Position estimation from relative distance measurements in multi-agents formations

2010 ◽  
Author(s):  
Giuseppe C. Calafiore ◽  
Luca Carlone ◽  
Mingzhu Wei
Keyword(s):  
Position Estimation ◽  
Relative Distance ◽  
Distance Measurements ◽  
Multi Agents

Regulating a Formation of a Large Number of Vehicles

2005 ◽  
Author(s):  
Akira Okamoto ◽  
Dean B. Edwards
Keyword(s):  
Control Problem ◽  
Coordinate System ◽  
Formation Control ◽  
Control Algorithm ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Relative Distance ◽  
Control Algorithms ◽  
Distance Measurements ◽  
Six Degree Of Freedom

Various control algorithms have been developed for fleets of autonomous vehicles. Many of the successful control algorithms in practice are behavior-based control or nonlinear control algorithms, which makes analyzing their stability difficult. At the same time, many system theoretic approaches for controlling a fleet of vehicles have also been developed. These approaches usually use very simple vehicle models such as particles or point-mass systems and have only one coordinate system which allows stability to be proven. Since most of the practical vehicle models are six-degree-of-freedom systems defined relative to a body-fixed coordinate system, it is difficult to apply these algorithms in practice. In this paper, we consider a formation regulation problem as opposed to a formation control problem. In a formation control problem, convergence of a formation from random positions and orientations is considered, and it may need a scheme to integrate multiple moving coordinates. On the contrary, in a formation regulation problem, it is not necessary since small perturbations from the nominal condition, in which the vehicles are in formation, are considered. A common origin is also not necessary if the relative distance to neighbors or a leader is used for regulation. Under these circumstances, the system theoretic control algorithms are applicable to a formation regulation problem where the vehicle models have six degrees of freedom. We will use a realistic six-degree-of-freedom model and investigate stability of a fleet using results from decentralized control theory. We will show that the leader-follower control algorithm does not have any unstable fixed modes if the followers are able to measure distance to the leader. We also show that the leader-follower control algorithm has fixed modes at the origin, indicating that the formation is marginally stable, when the relative distance measurements are not available. Multi-vehicle simulations are performed using a hybrid leader-follower control algorithm where each vehicle is given a desired trajectory to follow and adjusts its velocity to maintain a prescribed distance to the leader. Each vehicle is modeled as a three-degree-of-freedom system to investigate the vehicle’s motion in a horizontal plane. The examples show efficacy of the analysis.

scholarly journals An Adaptive Bluetooth/Wi-Fi Fingerprint Positioning Method based on Gaussian Process Regression and Relative Distance

Sensors ◽  
2019 ◽  
Vol 19 (12) ◽  
pp. 2784 ◽  
Author(s):  
Hongji Cao ◽  
Yunjia Wang ◽  
Jingxue Bi ◽  
Hongxia Qi
Keyword(s):  
Gaussian Process ◽  
Prediction Models ◽  
Gaussian Process Regression ◽  
Position Estimation ◽  
Relative Distance ◽  
Error Prediction ◽  
Estimation Result ◽  
Positioning Error ◽  
Positioning Method ◽  
Better Than

Trusted positioning data are very important for the fusion of Bluetooth fingerprint positioning (BFP) and Wi-Fi fingerprint positioning (WFP). This paper proposes an adaptive Bluetooth/Wi-Fi fingerprint positioning method based on Gaussian process regression (GPR) and relative distance (RD), which can choose trusted positioning results for fusion. In the offline stage, measurements of the Bluetooth and Wi-Fi received signal strength (RSS) were collected to construct Bluetooth and Wi-Fi fingerprint databases, respectively. Then, fingerprint positioning error prediction models were built with GPR and data from the fingerprint databases. In the online stage, online Bluetooth and Wi-Fi RSS readings were matched with the fingerprint databases to get a Bluetooth fingerprint positioning result (BFPR) and a Wi-Fi fingerprint positioning result (WFPR). Then, with the help of RD and fingerprint positioning error prediction models, whether the positioning results are trusted was determined. The trusted result is selected as the position estimation result when there is only one trusted positioning result among the BFPR and WFPR. The mean is chosen as the position estimation result when both the BFPR and WFPR results are trusted or untrusted. Experimental results showed that the proposed method was better than BFP and WFP, with a mean positioning error of 2.06 m and a root-mean-square error of 1.449 m.

A closed-form algorithm for the least-squares trilateration problem

Robotica ◽  
2010 ◽  
Vol 29 (3) ◽  
pp. 375-389 ◽  
Author(s):  
Yu Zhou
Keyword(s):  
Least Squares ◽  
Closed Form ◽  
Closed Form Solution ◽  
Nonlinear Least Squares ◽  
Form Solution ◽  
Position Estimation ◽  
Reference Points ◽  
Distance Measurements ◽  
Optimal Position ◽  
General Number

SUMMARYTrilateration is the most adopted external reference-based localization technique for mobile robots, given the correspondence of external references. The nonlinear least-squares trilateration formulation provides an optimal position estimate from a general number (greater than or equal to the dimension of the environment) of reference points and corresponding distance measurements. This paper presents a novel closed-form solution to the nonlinear least-squares trilateration problem. The performance of the proposed algorithm in dealing with erroneous inputs of reference points and distance measurements has been analyzed through representative examples. The proposed trilateration algorithm has low computational complexity, high operational robustness, and reduced systematic error and uncertainty in position estimation. The effectiveness of the proposed algorithm has been further verified through an experimental test.

scholarly journals Improved GPS-based Satellite Relative Navigation Using Femtosecond Laser Relative Distance Measurements

2016 ◽  
Vol 33 (1) ◽  
pp. 45-54 ◽  
Author(s):  
Hyungjik Oh ◽  
Han-Earl Park ◽  
Kwangwon Lee ◽  
Sang-Young Park ◽  
Chandeok Park
Keyword(s):  
Femtosecond Laser ◽  
Relative Distance ◽  
Relative Navigation ◽  
Distance Measurements

An Effective Trilateration Algorithm for Mobile Robot Positioning Based on Multiple Reference Points

2009 ◽  
Author(s):  
Yu Zhou
Keyword(s):  
Mobile Robot ◽  
Nonlinear Least Squares ◽  
Target Object ◽  
Position Estimation ◽  
Reference Points ◽  
Distance Measurements ◽  
Optimal Position ◽  
General Number ◽  
Robot Positioning ◽  
Multiple Reference

This paper presents a novel trilateration algorithm which estimates the position of a target object, such as a mobile robot, in a 2D or 3D space based on the simultaneous distance measurements from multiple reference points. The proposed algorithm is derived from the nonlinear least-squares formulation of trilateration, and provides a globally optimal position estimate from a general number of reference points and corresponding distance measurements. Using standard linear algebra techniques, the proposed algorithm has relatively low computational complexity and high operational robustness. Simulations have been conducted through representative examples to analyze the performance of the proposed trilateration algorithm in dealing with erroneous inputs of reference points and distance measurements. The results show that the proposed algorithm has lower systematic error and uncertainty in position estimation comparing with representative closed-form methods.

scholarly journals A Novel Hybrid NN-ABPE-Based Calibration Method for Improving Accuracy of Lateration Positioning System

Sensors ◽  
2021 ◽  
Vol 21 (24) ◽  
pp. 8204
Author(s):  
Milica Petrović ◽  
Maciej Ciężkowski ◽  
Sławomir Romaniuk ◽  
Adam Wolniakowski ◽  
Zoran Miljković
Keyword(s):  
Neural Network ◽  
Main Idea ◽  
Signal Propagation ◽  
Calibration Method ◽  
Position Estimation ◽  
Reference Points ◽  
Positioning System ◽  
Feed Forward Neural Network ◽  
Distance Measurements ◽  
Positioning Systems

Positioning systems based on the lateration method utilize distance measurements and the knowledge of the location of the beacons to estimate the position of the target object. Although most of the global positioning techniques rely on beacons whose locations are known a priori, miscellaneous factors and disturbances such as obstacles, reflections, signal propagation speed, the orientation of antennas, measurement offsets of the beacons hardware, electromagnetic noise, or delays can affect the measurement accuracy. In this paper, we propose a novel hybrid calibration method based on Neural Networks (NN) and Apparent Beacon Position Estimation (ABPE) to improve the accuracy of a lateration positioning system. The main idea of the proposed method is to use a two-step position correction pipeline that first performs the ABPE step to estimate the perceived positions of the beacons that are used in the standard position estimation algorithm and then corrects these initial estimates by filtering them with a multi-layer feed-forward neural network in the second step. In order to find an optimal neural network, 16 NN architectures with 10 learning algorithms and 12 different activation functions for hidden layers were implemented and tested in the MATLAB environment. The best training outcomes for NNs were then employed in two real-world indoor scenarios: without and with obstacles. With the aim to validate the proposed methodology in a scenario where a fast set-up of the system is desired, we tested eight different uniform sampling patterns to establish the influence of the number of the training samples on the accuracy of the system. The experimental results show that the proposed hybrid NN-ABPE method can achieve a high level of accuracy even in scenarios when a small number of calibration reference points are measured.

scholarly journals Person Tracking in Ultra-Wide Band Hybrid Localization System Using Reduced Number of Reference Nodes

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 1984 ◽  
Author(s):  
Piotr Rajchowski ◽  
Jacek Stefanski ◽  
Jaroslaw Sadowski ◽  
Krzysztof K. Cwalina
Keyword(s):  
Inertial Sensor ◽  
Experimental Studies ◽  
Inertial Navigation ◽  
Wide Band ◽  
Position Estimation ◽  
Distance Measurements ◽  
Localization System ◽  
Hybrid Localization ◽  
Radio Signals ◽  
Positional Data

In this article a novel method of positional data integration in an indoor hybrid localization system combining inertial navigation with radio distance measurements is presented. A point of interest is the situation when the positional data and the radio distance measurements are obtained from less than thee reference nodes and it is impossible to unambiguously localize the moving person due to undetermined set of positional equations. The presented method allows to continuously provide localization service even in areas with disturbed propagation of the radio signals. Authors performed simulation and measurement studies of the proposed method to verify the precision of position estimation of a moving person in an indoor environment. It is worth noting that to determine the simulation parameters and realize the experimental studies the hybrid localization system demonstrator was developed, combining inertial navigation and radio distance measurements. In the proposed solution, results of distance measurements taken to less than three reference nodes are used to compensate the drift of the position estimated using the inertial sensor. In the obtained simulation and experimental results it was possible to reduce the localization error by nearly 50% regarding the case when only inertial navigation was used, additionally keeping the long term root mean square error at the level of ca. 0.50 m. That gives a degradation of localization precision below 0.1 m with respect to the fusion Kalman filtration when four reference nodes are present.

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