scholarly journals State Uncertainty Normality Detection

2019 ◽  
Vol 67 (3) ◽  
pp. 1044-1062
Author(s):  
Sven K. Flegel ◽  
James C. Bennett
Keyword(s):  
State Estimation ◽  
Orbit Determination ◽  
Estimation Error ◽  
The State ◽  
Body Motion ◽  
Optical Observations ◽  
Test Cases ◽  
Unscented Transform ◽  
State Uncertainty ◽  
Random Particle

AbstractTwo fundamentally different approaches of determining normality of the probability density function of the state estimation error are compared by application to a range of test cases. The first method is the Henze-Zirkler test, which operates on a random particle sample. The variability of its result is quantified. Using this method, departure from normality has been found to occur in three stages which are detailed. The second test compares the offset in whitened space of the predicted state to the predicted covariance mean obtained from the unscented transform. This test is much more efficient than the random particle based approach and can be applied using any perturbations model. The comparison is performed on the state estimation error in Cartesian space and using two-body motion without process noise. The more efficient, unscented transform based approach shows excellent agreement with the Henze-Zirkler test for constructed test cases. Application to orbit determination results from passive optical observations assessed with a Batch-Least-Squares orbit determination however reveals some discrepancies which have yet to be understood and underline the importance of rigorous testing.

scholarly journals Performance and stochastic stability of the adaptive fading extended Kalman filter with the matrix forgetting factor

2016 ◽  
Vol 14 (1) ◽  
pp. 934-945
Author(s):  
Cenker Biçer ◽  
Levent Özbek ◽  
Hasan Erbay
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Extended Kalman Filter ◽  
Stochastic Systems ◽  
Estimation Error ◽  
The State ◽  
Forgetting Factor ◽  
The Matrix ◽  
Stochastic Framework ◽  
Theoretical Results

AbstractIn this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable.The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.

scholarly journals Parameter and State Estimation of Shear Buildings Using Spline Interpolation and Linear Integral Filters

2018 ◽  
Vol 2018 ◽  
pp. 1-21
Author(s):  
Antonio Concha ◽  
Luis Alvarez-Icaza
Keyword(s):  
State Estimation ◽  
Spline Interpolation ◽  
Estimation Error ◽  
Fast Response ◽  
High Gain ◽  
The State ◽  
Small Scale ◽  
Identification Method ◽  
Linear Integral ◽  
Shear Building

A parameter identification method and a high gain observer are proposed in order to identify the model and to recover the state of a seismically excited shear building using acceleration responses of the ground and instrumented floors levels, as well as the responses at noninstrumented floors, which are reconstructed by means of cubic spline shape functions. The identification method can be implemented online or offline and uses Linear Integral Filters, whose bandwidth must enclose the spectrum of a seismically excited building. On the other hand, the proposed state observer estimates the displacements and velocities of all the structure floors using the model estimated by the identification method. The observer allows obtaining a fast response and reducing the state estimation error, while depending on a single gain. The performance of the parameter and state estimators is verified through experiments carried out on a five-story small scale building.

scholarly journals Cooperative Localization Approach for Multi-Robot Systems Based on State Estimation Error Compensation

Sensors ◽  
2019 ◽  
Vol 19 (18) ◽  
pp. 3842 ◽  
Author(s):  
Zhang ◽  
Cao
Keyword(s):  
State Estimation ◽  
Error Compensation ◽  
Estimation Error ◽  
The State ◽  
Cooperative Localization ◽  
Communication Delays ◽  
Extended Kalman Filtering ◽  
Robot Systems ◽  
Localization Approach ◽  
Multi Robot

In order to improve the localization accuracy of multi-robot systems, a cooperative localization approach with communication delays was proposed in this paper. In the proposed method, the reason for the time delay of the robots’ cooperative localization approach was analyzed first, and then the state equation and measure equation were reconstructed by introducing the communication delays into the states and measurements. Furthermore, the cooperative localization algorithm using the extended Kalman filtering technique based on state estimation error compensation was proposed to reduce the state estimation error of delay filtering. Finally, the simulation and experiment results demonstrated that the proposed algorithm can achieve good performance in location in the presence of communication delay while having reduced computational and communicative cost.

scholarly journals Distributed State Estimation Based Distributed Model Predictive Control

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1327
Author(s):  
Jing Zeng ◽  
Jinfeng Liu
Keyword(s):  
Model Predictive Control ◽  
State Estimation ◽  
Predictive Control ◽  
Estimation Error ◽  
The State ◽  
Distributed Model ◽  
Actual State ◽  
Output Measurement ◽  
Distributed Model Predictive Control ◽  
Distributed State Estimation

In this work, we consider output-feedback distributed model predictive control (DMPC) based on distributed state estimation with bounded process disturbances and output measurement noise. Specifically, a state estimation scheme based on observer-enhanced distributed moving horizon estimation (DMHE) is considered for distributed state estimation purposes. The observer-enhanced DMHE ensures that the state estimates of the system reach a small neighborhood of the actual state values quickly and then maintain within the neighborhood. This implies that the estimation error is bounded. Based on the state estimates provided by the DMHE, a DMPC algorithm is developed based on Lyapunov techniques. In the proposed design, the DMHE and the DMPC are evaluated synchronously every sampling time. The proposed output DMPC is applied to a simulated chemical process and the simulation results show the applicability and effectiveness of the proposed distributed estimation and control approach.

Adaptive estimation algorithm of boost-phase trajectory using binary asynchronous observation

2016 ◽  
Vol 230 (14) ◽  
pp. 2661-2672 ◽  
Author(s):  
Nan Wu ◽  
Lei Chen ◽  
Yongjun Lei ◽  
Fankun Meng
Keyword(s):  
State Estimation ◽  
Phase Trajectory ◽  
Prior Information ◽  
Estimation Error ◽  
The State ◽  
Estimation Accuracy ◽  
Unknown Input ◽  
Noise Variance ◽  
Process Noise ◽  
Variance Matrix

A kind of adaptive filter algorithm based on the estimation of the unknown input is proposed for studying the adaptive adjustment of process noise variance of boost phase trajectory. Polynomial model is used as the motion model of the boost trajectory, truncation error is regarded as an equivalent to the process noise and the unknown input and process noise variance matrix is constructed from the estimation value of unknown input according to the quantitative relationship among the unknown input, the state estimation error, and optimal process noise variance. The simulation results show that in the absence of prior information, the unknown input is estimated effectively in terms of magnitude, a positive definite matrix of process noise covariance which is close to the optimal value is constructed real-timely, and the state estimation error approximates the error lower bound of the optimal estimation. The estimation accuracy of the proposed algorithm is similar to that of the current statistical model algorithm using accurate prior information.

Nonlinear State Estimation Using Aggregate Modeling

2007 ◽  
Author(s):  
Kiriakos Kiriakidis ◽  
Matthew Feemster ◽  
Richard T. O’Brien
Keyword(s):  
State Estimation ◽  
Estimation Error ◽  
The State ◽  
Linear Feedback ◽  
Aggregate Model ◽  
Nonlinear State Estimation ◽  
Aggregate Modeling ◽  
Error Dynamics ◽  
The Stability ◽  
Nonlinear State

The paper addresses the state estimation problem for a general class of nonlinear systems. Using an expansion of nonlinear drift dynamics in terms of an aggregate model, the authors analyze the stability of the estimation error equation. Although the treatment is limited to linear feedback, the method results in quadratically stable error dynamics inside a large subset of the state space. The authors tested and verified the proposed approach on the nonlinear dynamics of the rotary pendulum.

scholarly journals Design of a decentralized detection of interacting LTI systems

2002 ◽  
Vol 8 (3) ◽  
pp. 233-248 ◽  
Author(s):  
Shamanth Shankar ◽  
Swaroop Darbha ◽  
Aniruddha Datta
Keyword(s):  
State Estimation ◽  
Error Propagation ◽  
Estimation Error ◽  
Design Procedure ◽  
The State ◽  
Decentralized Detection ◽  
Estimation Errors ◽  
Look Ahead ◽  
Important Concern ◽  
Detection Filter

In this paper, the problem of designing a decentralized detection filter for a large homogeneous collection of LTI systems is considered. The collection of systems considered here draws inspiration from platoons of vehicles, and the considered interactions amongst systems in the collection are banded and lower triangular, mimicking the typical “look-ahead” nature of interactions in a platoon of vehicles. A fault in a system propagates to other systems in the collection via such interactions.The decentralized detection filter for the collection is composed of interacting detection filters, one for each system. The feasibility of communicating the state estimates to other systems in the collection is assumed here. An important concern is the propagation of state estimation errors. In order that the state estimation errors not amplify as they propagate, aℋ∞constraint on the state estimation error propagation dynamics is imposed. A sufficient condition for constructing a decentralized detection filter for the collection is presented. An example is provided to illustrate the design procedure.

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.

Sign in / Sign up

Export Citation Format

Share Document