State Estimation of an Advanced Rowing Machine Using Optimized Kalman Filtering

2017 ◽  
Author(s):  
Hanieh Mohammadi ◽  
Gholamreza Khademi ◽  
Dan Simon ◽  
Hanz Richter
Keyword(s):  
Standard Deviation ◽  
State Estimation ◽  
Estimation Error ◽  
Simultaneous Estimation ◽  
Force Estimation ◽  
Estimation Errors ◽  
Input Force ◽  
Load Cells ◽  
Friction Models ◽  
Active Impedance

This research addresses the problem of state estimation of an advanced rowing machine with energy regeneration. It is assumed that the states of the system, which are position, velocity, and capacitor charge, are measurable. The user force input to the system can be measured by load cells. It is shown that the need for load cells can be eliminated by estimating the force with an unknown-input Kalman filter. The estimated states and the unknown user force input are passed to the controller of the system, which is either an inversion-based controller or a semi-active impedance controller. Two friction models are considered for this system: Coulomb friction, and LuGre friction. The Kalman gains are tuned using an evolutionary algorithm to minimize the standard deviation of the estimation error. The results verify the effectiveness of the proposed approach for simultaneous estimation of the states and the input force. The standard deviation of the state estimation errors are only 10% of their measurement noise. The standard deviation of the input force estimation error is 0.1 N when using an optimized Kalman gain, which is only 25% of the value obtained when using manually tuned gains.

scholarly journals Ground Reaction Force Estimation in Prosthetic Legs With Nonlinear Kalman Filtering Methods

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
Seyed Fakoorian ◽  
Vahid Azimi ◽  
Mahmoud Moosavi ◽  
Hanz Richter ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Continuous Time ◽  
Lyapunov Functions ◽  
Unscented Kalman Filter ◽  
Estimation Error ◽  
Reaction Force ◽  
Force Estimation ◽  
Joint Angles ◽  
Estimation Errors ◽  
Reaction Forces

A method to estimate ground reaction forces (GRFs) in a robot/prosthesis system is presented. The system includes a robot that emulates human hip and thigh motion, along with a powered (active) transfemoral prosthetic leg. We design a continuous-time extended Kalman filter (EKF) and a continuous-time unscented Kalman filter (UKF) to estimate not only the states of the robot/prosthesis system but also the GRFs that act on the foot. It is proven using stochastic Lyapunov functions that the estimation error of the EKF is exponentially bounded if the initial estimation errors and the disturbances are sufficiently small. The performance of the estimators in normal walk, fast walk, and slow walk is studied, when we use four sensors (hip displacement, thigh, knee, and ankle angles), three sensors (thigh, knee, and ankle angles), and two sensors (knee and ankle angles). Simulation results show that when using four sensors, the average root-mean-square (RMS) estimation error of the EKF is 0.0020 rad for the joint angles and 11.85 N for the GRFs. The respective numbers for the UKF are 0.0016 rad and 7.98 N, which are 20% and 33% lower than those of the EKF.

scholarly journals Macroscopic Traffic State Estimation: Understanding Traffic Sensing Data-Based Estimation Errors

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Paul B. C. van Erp ◽  
Victor L. Knoop ◽  
Serge P. Hoogendoorn
Keyword(s):  
State Estimation ◽  
Traffic Management ◽  
Estimation Error ◽  
Ground Truth ◽  
Traffic Information ◽  
Estimation Errors ◽  
Sensing Data ◽  
Traffic Conditions ◽  
Traffic State ◽  
Traffic State Estimation

Traffic state estimation is a crucial element in traffic management systems and in providing traffic information to road users. In this article, we evaluate traffic sensing data-based estimation error characteristics in macroscopic traffic state estimation. We consider two types of sensing data, that is, loop-detector data and probe speed data. These data are used to estimate the mean speed in a discrete space-time mesh. We assume that there are no errors in the sensing data. This allows us to study the errors resulting from the differences in characteristics between the sensing data and desired estimate together with the incomplete description of the relation between the two. The aim of the study is to evaluate the dependency of this estimation error on the traffic conditions and sensing data characteristics. For this purpose, we use microscopic traffic simulation, where we compare the estimates with the ground truth using Edie’s definitions. The study exposes a relation between the error distribution characteristics and traffic conditions. Furthermore, we find that it is important to account for the correlation between individual probe data-based estimation errors. Knowledge related to these estimation errors contributes to making better use of the available sensing data in traffic state estimation.

scholarly journals Simultaneous Estimation of Rebar Diameter and Cover Thickness by a GPR-EMI Dual Sensor

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 2969 ◽  
Author(s):  
Feng Zhou ◽  
Zhongchang Chen ◽  
Hai Liu ◽  
Jie Cui ◽  
Billie Spencer ◽  
...  
Keyword(s):  
Estimation Error ◽  
Minimum Mean Square Error ◽  
Safety Evaluation ◽  
Concrete Surface ◽  
Simultaneous Estimation ◽  
Reinforcing Bars ◽  
Estimation Errors ◽  
Dual Sensor ◽  
Cover Thickness ◽  
Ground Penetrating

Precise characterization of reinforcing bars (rebars) in a concrete structure is of significant importance for construction quality control and post-disaster safety evaluation. This paper integrates ground-penetrating radar (GPR) and electromagnetic induction (EMI) methods for simultaneous estimation of rebar diameter and cover thickness. A prototype of GPR-EMI dual sensor is developed, and a calibration experiment is conducted to collect a standard EMI dataset corresponding to various rebar diameters and cover thicknesses. The handheld testing cart can synchronously collect both GPR and EMI data when moving on the concrete surface, from which a data processing algorithm is proposed to simultaneously estimate the rebar diameter and cover thickness. Firstly, by extracting the apex of the hyperbolic reflection from the rebar in the preprocessed GPR profile, the rebar position is determined and further used to extract the effective EMI curve. Then, the rebar diameter and cover thickness are simultaneously estimated from the minimum mean square error between the measured and calibrated EMI data under the constraint of the GPR-estimated cover thickness. A laboratory experiment is performed using four casted concrete specimens with 11 embedded steel rebars. The results show that the diameters of 10 rebars are correctly estimated out of the 11 rebars, and the maximum estimation error for the cover thickness is 6.7%. A field trial is carried out in a newly-constructed building, and the diameters of four tested rebars are all accurately estimated while the estimation errors of the cover thickness are less than 5%. It is concluded that the developed GPR-EMI dual sensor and the proposed algorithm can estimate the rebar diameter and cover thickness accurately by a single scan.

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.

Improved particle fusing geometric relation between particles in FastSLAM

Robotica ◽  
2009 ◽  
Vol 27 (6) ◽  
pp. 853-859 ◽  
Author(s):  
Inkyu Kim ◽  
Nosan Kwak ◽  
Heoncheol Lee ◽  
Beomhee Lee
Keyword(s):  
Standard Deviation ◽  
Particle Filter ◽  
Computer Simulations ◽  
Estimation Error ◽  
Simultaneous Localization And Mapping ◽  
Estimation Errors ◽  
Localization And Mapping ◽  
Geometric Relation ◽  
Error Standard Deviation ◽  
Over Time

SUMMARYFastSLAM is a framework for simultaneous localization and mapping using a Rao-Blackwellized particle filter (RBPF). But, FastSLAM is known to degenerate over time due to the loss of particle diversity, mainly caused by the particle depletion problem in resampling phase. In this work, improved particle filter using geometric relation between particles is proposed to restrain particle depletion and to reduce estimation errors and error variances. It uses a KD tree (k-dimensional tree) to derive geometric relation among particles and filters particles with importance weight conditions for resampling. Compared to the original particle filter used in FastSLAM, this technique showed less estimation error with lower error standard deviation in computer simulations.

Theoretical and Experimental Investigation of Force Estimation Errors Using Active Magnetic Bearings With Embedded Hall Sensors

2012 ◽  
Author(s):  
Andreas Jauernik Voigt ◽  
Ilmar F. Santos
Keyword(s):  
Dynamic Testing ◽  
Estimation Error ◽  
Magnetic Bearings ◽  
Fe Model ◽  
Active Magnetic Bearings ◽  
Force Estimation ◽  
Estimation Errors ◽  
Force Equation ◽  
Hall Sensors ◽  
Error Behavior

This paper gives an original theoretical and experimental contribution to the issue of reducing force estimation errors, which arise when applying Active Magnetic Bearings (AMBs) with pole embedded Hall sensors for force quantification purposes. Motivated by the prospect of increasing the usability of AMBs by embedding Hall sensors instead of mounting these directly on the pole surfaces, force estimation errors are investigated both numerically and experimentally. A linearized version of the conventionally applied quadratic correspondence between measured Hall voltage and applied AMB force is suggested and investigated. A finite element (FE) model is constructed to study force error behavior as a function of rotor offset. The investigation confirms that the magnitude of the force error is dependent on how well the rotor is centered in the AMB. Furthermore, below a rotor offset corresponding to ∼20% of the nominal air gap the force estimation error is found to be reduced by the linearized force equation as compared to the quadratic force equation, which is supported by experimental results. Additionally the FE model is employed in a comparative study of the force estimation error behavior for pole embedded and pole surface mounted Hall sensors. It is shown that in a given range of bias currents and rotor offsets, pole embedded and surface mounted Hall sensors perform equally well for the four pole heteropolar flux-split radial AMB under investigation. Furthermore, frequency dependence of the Hall sensor sensitivity factors is investigated, and found to be non-existing, hence static calibration of Hall sensors is sufficient, even for dynamic testing purposes.

scholarly journals Regional robust secure precise wireless transmission design for multi-user UAV broadcasting system

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Tong Shen ◽  
Tingting Liu ◽  
Yan Lin ◽  
Yongpeng Wu ◽  
Feng Shu ◽  
...  
Keyword(s):  
Estimation Error ◽  
Wireless Transmission ◽  
Artificial Noise ◽  
Target Area ◽  
Secrecy Rate ◽  
Estimation Errors ◽  
Transmission Design ◽  
Broadcasting System ◽  
Aerial Vehicle ◽  
Noise Ratio

Abstract In this paper, two regional robust secure precise wireless transmission (SPWT) schemes for multi-user unmanned aerial vehicle (UAV), (1)regional signal-to-leakage-and-noise ratio (SLNR) and artificial-noise-to-leakage-and-noise ratio (ANLNR) (R-SLNR-ANLNR) maximization and (2) point SLNR and ANLNR (P-SLNR-ANLNR) maximization, are proposed to tackle with the estimation errors of the target users’ location. In the SPWT system, the estimation error for SPWT cannot be ignored. However, the conventional robust methods in secure wireless communications optimize the beamforming vector in the desired positions only in statistical means and cannot guarantee the security for each symbol. The proposed regional robust schemes are designed for optimizing the secrecy performance in the whole error region around the estimated location. Specifically, with the known maximal estimation error, we define the target region and wiretap region. Then, we design an optimal beamforming vector and an artificial noise projection matrix, which achieve the confidential signal in the target area having the maximal power while only few signal power is conserved in the potential wiretap region. Instead of considering the statistical distributions of the estimated errors into optimization, we optimize the SLNR and ANLNR of the whole target area, which significantly decreases the complexity. Moreover, the proposed schemes can ensure that the desired users are located in the optimized region, which are more practical than the conventional methods. Simulation results show that our proposed regional robust SPWT design is capable of substantially improving the secrecy rate compared to the conventional non-robust method. The P-SLNR-ANLNR maximization-based method has the comparable secrecy performance with lower complexity than that of the R-SLNR-ANLNR maximization-based method.

scholarly journals Real-Time Hydraulic Interval State Estimation for Water Transport Networks: a Case Study

2017 ◽  
Author(s):  
Stelios G. Vrachimis ◽  
Demetrios G. Eliades ◽  
Marios M. Polycarpou
Keyword(s):  
State Estimation ◽  
Real Time ◽  
Water Distribution ◽  
Estimation Error ◽  
Distribution Networks ◽  
Water Levels ◽  
Water Distribution Networks ◽  
Unaccounted For Water ◽  
Tank Water

Abstract. Hydraulic state estimation in water distribution networks is the task of estimating water flows and pressures in the pipes and nodes of the network based on some sensor measurements. This requires a model of the network, as well as knowledge of demand outflow and tank water levels. Due to modeling and measurement uncertainty, standard state-estimation may result in inaccurate hydraulic estimates without any measure of the estimation error. This paper describes a methodology for generating hydraulic state bounding estimates based on interval bounds on the parametric and measurement uncertainties. The estimation error bounds provided by this method can be applied to estimate the unaccounted-for water in water distribution networks. As a case study, the method is applied to a transport network in Cyprus, using actual data in real-time.

scholarly journals Application of Attenuation Correction to Quantitative Precipitation Estimation on C-Band Weather Radar in Bengkulu

2021 ◽  
Vol 893 (1) ◽  
pp. 012054
Author(s):  
M F Handoyo ◽  
M P Hadi ◽  
S Suprayogi
Keyword(s):  
Attenuation Correction ◽  
Estimation Error ◽  
Weather Radar ◽  
Radar Data ◽  
Signal Interference ◽  
Active System ◽  
Estimation Errors ◽  
Rain Gauges ◽  
Quantitative Precipitation Estimation ◽  
Precipitation Estimation

Abstract A weather radar is an active system remote sensing tool that observes precipitation indirectly. Weather radar has an advantage in estimating precipitation because it has a high spatial resolution (up to 0.5 km). Reflectivity generated by weather radar still has signal interference caused by attenuation factors. Attenuation causes the Quantitative Precipitation Estimation (QPE) by the C-band weather radar to underestimate. Therefore attenuation correction on C-band weather radar is needed to eliminate precipitation estimation errors. This study aims to apply attenuation correction to determine Quantitative Precipitation Estimation (QPE) on the c-band weather radar in Bengkulu in December 2018. Gate-by-gate method attenuation correction with Kraemer approach has applied to c-band weather radar data from the Indonesian Agency for Meteorology and Geophysics (BMKG) weather radar network Bengkulu. This method uses reflectivity as the only input. Quantitative Precipitation Estimation (QPE) has obtained by comparing weather radar-based rain estimates to 10 observation rain gauges over a month with the Z-R relation equation. Root Mean Square Error (RMSE) is used to calculate the estimation error. Weather radar data are processed using Python-based libraries Wradlib and ArcGIS 10.5. As a result, the calculation between the weather radar estimate precipitation and the observed rainfall obtained equation Z=2,65R1,3. The attenuation correction process with Kreamer's approach on the c-band weather radar has reduced error in the Qualitative Precipitation Estimation (QPE). Corrected precipitation has a smaller error value (r = 0.88; RMSE = 8.38) than the uncorrected precipitation (r = 0.83; RMSE = 11.70).

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