetic resonance imaging (qMRI) is a powerful group of imaging techniques with a growing number of clinical applications, including synthetic image generation in post-processing, automatic segmentation, and diagnosis of disease from quantitative parameter values. Currently, acquisition parameter selection is performed empirically for quantitative MRI. Tuning parameters for different scan times, tissues, and resolutions requires some measure of trial and error. There is an opportunity to quantitatively optimize these acquisition parameters in order to maximize image quality and the reliability of the previously mentioned methods which follow image acquisition. The objective of this work is to introduce and evaluate a quantitative method for selecting parameters that minimize image variability. An information theory framework was developed for this purpose and applied to a 3D-quantification using an interleaved Look-Locker acquisition sequence with T2 preparation pulse (3D-QALAS) signal model for synthetic MRI. In this framework, mutual information is used to measure the information gained by a measurement as a function of acquisition parameters, quantifying the information content of the acquisition parameters and allowing informed parameter selection. The information theory framework was tested on synthetic data generated from a representative mathematical phantom, measurements acquired on a qMRI multiparametric imaging standard phantom, and in vivo measurements in a human brain. The application of this information theory framework resulted in successful parameter optimization with respect to mutual information. Both the phantom and in vivo measurements showed that higher mutual information calculated by the model correlated with smaller standard deviation in the reconstructed parametric maps. With this framework, optimal acquisition parameters can be selected to improve image quality, image repeatability, or scan time. This method could reduce the time and labor necessary to achieve images of the desired quality. Making an informed acquisition parameter selection reduces uncertainty in the imaging output and optimizes information gain within the bounds of clinical constraints

Nonlinear Gaussian Filtering : Theory, Algorithms, and Applications

By restricting to Gaussian distributions, the optimal Bayesian filtering problem can be transformed into an algebraically simple form, which allows for computationally efficient algorithms. Three problem settings are discussed in this thesis: (1) filtering with Gaussians only, (2) Gaussian mixture filtering for strong nonlinearities, (3) Gaussian process filtering for purely data-driven scenarios. For each setting, efficient algorithms are derived and applied to real-world problems

Bayesian Inference for Genomic Data Analysis

High-throughput genomic data contain gazillion of information that are influenced by the complex biological processes in the cell. As such, appropriate mathematical modeling frameworks are required to understand the data and the data generating processes. This dissertation focuses on the formulation of mathematical models and the description of appropriate computational algorithms to obtain insights from genomic data. Specifically, characterization of intra-tumor heterogeneity is studied. Based on the total number of allele copies at the genomic locations in the tumor subclones, the problem is viewed from two perspectives: the presence or absence of copy-neutrality assumption. With the presence of copy-neutrality, it is assumed that the genome contains mutational variability and the three possible genotypes may be present at each genomic location. As such, the genotypes of all the genomic locations in the tumor subclones are modeled by a ternary matrix. In the second case, in addition to mutational variability, it is assumed that the genomic locations may be affected by structural variabilities such as copy number variation (CNV). Thus, the genotypes are modeled with a pair of (Q + 1)-ary matrices. Using the categorical Indian buffet process (cIBP), state-space modeling framework is employed in describing the two processes and the sequential Monte Carlo (SMC) methods for dynamic models are applied to perform inference on important model parameters. Moreover, the problem of estimating gene regulatory network (GRN) from measurement with missing values is presented. Specifically, gene expression time series data may contain missing values for entire expression values of a single point or some set of consecutive time points. However, complete data is often needed to make inference on the underlying GRN. Using the missing measurement, a dynamic stochastic model is used to describe the evolution of gene expression and point-based Gaussian approximation (PBGA) filters with one-step or two-step missing measurements are applied for the inference. Finally, the problem of deconvolving gene expression data from complex heterogeneous biological samples is examined, where the observed data are a mixture of different cell types. A statistical description of the problem is used and the SMC method for static models is applied to estimate the cell-type specific expressions and the cell type proportions in the heterogeneous samples