scholarly journals A deterministic discretisation-step upper bound for state estimation via Clark transformations

2004 ◽  
Vol 2004 (4) ◽  
pp. 371-384 ◽  
Author(s):  
W. P. Malcolm ◽  
R. J. Elliott ◽  
J. van der Hoek
Keyword(s):  
State Estimation ◽  
Upper Bound ◽  
Continuous Time ◽  
A Priori ◽  
The State ◽  
Approximation Schemes ◽  
Grid Step ◽  
Robust Filters ◽  
Robust Smoothing ◽  
Standard Approximation

We consider the numerical stability of discretisation schemes for continuous-time state estimation filters. The dynamical systems we consider model the indirect observation of a continuous-time Markov chain. Two candidate observation models are studied. These models are (a) the observation of the state through a Brownian motion, and (b) the observation of the state through a Poisson process. It is shown that for robust filters (via Clark's transformation), one can ensure nonnegative estimated probabilities by choosing a maximum grid step to be no greater than a given bound. The importance of this result is that one can choose an a priori grid step maximum ensuring nonnegative estimated probabilities. In contrast, no such upper bound is available for the standard approximation schemes. Further, this upper bound also applies to the corresponding robust smoothing scheme, in turn ensuring stability for smoothed state estimates.

scholarly journals Study on the Initial Value Problem for Fractional-order Cubature Kalman Filters of Nonlinear Continuous-time Fractional-order Systems

2021 ◽  
Author(s):  
Chuang Yang ◽  
Zhe Gao ◽  
Yue Miao ◽  
Tao Kan
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Fractional Order ◽  
Continuous Time ◽  
Kalman Filters ◽  
The State ◽  
Order System ◽  
Initial Value ◽  
Cubature Kalman Filter ◽  
Augmented State

Abstract To realize the state estimation of a nonlinear continuous-time fractional-order system, two types of fractional-order cubature Kalman filters (FOCKFs) designed to solve problem on the initial value influence. For the first type of cubature Kalman filter (CKF), the initial value of the estimated system are also regarded as the augmented state, the augmented state equation is constructed to obtain the CKF based on Grünwald-Letnikov difference. For the second type of CKF, the fractional-order hybrid extended-cubature Kalman filter (HECKF) is proposed to weaken the influence of initial value by the first-order Taylor expansion and the third-order spherical-radial rule. These two methods can effectively reduce the influence of initial value on the state estimation. Finally, the effectiveness of the proposed CKFs is verified by two simulation examples.

scholarly journals On the Properties of the Reaction Counts Chemical Master Equation

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 607
Author(s):  
Sunkara
Keyword(s):  
Master Equation ◽  
State Space ◽  
Continuous Time ◽  
A Priori ◽  
Chemical Master Equation ◽  
The State ◽  
High Dimensional ◽  
Population Counts ◽  
Theoretical Results ◽  
Over Time

The reaction counts chemical master equation (CME) is a high-dimensional variant ofthe classical population counts CME. In the reaction counts CME setting, we count the reactionswhich have fired over time rather than monitoring the population state over time. Since a reactioneither fires or not, the reaction counts CME transitions are only forward stepping. Typically thereare more reactions in a system than species, this results in the reaction counts CME being higher indimension, but simpler in dynamics. In this work, we revisit the reaction counts CME frameworkand its key theoretical results. Then we will extend the theory by exploiting the reactions counts’forward stepping feature, by decomposing the state space into independent continuous-time Markovchains (CTMC). We extend the reaction counts CME theory to derive analytical forms and estimatesfor the CTMC decomposition of the CME. This new theory gives new insights into solving hittingtimes-, rare events-, and a priori domain construction problems.

An upper bound of mean-square error in state estimation with quantized measurements

2018 ◽  
Vol 41 (2) ◽  
pp. 582-590 ◽  
Author(s):  
Bin Hu ◽  
Zhiping Shen ◽  
Weizhou Su
Keyword(s):  
State Estimation ◽  
Upper Bound ◽  
Linear Time ◽  
Estimation Error ◽  
Data Rate ◽  
The State ◽  
Design Parameters ◽  
Discrete Time System ◽  
State Estimator ◽  
Linear Time Invariant

In this paper, we study the state estimation for a linear time-invariant (LTI) discrete-time system with quantized measurements. The quantization law under consideration has a time-varying data rate. To cope with nonlinearities in quantization laws and to analyse stability in the state estimation problem, a Kalman-filter-based sub-optimal state estimator is developed and an upper bound of its estimation error covariance is minimized. It turns out that, to guarantee the convergence of the upper bound, the averaged data rate of the quantization law must be greater than a minimum rate. This minimum data rate for the quantization law is presented in terms of the poles of the system and design parameters in the state estimator. Numerical examples are presented to illustrate the results in this work.

Analyzing the State Estimation Software Package Reliability Using the Fault Tree Technology

2018 ◽  
Vol 6 (6) ◽  
pp. 24-34
Author(s):  
Irina N. KOLOSOK ◽  
◽  
Elena S. KORKINA ◽  
Alexandr V. TIKHONOV ◽  
◽  
...  
Keyword(s):  
State Estimation ◽  
Software Package ◽  
Fault Tree ◽  
The State ◽  
Package Reliability

State Estimation Using Randomly Delayed Measurements

1993 ◽  
Vol 115 (1) ◽  
pp. 19-26 ◽  
Author(s):  
A. Ray ◽  
L. W. Liou ◽  
J. H. Shen
Keyword(s):  
State Estimation ◽  
Minimum Variance ◽  
The State ◽  
Sensor Data ◽  
State Estimator ◽  
Uniform Asymptotic Stability ◽  
Simulation Experiments ◽  
State Estimate ◽  
Sampling Instant ◽  
Recursive Relations

This paper presents a modification of the conventional minimum variance state estimator to accommodate the effects of randomly varying delays in arrival of sensor data at the controller terminal. In this approach, the currently available sensor data is used at each sampling instant to obtain the state estimate which, in turn, can be used to generate the control signal. Recursive relations for the filter dynamics have been derived, and the conditions for uniform asymptotic stability of the filter have been conjectured. Results of simulation experiments using a flight dynamic model of advanced aircraft are presented for performance evaluation of the state estimation filter.

scholarly journals A Two-Step State Estimation Algorithm for Hybrid AC-DC Distribution Grids

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1967
Author(s):  
Gaurav Kumar Roy ◽  
Marco Pau ◽  
Ferdinanda Ponci ◽  
Antonello Monti
Keyword(s):  
State Estimation ◽  
Distribution System ◽  
Renewable Energy Sources ◽  
Estimation Algorithm ◽  
The State ◽  
Second Step ◽  
Distribution Grid ◽  
Dc Distribution ◽  
Attractive Option ◽  
Distribution Grids

Direct Current (DC) grids are considered an attractive option for integrating high shares of renewable energy sources in the electrical distribution grid. Hence, in the future, Alternating Current (AC) and DC systems could be interconnected to form hybrid AC-DC distribution grids. This paper presents a two-step state estimation formulation for the monitoring of hybrid AC-DC grids. In the first step, state estimation is executed independently for the AC and DC areas of the distribution system. The second step refines the estimation results by exchanging boundary quantities at the AC-DC converters. To this purpose, the modulation index and phase angle control of the AC-DC converters are integrated into the second step of the proposed state estimation formulation. This allows providing additional inputs to the state estimation algorithm, which eventually leads to improve the accuracy of the state estimation results. Simulations on a sample AC-DC distribution grid are performed to highlight the benefits resulting from the integration of these converter control parameters for the estimation of both the AC and DC grid quantities.

scholarly journals State Estimation for Cooperative Lateral Vehicle Following Using Vehicle-to-Vehicle Communication

Electronics ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 651
Author(s):  
Wouter Schinkel ◽  
Tom van der Sande ◽  
Henk Nijmeijer
Keyword(s):  
State Estimation ◽  
Cooperative Control ◽  
The State ◽  
State Estimator ◽  
Estimation Process ◽  
Vehicle Communication ◽  
Vehicle To Vehicle ◽  
Control Schemes ◽  
Input Signals ◽  
Vehicle To Vehicle Communication

A cooperative state estimation framework for automated vehicle applications is presented and demonstrated via simulations, the estimation framework is used to estimate the state of a lead and following vehicle simultaneously. Recent developments in the field of cooperative driving require novel techniques to ensure accurate and stable vehicle following behavior. Control schemes for the cooperative control of longitudinal and lateral vehicle dynamics generally require vehicle state information about the lead vehicle, which in some cases cannot be accurately measured. Including vehicle-to-vehicle communication in the state estimation process can provide the required input signals for the practical implementation of cooperative control schemes. This study is focused on demonstrating the benefits of using vehicle-to-vehicle communication in the state estimation of a lead and following vehicle via simulations. The state estimator, which uses a cascaded Kalman filtering process, takes the operating frequencies of different sensors into account in the estimation process. Simulation results of three different driving scenarios demonstrate the benefits of using vehicle-to-vehicle communication as well as the attenuation of measurement noise. Furthermore, in contrast to relying on low frequency measurement data for the input signals of cooperative control schemes, the state estimator provides a state estimate at every sample.

scholarly journals Methodology for Implementing the State Estimation in Renewable Energy Management Systems

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2301
Author(s):  
Yun-Sung Cho ◽  
Yun-Hyuk Choi
Keyword(s):  
Renewable Energy ◽  
Power Systems ◽  
State Estimation ◽  
Measurement Errors ◽  
Large Scale ◽  
Test System ◽  
The State ◽  
Inner Function ◽  
Outer Function ◽  
Bad Data

This paper describes a methodology for implementing the state estimation and enhancing the accuracy in large-scale power systems that partially depend on variable renewable energy resources. To determine the actual states of electricity grids, including those of wind and solar power systems, the proposed state estimation method adopts a fast-decoupled weighted least square approach based on the architecture of application common database. Renewable energy modeling is considered on the basis of the point of data acquisition, the type of renewable energy, and the voltage level of the bus-connected renewable energy. Moreover, the proposed algorithm performs accurate bad data processing using inner and outer functions. The inner function is applied to the largest normalized residue method to process the bad data detection, identification and adjustment. While the outer function is analyzed whether the identified bad measurements exceed the condition of Kirchhoff’s current law. In addition, to decrease the topology and measurement errors associated with transformers, a connectivity model is proposed for transformers that use switching devices, and a transformer error processing technique is proposed using a simple heuristic method. To verify the performance of the proposed methodology, we performed comprehensive tests based on a modified IEEE 18-bus test system and a large-scale power system that utilizes renewable energy.

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