scholarly journals Mathematical Model and Calibration Procedure of a PSD Sensor Used in Local Positioning Systems

Sensors ◽  
2016 ◽  
Vol 16 (9) ◽  
pp. 1484 ◽  
Author(s):  
David Rodríguez-Navarro ◽  
José Lázaro-Galilea ◽  
Ignacio Bravo-Muñoz ◽  
Alfredo Gardel-Vicente ◽  
Francisco Domingo-Perez ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Calibration Procedure ◽  
Positioning Systems ◽  
Psd Sensor

scholarly journals Erratum: Rodríguez-Navarro, D., et al. Mathematical Model and Calibration Procedure of a PSD Sensor Used in Local Positioning Systems. Sensors 2016, 16, 1484

Sensors ◽  
2016 ◽  
Vol 16 (11) ◽  
pp. 1788
Author(s):  
David Rodríguez-Navarro ◽  
José Lázaro-Galilea ◽  
Ignacio Bravo-Muñoz ◽  
Alfredo Gardel-Vicente ◽  
Francisco Domingo-Perez ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Calibration Procedure ◽  
Positioning Systems ◽  
Psd Sensor

scholarly journals MODELLING A COMPLIANT-BASED PRECISE POSITIONING STAGE / AUKŠTO TIKSLUMO POZICIONAVIMO SISTEMOS MODELIAVIMAS TAIKANT BESIDEFORMUOJANČIUS MECHANIZMUS

2013 ◽  
Vol 6 (4) ◽  
pp. 523-527 ◽  
Author(s):  
Giedrius Augustinavičius ◽  
Audrius Čereška
Keyword(s):  
Mathematical Model ◽  
Finite Element Analysis ◽  
Positioning System ◽  
Element Analysis ◽  
Precise Positioning ◽  
Positioning Systems ◽  
Positioning Stage ◽  
Amplification Mechanism ◽  
Analytical Approaches ◽  
The Mathematical Model

The paper presents modelling precise dual axis flexure-based precision positioning systems for micro-positioning applications. The positioning system is featured with monolithic architecture, flexure-based joints and piezo stacks. Its workspace has been evaluated via analytical approaches. Amplification mechanism is optimally designed. The mathematical model of the positioning system has been derived and verified by resorting to finite element analysis (FEA). The established analytical and (FEA) models are helpful for optimizing reliable architecture and improving the performance of the positioning system. Santrauka Straipsnyje pristatomas dviejų ašių didelio tikslumo pozicionavimo sistemos su paketiniais pjezovykdikliais modeliavimas, taikant besideformuojančius vientiso kūno mechanizmus. Pozicionavimo sistemą sudaro besideformuojančio vientiso kūno mechanizmas ir paketiniai pjezovykdikliai. Besideformuojantis vientiso kūno mechanizmas norimam poslinkiui pasiekti buvo optimizuotas Solidworks Simulation programiniu paketu. Platformų poslinkiams apskaičiuoti sudarytas matematinis modelis, kurio patikimumas patikrintas baigtinių elementų metodu. Sudaryto matematinio modelio ir rezultatų, gautų baigtinių elementų metodu, skirtumai yra mažesni nei 5 %, todėl pasiūlyta modeliavimo metodika gali būti taikoma kuriant pozicionavimo sistemas su besideformuojančiais elementais.

scholarly journals DETERMINATION OF TRANSFER FUNCTION OF MAGNETIC LEVITATION MODEL AND EXPERIMENTAL VERIFICATION OF OPTICAL SENSOR

2019 ◽  
pp. 148-154
Author(s):  
Erik Prada
Keyword(s):  
Mathematical Model ◽  
Transfer Function ◽  
Experimental Verification ◽  
Optical Sensor ◽  
Magnetic Levitation ◽  
Positioning Systems ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
The Mathematical Model

Urgency of the research. The potential of controlling the position of levitating objects has great application in deposition and in various positioning systems. Magnetic levitation eliminates direct mechanical friction between moving parts. Target setting. The measurement shielding method used is one of the methods of determining the position of a levitating object. By combining positioning and regulating elements, we achieve a feedback control. The use of a given type of measurement has advantages in places where the use of other methods is not appropriate. Actual scientific researches and issues analysis. The problem of magnetic levitation is addressed by several research laboratories with a direct connection to practice. The problem that is currently solved within magnetic levitation is the regulation of the levitating object using various types of regulators. The research objective. Derivation of mathematical model of magnetic levitation and examination of nonlinear system followed by linearization by Taylor series. Experimental determination of characteristics and dependence between object position, voltage and current. The statement of basic materials. The position of the levitating object is determined by the shading of the optical sensor. The light source is a laser light. Conclusions. In this work we defined the mathematical model of the magnetic levitation system and subsequently derived the transfer function of the levitation system and the position sensor. From the experimental verification of the shadow method for the determination of the position of the levitating object and the consequent need for regulation, we found that the dependence of the position of the levitating object on current and voltage on the photodiode is linear in the active region.

scholarly journals Optical Boundaries for LED-Based Indoor Positioning System

Computation ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 7 ◽  
Author(s):  
Olaoluwa Popoola ◽  
Sinan Sinanović ◽  
Wasiu Popoola ◽  
Roberto Ramirez-Iniguez
Keyword(s):  
Mathematical Model ◽  
Indoor Positioning ◽  
Experimental Measurements ◽  
Positioning System ◽  
Positioning Error ◽  
Positioning Accuracy ◽  
Light Emitting ◽  
Positioning Systems ◽  
Indoor Positioning System ◽  
Positioning Time

Overlap of footprints of light emitting diodes (LEDs) increases the positioning accuracy of wearable LED indoor positioning systems (IPS) but such an approach assumes that the footprint boundaries are defined. In this work, we develop a mathematical model for defining the footprint boundaries of an LED in terms of a threshold angle instead of the conventional half or full angle. To show the effect of the threshold angle, we compare how overlaps and receiver tilts affect the performance of an LED-based IPS when the optical boundary is defined at the threshold angle and at the full angle. Using experimental measurements, simulations, and theoretical analysis, the effect of the defined threshold angle is estimated. The results show that the positional time when using the newly defined threshold angle is 12 times shorter than the time when the full angle is used. When the effect of tilt is considered, the threshold angle time is 22 times shorter than the full angle positioning time. Regarding accuracy, it is shown in this work that a positioning error as low as 230 mm can be obtained. Consequently, while the IPS gives a very low positioning error, a defined threshold angle reduces delays in an overlap-based LED IPS.

scholarly journals A Method for The Assessing of Reliability Characteristics Relevant to an Assumed Position-Fixing Accuracy in Navigational Positioning Systems

2016 ◽  
Vol 23 (3) ◽  
pp. 20-27 ◽  
Author(s):  
Cezary Specht ◽  
Jacek Rudnicki
Keyword(s):  
Mathematical Model ◽  
Markov Processes ◽  
Real Data ◽  
Maximum Error ◽  
Positioning System ◽  
Positioning Systems ◽  
Permissible Error ◽  
Reliability Characteristics ◽  
Formal Requirements ◽  
Working Out

Abstract This paper presents a method which makes it possible to determine reliability characteristics of navigational positioning systems, relevant to an assumed value of permissible error in position fixing. The method allows to calculate: availability , reliability as well as operation continuity of position fixing system for an assumed, determined on the basis of formal requirements - both worldwide and national, position-fixing accuracy. The proposed mathematical model allows to satisfy, by any navigational positioning system, not only requirements as to position-fixing accuracy of a given navigational application (for air , sea or land traffic) but also the remaining characteristics associated with technical serviceability of a system. Essence of the method in question consists in the working-out of recorded empirical position-fixing data as well as the making use of multi-state Markov processes ( appropriate to a maximum error value permissible for various navigational applications ) as a result of which reliability characteristics based on real data would be determined. About usefulness of a given navigational positioning system for its possible application would decide a vector of variables (both dealing with position and reliability) which satisfies / or does not satisfy / formal navigational requirements for a given application.

scholarly journals Weak Calibration of a Visible Light Positioning System Based on a Position-Sensitive Detector: Positioning Error Assessment

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3924
Author(s):  
Álvaro De-La-Llana-Calvo ◽  
José-Luis Lázaro-Galilea ◽  
Alfredo Gardel-Vicente ◽  
David Salido-Monzú ◽  
Ignacio Bravo-Muñoz ◽  
...  
Keyword(s):  
Cost Effective ◽  
Calibration Method ◽  
Calibration Procedure ◽  
Indoor Positioning ◽  
Positioning System ◽  
Positioning Error ◽  
Error Assessment ◽  
Sensitive Detector ◽  
Positioning Systems ◽  
Weak Calibration

Reduced deployment and calibration requirements are key for scalable and cost-effective indoor positioning systems. In this work, we propose a low-complexity, weak calibration procedure for an indoor positioning system based on infrastructure lighting and a positioning-sensitive detector. The proposed calibration relies on genetic algorithms to obtain the relevant system parameters in the real positioning environment without a priori information, and requires a low number of simple measurements. The achievable performance of the proposal was assessed by direct comparison with a formal offline calibration method requiring complex dedicated infrastructure and instruments. The comparative error assessment showed that the maximum accuracy reduction compared to the significantly more costly formal calibration was below 25 mm, and the overall absolute positioning error was smaller than 35 mm with orientation errors of around 0.25°. The performance achieved with the proposed weak calibration procedure is sufficient for many indoor positioning applications and largely reduces the cost and complexity of setting up the positioning system in real environments.

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model
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