State Estimation Algorithm Research Articles

Target State Estimation Based on Kalman Filter in Terminal Guidance

In order to settle the requirement of target location and line-of-sight (LOS) rate estimation with multi-angle measurement in terminal guidance process, the state estimation algorithm based on Kalman filter is proposed in this paper. The linearized system model is established, and the extended Kalman filter is used to estimate the position and LOS rate of the target. The simulation results show that this method exhibits high accuracy for position estimation, and it can precisely track the change of LOS angular rate in real time. The algorithm is simple in principle, easy to implement and of high value in practice.

POWER SYSTEM STATE ESTIMATION USING A ROBUST ESTIMATOR

State estimation (SE) is a primary data processing algorithm which is utilised by the control centres of advanced power systems. The most generally utilised state estimator is based on the weighted least squares (WLS) approach which is ineffective in addressing gross errors of input data of state estimator. This paper presents an innovative robust estimator for SE environments to overcome the non-robustness of the WLS estimator. The suggested approach not only includes the similar functioning of the customary loss function of WLS but also reflects loss function built on the modified WLS (MWLS) estimator. The performance of the proposed estimator was assessed based on its ability to decrease the impacts of gross errors on the estimation results. The properties of the suggested state estimator were investigated and robustness of the estimator was studied considering the influence function. The effectiveness of the proposed estimator was demonstrated with the help of examples which also indicated non-robustness of MWLS estimator in SE algorithm.

A Simple And Novel Algorithm For State Estimation Of Continuous Time Linear Stochastic Dynamic Systems Excited By Random Inputs

The major goal of this paper is to explore the effective state estimation algorithm for continuous time dynamic system under the lossy environment without increasing the complexity of hardware realization. Though the existing methods of state estimation of continuous time system provides effective estimation with data loss, the real time hardware realization is difficult due to the complexity and multiple processing. Kalman Filter and Particle Filer are fundamental algorithms for state estimation of any linear and non-linear system respectively, but both have its limitation. The approach adopted here, detect the expected state value and covariance, existed by random input at each stage and filtered the noisy measurement and replace it with predicted modified value for the effective state estimation. To demonstrate the performance of the results, the continuous time dynamics of position of the Aerial Vehicle is used with proposed algorithm under the lossy measurements scenario and compared with standard Kalman filter and smoothed filter. The results show that the proposed method can effectively estimate the position of Aerial Vehicle compared to standard Kalman and smoothed filter under the non-reliable sensor measurements with less hardware realization complexity.

Selection of an Efficient Linear State Estimator for Unified Real Time Dynamic State Estimation in Indian Smart Grid

Abstract As electricity demand is continuously increasing, the complexity and criticality of the power system infrastructure is increasing. After suffering from world’s largest power blackout on 30th and 31st July, 2012, the Indian power grids are now adopting the smart grid technologies to prevent such massive power failures. It initiated with the installation of PMUs on each strategically selected critical location in the entire grid under the Real Time Dynamic State measurements (URTDSM) scheme to attain the complete observability of the system. However, attainment of complete observability further demands selection of accurate and fast SE algorithm which is still a challenging task. The aim of this paper is to recommend the most efficient and accurate state estimator based on Linear State Estimation (LSE) algorithms for efficient real time monitoring and control of the grid, especially for Indian Power Grid. The performance test was conducted on two different SE algorithms, the Weighted Least Square (WLS) algorithm and recursive Kalman Filter algorithm. The test results are obtained on Indian 75-bus transmission system and validation is done by comparing the test results with the results obtained on standard IEEE-39 bus test system. Based on the performance comparison of the two algorithms, the selection of most suitable algorithm to be implemented in Indian power grid is achieved.

Complex system decomposition for distributed state estimation based on weighted graph

In this work, a systematic subsystem decomposition procedure for complex process systems is proposed for distributed state estimation. In the proposed procedure, both the connectivity within a system and the strength of connections are taken into account. A nonlinear process is first presented by a directed graph in which a node denotes either a state or a measured output of the nonlinear process. In the directed graph, nodes are connected via weighted edges and the weights reflect the strength of connection between two nodes. Based on the weighted directed graph, community structure detection is used to divide all the variables into smaller groups, such that the intra-connection within each group is made much stronger than the interaction among different groups. Subsystem models that are appropriate for distributed state estimation are configured based on the variables assigned to the groups. A comparative study between the proposed procedure with a procedure based on unweighted directed graph is conducted through extensive simulations. In the simulations, a numerical example and a chemical process example are considered. Three commonly used distributed state estimation algorithms designed based on the two decomposition procedures are applied to the two examples. A few guidelines on when to use weighted graphs for decomposition for distributed state estimation are concluded.

Power system state estimation with extended power formulations

An extended formulation for power system state estimation is presented. The paper shows that any active or reactive power measurement can be implemented linearly independent twice in state estimation algorithms. Thus, redundancy can be increased and, in some cases, even unobservable systems can become observable to a certain degree. The applicability and accuracy of the new formulation are investigated on two synthetic low voltage grids of different size and compared with the conventional state estimation. Five cases with different measurement configurations are considered. In cases where the conventional state estimation formulation cannot be performed, the new formulation produces good results. The paper is a contribution to problems with lack of system observability, a problem particularly often occurring in the monitoring of distribution grids.

Smoothing and parameter estimation by soft-adherence to governing equations

The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to produce accurate dimensionality reduction, parameter estimation, reduced order models, and/or balanced models for control. Data assimilation attempts to overcome the deleterious effects of noise by producing a set of algorithms for state estimation from noisy and possibly incomplete measurements. Indeed, methods such as Kalman filtering and smoothing are vital tools for scientists in fields ranging from electronics to weather forecasting. In this work we develop a novel framework for smoothing data based on known or partially known nonlinear governing equations. The method yields superior results to current techniques when applied to problems with known deterministic dynamics. By exploiting the numerical time-stepping constraints of the deterministic system, an optimization formulation can readily extract the noise from the nonlinear dynamics in a principled manner. The superior performance is due in part to the fact that it optimizes global state estimates. We demonstrate the efficiency and efficacy of the method on a number of canonical examples, thus demonstrating its viability for the wide range of potential applications stated above.

Square-root accurate continuous-discrete extended-unscented Kalman filtering methods with embedded orthogonal and J-orthogonal QR decompositions for estimation of nonlinear continuous-time stochastic models in radar tracking

This paper presents a number of new state estimation algorithms, which unify the best features of the accurate continuous-discrete extended and unscented Kalman filters in treating nonlinear continuous-time stochastic systems with discrete measurements. In particular, our mixed-type algorithms succeed in estimating continuous-discrete stochastic systems with nonlinear and/or nondifferentiable measurements. The main weakness of these methods is the need for the Cholesky decomposition of predicted covariance matrices. Such a factorization is highly sensitive to numerical integration and round-off errors committed, which may result in losing the covariance’s positivity and, hence, failing the Cholesky decomposition. The latter problem is usually solved in the form of square-root filtering implementations, which propagate not the covariance matrix but its square root (Cholesky factor), only. Unfortunately, negative weights arising in applications of our mixed-type methods to high-dimensional stochastic systems preclude from designing conventional square-root filters. We address the mentioned issue with one-rank Cholesky factor updates or with hyperbolic QR transforms used for yielding J-orthogonal square-root filters. These novel algorithms are justified theoretically and examined and compared numerically to the non-square-root one in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn, in the presence of Gaussian or glint noise.

Simultaneous spatiotemporal bias and state estimation for asynchronous multi‐sensor system

Elimination of spatiotemporal bias of asynchronous multiple sensors is the foundation of accurate multi-sensor data fusion. In this article, a sequential processing simultaneous spatiotemporal bias and state estimation algorithm for asynchronous multi-sensor system is proposed. The spatiotemporal bias is combined with target state to obtain an augmented state vector, and the augmented state model is formulated. For asynchronous multi-sensor with known but different sampling periods, a sequential processing method is proposed to handle the multiple measurements. The relationship of sensor measurements, target state and spatiotemporal bias is analysed, and the corresponding measurement model is formulated. A novel algorithm, in which the unscented Kalman filter is used to handle the nonlinearity between the augmented measurement and state vectors, is proposed to jointly estimate the spatiotemporal bias and target state. Simulation results verify the effectiveness of the proposed algorithm.

Iterated Extended Kalman Smoother-Based Variable Splitting for $L_1$-Regularized State Estimation

In this paper, we propose a new framework for solving state estimation problems with an additional sparsity-promoting $L_1$-regularizer term. We first formulate such problems as minimization of the sum of linear or nonlinear quadratic error terms and an extra regularizer, and then present novel algorithms which solve the linear and nonlinear cases. The methods are based on a combination of the iterated extended Kalman smoother and variable splitting techniques such as alternating direction method of multipliers (ADMM). We present a general algorithmic framework for variable splitting methods, where the iterative steps involving minimization of the nonlinear quadratic terms can be computed efficiently by iterated smoothing. Due to the use of state estimation algorithms, the proposed framework has a low per-iteration time complexity, which makes it suitable for solving a large-scale or high-dimensional state estimation problem. We also provide convergence results for the proposed algorithms. The experiments show the promising performance and speed-ups provided by the methods.

Variance-Constrained Recursive State Estimation for Time-Varying Complex Networks With Quantized Measurements and Uncertain Inner Coupling.

In this paper, a new recursive state estimation problem is discussed for a class of discrete time-varying stochastic complex networks with uncertain inner coupling and signal quantization under the error-variance constraints. The coupling strengths are allowed to be varying within certain intervals, and the measurement signals are subject to the quantization effects before being transmitted to the remote estimator. The focus of the conducted topic is on the design of a variance-constrained state estimation algorithm with the aim to ensure a locally minimized upper bound on the estimation error covariance at every sampling instant. Furthermore, the boundedness of the resulting estimation error is analyzed, and a sufficient criterion is established to ensure the desired exponential boundedness of the state estimation error in the mean square sense. Finally, some simulations are proposed with comparisons to illustrate the validity of the newly developed variance-constrained estimation method.

ADMM-Based Distributed State Estimation of Smart Grid Under Data Deception and Denial of Service Attacks

Smart grid (SG) represents a large-scale network system with the tight integration of a physical power network and an information network, which makes it more vulnerable to hybrid cyber attacks against different regional subsystems. First, an alternating direction method of multipliers-based distributed state estimation method is developed to overcome the limitation of conventional state estimation and performance analysis of SG against a single type of cyber attacks. Regional subsystems are partitioned via the ${K}$ -means method. Second, a novel distributed state estimation method integrated with the characteristics of data deception attacks and denial of service (DoS) attacks is proposed to account for the simultaneous presence of different cyber attacks on individual regional subsystems. Third, the convergence of a distributed state estimation algorithm under hybrid cyber attacks is proved theoretically. Furthermore, the relationships between the convergence and algorithm parameters as well as the occurring probability of DoS attacks are established. Finally, the simulations on a modified IEEE 118-bus system are given to demonstrate the feasibility and effectiveness of the proposed method.

모델 기반 배전계통 동적 상태 추정 알고리즘

Recently, some novel researches regarding the state estimation for power distribution system have been focused on the dynamic state estimation algorithm due to trend abrupt changes in the distribution system such as actions of prosumers. The previous works studied the Kalman filter for nonlinear system such as extended Kalman filter, unscented Kalman filter. They assume that the state transient model follows smoothing model of the previous states. However, it is hard to set the smoothing coefficient for the estimated states. Thus, this paper proposes the mathematical model of state transient model of power distribution system. Based on the proposed mathematical model, extended Kalman filter algorithm is adopted for dynamic state estimation. All jacobian matrices for the extended Kalman filter is derived as a function of system states, and the proposed algorithm is verified by using IEEE 15 test bus.

Dynamic Locomotion on Slippery Ground

Dynamic locomotion on unstructured and uneven terrain is a challenging task in legged robotics. Especially when it comes to slippery ground conditions, common state estimation and control algorithms suffer from the usual no-slip assumption. In fact, there has been only little research on this subject. This paper addresses the problem of slipping by treating slip detection and recovery tasks separately. Our contribution to the former is a probabilistic slip estimator based on aHidden Markov Model. In the second part of this paper, we propose impedance control and friction modulation as useful tools to recover stability during traction loss. We demonstrate the success of our estimation/control architecture by enabling ANYmal, a quadrupedal torque-controllable robot, to dynamically walk over slippery terrain.

Laser-scanner-based object state estimation and tracking control algorithms of autonomous truck using single-wheel driving module

This paper describes state estimation and tracking control algorithms for use in an autonomous truck using a single-wheel driving module and simulation-based performance evaluation with actual data from a one-layer laser scanner. In order to construct the tracking control algorithm, the one-layer laser scanner has been used to detect the object as two-dimensional point cloud data. The tracking control algorithm consists of three routines—perception, decision, and control. In the perception routine, the coordinate transformation, downsizing, clustering, and state estimation have been conducted for calculation of the object states, such as position and velocity, using point data from the one-layer laser scanner. The velocity components of the object have been estimated based on the extended Kalman filter, and the desired straight path has been derived using the estimated velocity of the object. To track the object reasonably, lateral error and yaw angle error have been defined with respect to the desired straight path. The error dynamics has been derived using a single-wheel driving module, equipped with a planar truck model based on the vehicle dynamics. Using the derived planar truck model, the optimal steering input for tracking the object has been computed based on the linear quadratic regulator. The actual point cloud data from the one-layer laser scanner has been used to conduct reasonable performance evaluation of the tracking control algorithm proposed in this study. The actual data-based performance evaluation of the algorithm has been conducted in the MATLAB/SIMULINK environment with various scenarios. The performance evaluation results show that the tracking control algorithm proposed in this study can manipulate the single-wheel driving module of the autonomous truck to track the object soundly, based on the state estimation algorithm.

Byzantine-resilient distributed observers for LTI systems

Consider a linear time-invariant (LTI) dynamical system monitored by a network of sensors, modeled as nodes of an underlying directed communication graph. We study the problem of collaboratively estimating the state of the system when certain nodes are compromised by adversaries. Specifically, we consider a Byzantine adversary model, where a compromised node possesses complete knowledge of the system dynamics and the network, and can deviate arbitrarily from the rules of any prescribed algorithm. We first characterize certain fundamental limitations of any distributed state estimation algorithm in terms of the measurement and communication structure of the nodes. We then develop an attack-resilient, provably correct state estimation algorithm that admits a fully distributed implementation. To characterize feasible network topologies that guarantee success of our proposed technique, we introduce a notion of ‘strong-robustness’ that captures both measurement and communication redundancy. Finally, by drawing connections to bootstrap percolation theory, we argue that given an LTI system and an associated sensor network, the ‘strong-robustness’ property can be checked in polynomial time.

Event based estimation with correlated noises

For a linear system having event based measurements and correlated noises, a state estimation algorithm is proposed. A general event based sampling is employed to obtain the measurements, where in the case of unavailability of measurements, event based strategy itself is used to obtain approximate state and covariance estimates. To deal with correlated noises, a two-step ahead prediction approach is employed to obtain recursive equations for estimated state and covariance. The obtained results are illustrated using a simulation example.

Vulnerability Analysis of Smart Grids to GPS Spoofing

Sensors such as phasor measurement units (PMUs) endowed with GPS receivers are ubiquitously installed providing real-time grid visibility. A number of PMUs can cooperatively enable state estimation routines. However, GPS spoofing attacks can notably alter the PMU measurements, mislead the network operator, and drastically impact subsequent corrective control actions. Leveraging a novel measurement model that explicitly accounts for the GPS spoofing attacks, this paper formulates an optimization problem to identify the most vulnerable PMUs in the network. A greedy algorithm is developed to solve the aforementioned problem. Furthermore, the paper develops a computationally efficient alternating minimization algorithm for joint state estimation and attack reconstruction. Numerical tests on IEEE benchmark networks validate the developed methods.

Power System Dynamic State Estimation: Motivations, Definitions, Methodologies, and Future Work

This paper summarizes the technical activities of the Task Force on Power System Dynamic State and Parameter Estimation. This Task Force was established by the IEEE Working Group on State Estimation Algorithms to investigate the added benefits of dynamic state and parameter estimation for the enhancement of the reliability, security, and resilience of electric power systems. The motivations and engineering values of dynamic state estimation (DSE) are discussed in detail. Then, a set of potential applications that will rely on DSE is presented and discussed. Furthermore, a unified framework is proposed to clarify the important concepts related to DSE, forecasting-aided state estimation, tracking state estimation, and static state estimation. An overview of the current progress in DSE and dynamic parameter estimation is provided. The paper also provides future research needs and directions for the power engineering community.

Estimating and Controlling the Renewable Microgrid States Using IoT Infrastructure

AbstractThis paper considers the optimal filter design issue for microgrid state estimation and stabilisation under packet loss conditions. The considered internet of things (IoT) technologies collect system state information from sensors and send control messages to actuators where they are connected over a lossy communication network. From signal processing point of view, this paper develops an optimal state estimation algorithm using the mean squared error principle. Then a feedback controller is designed under the condition of packet dropouts in the communication network. Finally, the convergence of the developed algorithm is numerically shown. The performance of the proposed schemes are demonstrated using the renewable microgrid.