scholarly journals Mathematical Analysis of Line Intersection and Shortest Distance Algorithms

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1492
Author(s):  
Sajina Pradhan ◽  
Suk-seung Hwang ◽  
Dongbin Lee
Keyword(s):  
Mathematical Analysis ◽  
Estimation Error ◽  
Mobile Station ◽  
Intersection Point ◽  
Location Estimation ◽  
Estimation Performance ◽  
Mathematical Expressions ◽  
Shortest Distance ◽  
Intersection Algorithm ◽  
Intersection Points

The time of arrival (TOA) trilateration is one of the representative location detection technologies (LDT) that determines the true location of a mobile station (MS) using a unique intersection point of three circles based on three radii corresponding to distances between MS and base stations (BSs) and center coordinates of BSs. Since the distance between MS and BS is estimated by using the number of time delays, three circles based on the estimated radii are generally increased and they may not meet at a single point, resulting in the location estimation error. In order to compensate this estimation error and to improve estimation performance, we present two advanced TOA trilateration localization algorithms with detail mathematical expressions. The considered algorithms are the shortest distance algorithm, which calculates an average of three interior intersection points among an entire six intersection points from three intersecting circles, and the line intersection algorithm, which calculates an intersection point of three lines connecting two intersection points of two circles among the three circles, as the estimated location of the MS. In this paper, we present both algorithms with detailed mathematical expressions. The computer simulation results are provided to compare the location estimation performance of both algorithms. In addition, in this paper, mathematical analysis is provided to indicate the relation between the line intersection algorithm and the shortest distance algorithm. In this analysis, we verify that line equations based on the intersection points obtained from the shortest distance algorithm are identical to those obtained from the line intersection algorithm.

scholarly journals Hybrid TOA Trilateration Algorithm Based on Line Intersection and Comparison Approach of Intersection Distances

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1668 ◽  
Author(s):  
Sajina Pradhan ◽  
Youngchul Bae ◽  
Jae-Young Pyun ◽  
Nak Yong Ko ◽  
Suk-seung Hwang
Keyword(s):  
Estimation Error ◽  
Single Point ◽  
Mode Selection ◽  
Mobile Station ◽  
Location Estimation ◽  
Cellular Systems ◽  
Base Stations ◽  
Time Of Arrival ◽  
Comparison Approach ◽  
Intersection Algorithm

The ever-growing mobile station (MS) localization technologies provide an increasingly important role in all aspects of the wireless cellular systems and Internet of Things (IoT). The accurate MS location information is the basis in connection of different devices in IoT. The MS localization techniques based on time of arrival (TOA) trilateration algorithm, which determines the location of MS using an intersection point of three circles based on distances between MS and base stations (BS) and coordinates of BSs, have been actively studied. In general, the distance between the MS and BS is calculated by counting the number of delay samples or measuring the power of the received signal. Since the estimated distance (radius of a circle) between MS and BS is commonly increased, three circles may not meet at a single point, resulting in the estimation error of MS localization. In order to improve this problem, in this paper, we propose the hybrid TOA trilateration algorithm based on the line intersection algorithm for the general case for intersection of three circles and the comparison approach of intersection distances for the specific case where a small circle is located inside the area of two large circles. The line intersection algorithm has an excellent location estimation performance in the general case, but it does not work in the specific case. The comparison approach of intersection distances has good performance only for the specific case. In addition, we propose the mode selection algorithm to efficiently select a proper mode between the general and specific cases. The representative computer simulation examples are provided to verify the localization performance of the proposed algorithm.

Comparison Approach of Intersection Distances for Advanced TOA Trilateration

2017 ◽  
Vol 14 (03) ◽  
pp. 1750019 ◽  
Author(s):  
Suk-Seung Hwang ◽  
Sajina Pradhan
Keyword(s):  
Mobile Station ◽  
Estimation Algorithm ◽  
Intersection Point ◽  
Location Estimation ◽  
Base Stations ◽  
Time Of Arrival ◽  
Estimation Errors ◽  
Small Circle ◽  
Detection Technology ◽  
Shortest Distance

The time of arrival trilateration method is one of the representative algorithms for the location detection technology, which estimates the location of mobile station (MS) at a unique intersection point of three circles with radiuses corresponding to distances between MS and base stations (BSs) and centers corresponding to coordinates of BSs. However, there may be serious estimation errors, when they do not meet at a point because the estimated radiuses of them are increased. The solutions for reducing the estimation position error in the main case of meeting three circles with the extended radius have been recently provided as the shortest distance algorithm and the line intersection algorithm. In general, they have good performance for the location estimation, but they may have serious errors in some cases. In this paper, we propose the efficient location estimation algorithm for the specific case of two large circles and one relatively small circle, which is located in the area of two large circles. In this case, there are six intersections in total based on the three extended circles and a small circle has four intersections with two large circles. The proposed approach compares four distances based on four neighboring intersections and selects the shortest one. Finally, it determines the averaged coordinate of two intersections corresponding to the shortest distance, as the location of MS. The location-estimating performance of the proposed algorithm is illustrated by the computer simulation example.

Line Intersection Algorithm for the Enhanced TOA Trilateration Technique

2014 ◽  
Vol 11 (04) ◽  
pp. 1442003 ◽  
Author(s):  
Sajina Pradhan ◽  
Suk-Seung Hwang ◽  
Hyun-Rok Cha ◽  
Young-Chul Bae
Keyword(s):  
Mobile Station ◽  
Detection Algorithm ◽  
Intersection Point ◽  
Location Based Services ◽  
Base Stations ◽  
Time Of Arrival ◽  
True Location ◽  
Intersection Algorithm ◽  
Location Detection ◽  
Intersection Points

The location determination technology (LDT) is one of the core techniques for the location-based services (LBS) which has various applications, including a mobile robot, for the modern wireless communication system. The time of arrival (TOA), which is a kind of LDTs based on the cellular network, estimates the location of the specific user or object using a trilateration method based on the received signals from three base stations (BS). The true location of a mobile station (MS) is determined based on an intersection point of three circles with the radius corresponding to the distance between each BS to MS. Since the TOA method estimates the distance between BS and MS using the number of time delay, these three circles should not generally meet at a point and the performance of the location detection should be degraded in this case. In order to overcome this problem, we propose the mobile location detection algorithm based on a line intersection of the TOA geometry. In the case of those three circles do not meet at a point; in general, there are six intersection points and three lines which connect two intersection points. In this paper, we determine an intersection point of three lines as the location of a MS. The computer simulation example is provided to illustrate the location detection performance of the proposed algorithm.

scholarly journals Practical Fingerprinting Localization for Indoor Positioning System by Using Beacons

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Santosh Subedi ◽  
Jae-Young Pyun
Keyword(s):  
Estimation Error ◽  
Indoor Positioning ◽  
Location Estimation ◽  
Reference Points ◽  
Ultra Wideband ◽  
Positioning System ◽  
Localization Method ◽  
Weighted Centroid Localization ◽  
Time Required ◽  
Indoor Positioning System

Recent developments in the fields of smartphones and wireless communication technologies such as beacons, Wi-Fi, and ultra-wideband have made it possible to realize indoor positioning system (IPS) with a few meters of accuracy. In this paper, an improvement over traditional fingerprinting localization is proposed by combining it with weighted centroid localization (WCL). The proposed localization method reduces the total number of fingerprint reference points over the localization space, thus minimizing both the time required for reading radio frequency signals and the number of reference points needed during the fingerprinting learning process, which eventually makes the process less time-consuming. The proposed positioning has two major steps of operation. In the first step, we have realized fingerprinting that utilizes lightly populated reference points (RPs) and WCL individually. Using the location estimated at the first step, WCL is run again for the final location estimation. The proposed localization technique reduces the number of required fingerprint RPs by more than 40% compared to normal fingerprinting localization method with a similar localization estimation error.

Improved Taylor-Series Expansion for MS Location Estimation

2011 ◽  
Vol 52-54 ◽  
pp. 1777-1782 ◽  
Author(s):  
Chien Sheng Chen ◽  
Yung Chuan Lin ◽  
Wen Hsiung Liu ◽  
He Nian Shou
Keyword(s):  
Taylor Series ◽  
Solution Process ◽  
Selection Criterion ◽  
Mobile Station ◽  
Iteration Process ◽  
Taylor Series Expansion ◽  
Initial Position ◽  
Location Estimation ◽  
Least Square ◽  
Location Selection

The objective of wireless location is to determine the mobile station (MS) location in a wireless cellular communications system. Due to the measurement with large errors, location schemes give poorer performance in non-line-of-sight (NLOS) environments. To determine MS location, Taylor-series algorithm (TSA) is commonly used scheme. TSA can give a least-square (LS) solution to a set of simultaneous linearized equations. The disadvantage of TSA is the need for an initial position guess to start the solution process. The iteration process may not converge due to a poor initial estimate of the MS location. To improve the location accuracy with less complexity, the initial MS location selection criterion is proposed. Numerical results demonstrate that the proposed criterion always provides more accurate positioning.

scholarly journals Emitter Velocity Estimation Comparison for Frequency Difference of Arrival Measurement Based Single and Multiple Reference Lateration Algorithm

2018 ◽  
Vol 17 (1) ◽  
pp. 9-15
Author(s):  
Abdulmalik Shehu Yaro ◽  
Ahmad Zuri Sha'ameri
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Equilateral Triangle ◽  
Estimation Error ◽  
Velocity Estimation ◽  
Instantaneous Velocity ◽  
Frequency Difference ◽  
Estimation Accuracy ◽  
Estimation Performance ◽  
Multiple Reference

The accuracy at which the instantaneous velocity and position of a non-stationary emitting source estimated using a lateration algorithm depends on several factors such as the lateration algorithm approach, the number and choice of reference receiving station (RS) used in developing the lateration algorithm. In this paper, the use of multiple reference RSs was proposed to improve the velocity estimation accuracy of the frequency difference of arrival (FDOA) based lateration algorithm. The velocity estimation performance of the proposed multiple reference FDOA based lateration algorithm is compared with the conventional approach of using single reference RS at some selected emitter positions using Monte Carlo simulation. Simulation result based on an equilateral triangle RS configuration shows that the use of multiple reference RSs improved the velocity estimation accuracy of the lateration algorithm. Based on the selected emitter positions, a reduction in velocity estimation error of about 0.033  and 1.31  for emitter positions at ranges 0.5 km and 5 km respectively was achieved using the multiple reference lateration algorithm.

scholarly journals Mathematical expressions describing enzyme velocity and inhibition at high enzyme concentration

2021 ◽  
Author(s):  
Agustin Hernandez
Keyword(s):  
Enzyme Concentration ◽  
Allosteric Inhibitors ◽  
Mathematical Expressions ◽  
Molecule Inhibitor ◽  
High Enzyme ◽  
Biotechnological Processes ◽  
Intersection Points ◽  
High Enzyme Concentration

ABSTRACTEnzyme behaviour is typically characterised in the laboratory using very diluted solutions of enzyme. However, in vivo processes usually occur at [ST] ≈ [ET] ≈ Km. Furthermore, the study of enzyme action usually involves analysis and characterisation of inhibitors and their mechanisms. However, to date, there have been no reports proposing mathematical expressions that can be used to describe enzyme activity at high enzyme concentration apart from the simplest single substrate, irreversible case. Using a continued fraction approach, equations can be easily derived to apply to the most common cases in monosubstrate reactions, such as irreversible or reversible reactions and small molecule (inhibitor or activator) kinetic interactions. These expressions are simple and can be understood as an extension of the classical Michaelis-Menten equations. A first analysis of these expressions permits to deduce some differences at high vs low enzyme concentration, such as the greater effectiveness of allosteric inhibitors compared to catalytic ones. Also, they can be used to understand catalyst saturation in a reaction. Although they can be linearised following classical approaches, these equations also show some differences that need to be taken into account. The most important one may be the different meaning of line intersection points in Dixon plots. All in all, these expressions may be useful tools for the translation in vivo of in vitro experimental data or for modelling in vivo and biotechnological processes.

scholarly journals Improved Location Estimation in Wireless Sensor Networks Using a Vector-Based Swarm Optimized Connected Dominating Set

Sensors ◽  
2019 ◽  
Vol 19 (2) ◽  
pp. 376 ◽  
Author(s):  
Gulshan Kumar ◽  
Rahul Saha ◽  
Mritunjay Rai ◽  
Reji Thomas ◽  
Tai-Hoon Kim ◽  
...  
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Network Lifetime ◽  
Estimation Error ◽  
Dominating Set ◽  
Connected Dominating Set ◽  
Location Estimation ◽  
Wireless Sensor ◽  
Minimum Number ◽  
Anchor Nodes

Location estimation in wireless sensor networks (WSNs) has received tremendous attention in recent times. Improved technology and efficient algorithms systematically empower WSNs with precise location identification. However, while algorithms are efficient in improving the location estimation error, the factor of the network lifetime has not been researched thoroughly. In addition, algorithms are not optimized in balancing the load among nodes, which reduces the overall network lifetime. In this paper, we have proposed an algorithm that balances the load of computation for location estimation among the anchor nodes. We have used vector-based swarm optimization on the connected dominating set (CDS), consisting of anchor nodes for that purpose. In this algorithm, major tasks are performed by the base station with a minimum number of messages exchanged by anchor nodes and unknown nodes. The simulation results showed that the proposed algorithm significantly improves the network lifetime and reduces the location estimation error. Furthermore, the proposed optimized CDS is capable of providing a global optimum solution with a minimum number of iterations.

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