Recursive Estimation Research Articles

Finite-Horizon H∞ State Estimation for Complex Networks With Uncertain Couplings and Packet Losses: Handling Amplify-and-Forward Relays.

This article is concerned with the state estimation problem for a class of complex networks (CNs) with uncertain inner couplings and packet losses over communication networks. The inner couplings are allowed to be uncertain and varying in a specific interval. The amplify-and-forward (AaF) relay protocols are introduced to improve the communication quality and enhance the propagation distance. The Bernoulli random variables are used to characterize the randomly occurring packet losses encountered in communication channels. The focus of this article is on the design of a state estimator for each node of CNs such that a prescribed H∞ performance constraint is satisfied for the dynamical error system over a finite horizon. A sufficient condition is first provided to verify the existence of the desired H∞ state estimator, and the estimator gain is then determined by solving two coupled backward Riccati difference equations (RDEs). Subsequently, a recursive state estimation algorithm is put forward that is suitable for online computation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed estimation method.

Bayesian model selection for COVID-19 pandemic state estimation using extended Kalman filters: Case study for Saudi Arabia.

Quantifying the uncertainty in data-driven mechanistic models is fundamental in public health applications. COVID-19 is a complex disease that had a significant impact on global health and economies. Several mathematical models were used to understand the complexity of the transmission dynamics under different hypotheses to support the decision-making for disease management. This paper highlights various scenarios of a 6D epidemiological model known as SEIQRD (Susceptible-Exposed-Infected-Quarantined-Recovered-Deceased) to evaluate its effectiveness in prediction and state estimation during the spread of COVID-19 pandemic. Then we investigate the suitability of the classical 4D epidemiological model known as SIRD (Susceptible-Infected-Recovered-Deceased) in the long-term behaviour in order to make a comparison between these models. The primary aim of this paper is to establish a foundational basis for the validity and epidemiological model comparisons in long-term behaviour which may help identify the degree of model complexity that is required based on two approaches viz. the Bayesian inference employing the nested sampling algorithm and recursive state estimation utilizing the Extended Kalman Filter (EKF). Our approach acknowledges the potential imperfections and uncertainties inherent in compartmental epidemiological models. By integrating our proposed methodology, these models can consistently generate predictions closely aligned with the observed data on active cases and deaths. This framework, implemented within the EKF algorithm, offers a robust tool for addressing future, unknown pandemics. Moreover, we present a systematic methodology for time-varying parameter estimation along with uncertainty quantification using Saudi Arabia COVID-19 data and obtain the credible confidence intervals of the epidemiological nonlinear dynamical system model parameters.

3D Local Crime Type Models Based on Crime Hotspot Detection

This paper deals with the analysis of the relationship between locations and types of crime observed in the Czech Republic. Cluster analysis of crime data based on the recursive Bayesian mixture estimation algorithm is used to identify crime hotspots and estimate local models of crime type. The experiments report that the 2D configuration of the algorithm allows the detection of crime hotspots online. The 3D configuration provides 29% more accurate crime type models than 2D clustering and alternative data mining algorithms. For the data set used, it was determined in which crime hotspots the most serious and most frequent types of crime can be expected to occur with the highest probability. The limitation of the study is the artificial support of the 3D clusters by the fully continuous data vector with the recoded values of the crime type. The potential use of the algorithm is expected in online web applications for sharing information on criminal offenses managed by the Police of the Czech Republic with the public and local government entities in the Czech Republic.

Real-time recursive estimation of, and uncertainty quantification for, breath alcohol concentration via LQ tracking control-based inverse filtering of transdermal alcohol biosensor signals

Real-time recursive estimation of, and uncertainty quantification for, breath alcohol concentration via LQ tracking control-based inverse filtering of transdermal alcohol biosensor signals

Modified Adaptive RFT with Sample Covariance Matrix Inversion Recursive Estimation

Modified Adaptive RFT with Sample Covariance Matrix Inversion Recursive Estimation

Parameters estimation for the Hammerstein‐Wiener models with colored noise based on hybrid signals

SummaryA three‐stage estimation approach of the Hammerstein‐Wiener model with colored noise using hybrid signals is considered in this article. The Hammerstein‐Wiener model where a linear dynamic block is embedded between two static nonlinear elements, in which two nonlinear elements represented by two independent neural fuzzy models and a linear element represented by autoregressive exogenous model. The designed hybrid signals that consist of separable signals and random signals are devoted to estimating independently. First, the characteristics of separable signals in the action of the static nonlinear element are analyzed, then the output nonlinear element parameters are estimated utilizing two groups of separable signals with a multiple. Moreover, least squares based on correlation analysis method is applied to estimate linear element using one set of separable signals, which handles the interference of colored process noise. Finally, the recursive extended least squares algorithm is derived to estimate the input nonlinear element and the autoregressive moving average noise model, which improves parameters estimation accuracy owing to estimating colored noise model parameters in recursive estimate process. The feasibility of the presented estimation technique is demonstrated by an illustrative simulation example and a practical nonlinear process.

An adaptive fractional order controller design: A realization for liquid level regulation in liquid level plant

In this paper, an adaptive FO − IλD1−λ controller design is proposed using a frequency domain approach. The proposed adaptive controller parameters are tuned based on the frequency domain specifications. To realize the velocity error constant for the proposed controller, Oustaloup Recursive Approximation (ORA) method is employed. The proposed controller is realized for liquid level regulation in the Liquid Level Plant (LLP). An identification technique is proposed to identify a linear adaptable parameter transfer function (LAPTF) model of LLP. The performance of the proposed controller is compared with the existing works. It is observed that the proposed controller outperforms the existing controllers in the literature.

Modified Induction Machine Equivalent Circuit Including Solid Shaft Eddy Currents

The shaft eddy currents cause a significant saturation in two-pole induction machines (IMs) as they generate an opposing field and repulse the main flux, thus tightening the flux path. This results in inaccurate performance estimations with the magnetizing inductance measured in no-load conditions when the machine is loaded. This article presents a modified IM equivalent circuit considering the rotor back iron saturation effects caused by the solid shaft eddy currents using experimental measurements and recursive parameter estimation techniques. The classical equivalent circuit (CEC) parameters are determined with the standard test techniques followed by the parameter estimation of the newly introduced modified equivalent circuit (MEC) parameters. The proposed modified equivalent circuit is benchmarked with CEC and finite element analysis (FEA) simulations with and without considering eddy effects. The proposed MEC model and the FEA that consider eddy effects performed better than the other models and yielded a negligibly small error over a wide range of loading conditions. Compared to the FEA, the proposed MEC estimates the IM performance much faster, which makes it more appealing for IM performance estimations.

Remaining useful life prediction for lithium-ion batteries with an improved grey particle filter model

Accurate prediction of remaining useful life is of great value for the maintenance and replacement of electric vehicles lithium-ion batteries. This paper aims to present a grey particle filter model for improving remaining useful life forecast accuracy. Firstly, a grey particle filter model with recursive least square parameter estimation is built, and the proposed model’s parameters are trained. Secondly, RUL is predicted by using the parameters and proposed model. Finally, NASA lithium-ion battery open data set was used for verification. The model was evaluated from two perspectives of RUL accuracy and mean absolute percentage error. Predictions are also made for lithium-ion batteries under conditions of elevated temperature. The findings demonstrate that the proposed model outperforms the other models.

Streaming variational probabilistic principal component analysis for monitoring of nonstationary process

Modern industrial processes are characteristic of nonstationary and uncertainty. To address these issues, this paper proposes a probabilistic principal component analysis based model that utilizes streaming variational inference for online monitoring of nonstationary process. The model parameters are updated in a streaming/batch-wise manner to track the nonstationary behavior in the process. In the updating procedures, the posterior distributions obtained from the previous data batch are used as priors for the current model, whose parameters can be estimated using the variational Bayesian inference. The streaming variational inference enables recursive parameter estimation over time. Additionally, in order to improve computational efficiency, a distributed update strategy is also applied to the proposed model. For online process monitoring, the noncentral chi-square distributions are derived to estimate the statistical control limits for each data batch, resulting in better adaptation to the nonstationary characteristics. The effectiveness and superiority of the proposed method are validated through simulation example and real-world industrial application.

Detection of Data Integrity Attack Using Model and Data-Driven-Based Approach in CPPS

The cyber-physical power system (CPPS) is a modern infrastructure utilising information and communication technology that has become more vulnerable to cyberattacks in recent years. The attack magnitude injected by the adversary is stealthier and it cannot be detected using conventional bad data detection techniques. Protecting sensitive data from data integrity attacks (DIA) is essential for ensuring system security and reliability. A tragic event will occur if the attack goes unreported. Therefore, DIA detection is highly vital for the operator in the control centre to make important decisions. This paper addresses the attack impact on WAC applications and attack detection using the model-based method and data-driven-based methods. On the basis of the validation of performance indicators, various detection approaches are simulated and compared to determine the best detection strategy. Simulation results show that in the model-based anomaly detection method, the recursive polynomial model estimator (RPME) has better detection performance than the recursive least square estimator (RLSE). The convolutional neural network- (CNN-) based data-driven anomaly detection technique outperforms other machine learning (ML) techniques such as support vector machine (SVM), K-nearest neighbour (KNN), and random forest (RF). On the WSCC 3 machine 9-bus system, the efficacy of the suggested methods is evaluated.

Encryption-Decryption-Based State Estimation With Multirate Measurements Against Eavesdroppers: A Recursive Minimum-Variance Approach

This paper is concerned with the secure state estimation problem for a networked system with multi-rate measurements. The measurement data are transmitted to the estimator over a communication network, where an eavesdropper could intercept the transmitted information and generate the state estimates based on the overheard signals. In order to protect the privacy of the system state from information leakage, a novel encryptor is proposed to encrypt the measurement signals into codewords before being transmitted, and a decryptor is then adopted at the user side to decrypt the received codewords into the desired measurement signals, based on which a recursive state estimator is developed whose parameter is calculated by solving several coupled difference equations. Here, the secret key for decryption is available to the user but is unknown to the eavesdropper. The encryptor and the estimator are co-designed such that 1) at the user side, the estimation error covariance has an upper bound that is subsequently minimized in the sense of the matrix trace, where the uniform boundedness of the error covariance is also examined; and 2) at the eavesdropper side, the corresponding state estimation error is divergent. Two simulation examples are provided to demonstrate the effectiveness of our developed secure state estimation scheme.

Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions

Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately account for certain non-local phenomena such as, e.g., interactions at a distance. Non-local nonlinear PDE models can accurately capture these phenomena, but traditional numerical approximation methods are infeasible when the considered non-local PDE is high-dimensional. In this article we propose two numerical methods based on machine learning and on Picard iterations, respectively, to approximately solve non-local nonlinear PDEs. The proposed machine learning-based method is an extended variant of a deep learning-based splitting-up type approximation method previously introduced in the literature and utilizes neural networks to provide approximate solutions on a subset of the spatial domain of the solution. The Picard iterations-based method is an extended variant of the so-called full history recursive multilevel Picard approximation scheme previously introduced in the literature and provides an approximate solution for a single point of the domain. Both methods are mesh-free and allow non-local nonlinear PDEs with Neumann boundary conditions to be solved in high dimensions. In the two methods, the numerical difficulties arising due to the dimensionality of the PDEs are avoided by (i) using the correspondence between the expected trajectory of reflected stochastic processes and the solution of PDEs (given by the Feynman–Kac formula) and by (ii) using a plain vanilla Monte Carlo integration to handle the non-local term. We evaluate the performance of the two methods on five different PDEs arising in physics and biology. In all cases, the methods yield good results in up to 10 dimensions with short run times. Our work extends recently developed methods to overcome the curse of dimensionality in solving PDEs.

Online estimation of PID controllers and plant dynamics via multi‐recursive least squares estimation from closed‐loop I/O data

AbstractThis article proposes an online solution to address the problem of closed‐loop system identification using multiple recursive least squares estimation protocols. Some control systems cannot be analysed in an open‐loop form for stability reasons or the requirement for online control system operation. So, it is necessary to identify plant dynamics and controller parameters based on input–output data from the feedback structure. The presented method identifies real‐time parameters of plant dynamics and controller parameters by utilising a series of recursive least square estimation algorithms that estimate open‐loop data from noisy input–output data measured from the closed‐loop feedback structure. The proposed method can effectively identify abrupt variations in both the controller parameters and plant dynamics. This capability makes it valuable for deployment as a supervisory component, enabling the detection of any faults that may arise in operating systems. Mathematical formulations and theorems are developed, and two numerical case studies are presented to examine the feasibility and performance of the presented closed‐loop system identification protocol.

Updating singular value decomposition for modal analysis of slow-varying non-stationary vibration structures

This paper proposes a novel method for the modal analysis of slow-varying vibration structures based on vector autoregressive models. The basic idea of this method consists of using a short-time sliding window (STSW) to identify modal parameters for non-stationary vibrations. This method uses the recursive least-squares estimation for multivariable systems with the singular value decomposition (SVD) method to find the solutions within a segment of the data from each time window. Model identification is conducted by updating the SVD of the data matrix using the order and time from the previous computational window to monitor the modal parameters of a slow-varying system. Finally, this work was validated first by numerically simulating a system's gradual changes submitted to an exciting force and further by an experiment on a hydraulic turbine blade.

Novel applications of oustaloup recursive approximation and modified oustaloup recursive approximation methods in linear fractional order control design

Novel applications of oustaloup recursive approximation and modified oustaloup recursive approximation methods in linear fractional order control design

Anisotropically suppressed frustration in antiferromagnetic systems on the kagome lattice

The influence of the interactionally generated anisotropy on the magnetic as well as thermodynamic properties of geometrically frustrated antiferromagnetic systems is investigated in the framework of the interactionally generated uniaxially-anisotropic antiferromagnetic J1−J2 spin-1/2 Ising model on the kagome lattice within the recursive lattice approximation. The exact solution of the corresponding model on the star kagome-like recursive lattice is found and the phase diagrams of the ground states of the model with and without the presence of the external magnetic field are identified from the magnetization as well as the entropy point of view. The magnetization, the entropy, and the specific heat properties of the model are investigated. It is shown that the presence of even a negligibly small interactionally generated anisotropy can lead not only to the quantitative but also to the significant qualitative changes in the magnetic and thermodynamic properties of frustrated magnetic systems, e.g., it can suppress the presence of frustration itself and, at the same time, generate the appearance of the first and second order phase transitions.

Error- and Tamper-Tolerant State Estimation for Discrete Event Systems Under Cost Constraints

This paper deals with the state estimation problem in discrete-event systems modeled with nondeterministic finite automata, partially observed via a sensor measuring unit whose measurements (reported observed symbols) may be vitiated by a malicious attacker. The attacks considered in this paper include arbitrary deletions, insertions, or substitutions of observed symbols by taking into account a bounded number of attacks or, more generally, a total cost constraint (assuming that each deletion, insertion, or substitution bears a positive cost to the attacker). We provide a characterization of the sequences of symbols that match the received sequence of possibly corrupted symbols, and subsequently use them to recursively perform tamper-tolerant state estimation subject to cost constraints. Each step of the recursive state estimation procedure has complexity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(|X||\Sigma |C)$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$|X|$</tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$|\Sigma |$</tex-math></inline-formula> ) is the number of states (events) of the given finite automaton and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C$</tex-math></inline-formula> is the maximum total cost that is allowed for all deletions, insertions, and substitutions.

Multiple passive-sensor distributed target tracking approach with Machine Learning Feedback

In this paper, a novel recursive state estimation approach in three-dimensional space for a non-maneuvering target is developed. The proposed technique employs angle and amplitude information in a distributed fusion setup, tackling the issue of target state estimation in cluttered environments, as well as target detection with a machine learning feedback mechanism with sequence measurements from multiple passive sensors. A new Integrated Probabilistic Data Association technique with Machine Learning Feedback (IPDA-MLF) is proposed. Most of the clutter measurements are eliminated by fusing angles and amplitude information in the Local Sensor tracker with an Integrated Probabilistic Data Association algorithm (LS-IPDA) framework. To deal with low observability issues, as well as to fuse information from multiple sensors, a Machine Learning (ML) algorithm is deployed, which utilizes a convolutional neural networks-based algorithm. The proposed IPDA-MLF algorithm resolves possible track-to-track associations and provides feedback to the local tracker for increased track retention. The refined information from local trackers is again converted to heat maps and the ML-based solution is used to fuse the local tracks at a central level. Simulation results show that the performance of the proposed algorithm is improved by the incorporation of the machine learning feedback, reducing false tracks, increasing true track retention, and eliminating mismatched fusion at the central tracker.

Decentralized discrete adaptive sliding mode control for interconnected nonlinear systems

This article presents a study on controlling a class of large-scale systems composed of interconnected subsystems. The systems are represented by discrete block-oriented models with unknown parameters. This article proposes a novel adaptive sliding mode control strategy to address the tracking control problem and minimize the impact of interconnection. This approach leverages the robustness of sliding mode control against unmodeled dynamics and disturbances with the advantages of adaptive control. To adapt the system’s parameters, a recursive parametric estimation algorithm using least-squares techniques is employed. The proposed method offers benefits such as robustness against parameter uncertainties, handling of nonlinearities, improved tracking accuracy, and reduced chattering phenomena. The effectiveness of the method is demonstrated through the evaluation of two simulation examples.