An upper bound on average estimation error in nonlinear systems

1968 ◽  
Vol 14 (2) ◽  
pp. 243-250 ◽  
Author(s):  
L. Seidman
Keyword(s):  
Nonlinear Systems ◽  
Upper Bound ◽  
Estimation Error ◽  
Average Estimation Error

scholarly journals Event-Triggering State and Fault Estimation for a Class of Nonlinear Systems Subject to Sensor Saturations

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1242
Author(s):  
Cong Huang ◽  
Bo Shen ◽  
Lei Zou ◽  
Yuxuan Shen
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations ◽  
Estimation Error ◽  
Upper Bounds ◽  
The State ◽  
Fault Estimation ◽  
Triggering Mechanism ◽  
Transmission Frequency ◽  
Current Transmission ◽  
Event Triggering

This paper is concerned with the state and fault estimation issue for nonlinear systems with sensor saturations and fault signals. For the sake of avoiding the communication burden, an event-triggering protocol is utilized to govern the transmission frequency of the measurements from the sensor to its corresponding recursive estimator. Under the event-triggering mechanism (ETM), the current transmission is released only when the relative error of measurements is bigger than a prescribed threshold. The objective of this paper is to design an event-triggering recursive state and fault estimator such that the estimation error covariances for the state and fault are both guaranteed with upper bounds and subsequently derive the gain matrices minimizing such upper bounds, relying on the solutions to a set of difference equations. Finally, two experimental examples are given to validate the effectiveness of the designed algorithm.

RF Vital Sign Sensing under Free Body Movement

2021 ◽  
Vol 5 (3) ◽  
pp. 1-22
Author(s):  
Jian Gong ◽  
Xinyu Zhang ◽  
Kaixin Lin ◽  
Ju Ren ◽  
Yaoxue Zhang ◽  
...  
Keyword(s):  
Vital Sign ◽  
Estimation Error ◽  
Body Movement ◽  
Vital Signs ◽  
Motion Artifacts ◽  
Body Parts ◽  
Training Scheme ◽  
Pattern Movement ◽  
Free Body ◽  
Average Estimation Error

Radio frequency (RF) sensors such as radar are instrumental for continuous, contactless sensing of vital signs, especially heart rate (HR) and respiration rate (RR). However, decades of related research mainly focused on static subjects, because the motion artifacts from other body parts may easily overwhelm the weak reflections from vital signs. This paper marks a first step in enabling RF vital sign sensing under ambulant daily living conditions. Our solution is inspired by existing physiological research that revealed the correlation between vital signs and body movement. Specifically, we propose to combine direct RF sensing for static instances and indirect vital sign prediction based on movement power estimation. We design customized machine learning models to capture the sophisticated correlation between RF signal pattern, movement power, and vital signs. We further design an instant calibration and adaptive training scheme to enable cross-subjects generalization, without any explicit data labeling from unknown subjects. We prototype and evaluate the framework using a commodity radar sensor. Under a variety of moving conditions, our solution demonstrates an average estimation error of 5.57 bpm for HR and 3.32 bpm for RR across multiple subjects, which largely outperforms state-of-the-art systems.

GET: A Function for Preferential Site Selection of Additional Borehole Drilling

2004 ◽  
Vol 13 (1-4) ◽  
pp. 139-146 ◽  
Author(s):  
A.A. HASSANIPAK ◽  
M. SHARAFODIN
Keyword(s):  
Site Selection ◽  
Estimation Error ◽  
Central Iran ◽  
Vertical Column ◽  
Preferential Site ◽  
Borehole Drilling ◽  
Average Estimation Error ◽  
Linear Product ◽  
Selection Of

Abstract The essential aims of additional borehole drilling are to improve the reliability of grade and tonnage estimates in each reserve class and to increase ore tonnages. The “GET” function presented in this paper considers strategies for achieving both of these goals simultaneously, and therefore is advantageous for selecting sites for additional boreholes. The “GET” function is either a linear or a non-linear product of three variables G, E, and T: f(G,E,T,) = GαEβTγ where the values of any or all of the exponents α, β, and γ may differ from unity at the discretion of the user. G and E are the average estimated block grade and the average estimation error for ore blocks in one vertical column, and T is the compounded ore thickness within the column. To illustrate its utility, the GET function has been used for determination of the most advantageous sites for additional drilling in the Shah-Kuh Pb-Zn deposit in west central Iran.

Robust State Estimation for Linear Systems

1993 ◽  
Vol 115 (1) ◽  
pp. 193-196
Author(s):  
S. S. Garimella ◽  
K. Srinivasan
Keyword(s):  
Dynamic System ◽  
State Estimation ◽  
Real Time ◽  
Linear Systems ◽  
Upper Bound ◽  
Estimation Error ◽  
System Model ◽  
Linear Dynamic ◽  
Modeling Errors ◽  
System States

Real-time state estimation of a linear dynamic system using an observer, in the presence of modeling errors in the system model used by the observer and uncertainty in the initial system states, is considered here. A guideline for designing observers for multioutput systems is established, based on an expression for an upper bound on the norm of the state estimation error derived in this paper. An example is presented to illustrate the usefulness of this guideline.

scholarly journals An interval observer design for uncertain nonlinear systems based on the T-S fuzzy model

2017 ◽  
Vol 27 (3) ◽  
pp. 397-407 ◽  
Author(s):  
Yamina Menasria ◽  
Hichem Bouras ◽  
Nasreddine Debbache
Keyword(s):  
Nonlinear Systems ◽  
Estimation Error ◽  
Fuzzy Model ◽  
Observer Design ◽  
Pole Placement ◽  
Dynamic State ◽  
New Approach ◽  
Dynamic State Estimation ◽  
Interval Observer ◽  
Takagi Sugeno

AbstractA new approach to build an interval observer for nonlinear uncertain systems is presented in this paper. Nonlinear systems modeled in the Takagi-Sugeno (T-S) form are studied. A T-S proportional observer is first issued by pole-placement and LMI tools. Secondly, time-varying change of coordinates for each dynamic state estimation error is used to design an interval observer. The system state bounds are then directly deduced.

Perturbation observer-based adaptive passive control for nonlinear systems with uncertainties and disturbances

2016 ◽  
Vol 40 (4) ◽  
pp. 1223-1236 ◽  
Author(s):  
B Yang ◽  
L Jiang ◽  
CK Zhang ◽  
YY Sang ◽  
T Yu ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Passive Control ◽  
Estimation Error ◽  
High Gain ◽  
Parametric Estimation ◽  
System Stability ◽  
Nonlinearity Parameter ◽  
Fast Time ◽  
Control Effort ◽  
Control Scheme

In this paper, a perturbation observer-based adaptive passive control scheme is developed to provide great robustness of nonlinear systems against the unpredictable uncertainties and disturbances therein. The proposed scheme includes a high-gain perturbation observer and a robust passive controller. The high-gain perturbation observer is designed to estimate online the perturbation aggregated from the combinatorial effect of system nonlinearity, parameter uncertainty, unmodelled dynamics and fast time-varying external disturbances. Then the robust passive controller, using the estimated perturbation, can produce the minimal control effort needed to compensate for the magnitude of the actual current perturbation. Furthermore, the convergence of estimation error of the high-gain perturbation observer and the closed-loop system stability are analyzed theoretically. Finally, two practical examples are given to show the effectiveness and advantages of the proposed approach over the accurate model-based passive control scheme and the linearly parametric estimation-based adaptive passive control scheme.

scholarly journals Impulsive State Estimation for Nonlinear Systems with Redundant Communication Channels and Markov Delay

2021 ◽  
Author(s):  
Hong-Xia Rao ◽  
Yuru Guo ◽  
Ye Kuang ◽  
Ming Lin ◽  
Yong Xu
Keyword(s):  
Nonlinear Systems ◽  
State Estimation ◽  
Communication Channel ◽  
Impulsive Control ◽  
Estimation Error ◽  
Packet Dropout ◽  
Moving Vehicle ◽  
Current State ◽  
Error System ◽  
Impulsive Control Strategy

Abstract The state estimation issue for the discrete-time nonlinear systems with Markov delay is investigated in this paper, where the redundant communication channel is considered to ensure the reliability of transmission. Because the channel capacity is limited, the packet dropout conditions of the main channel and the redundant channel are described by the Bernoulli stochastic variables. In addition, a mode-dependent estimator is proposed based on the current state and the delayed state, simultaneously. Combining with the impulsive control strategy, the efficiency of estimator is improved. An augmented estimation error system is proposed to deal with the Markov delay in the nonlinear system, subsequently, a sufficient condition that ensures the asymptotic stability of the augmented error system is obtained by a constructed Lyapunov functional candidate and the gains of the impulsive estimator are derived. Finally, a numerical example of moving vehicle is utilized to illustrate the developed results.

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