Absolute Coordinates Research Articles

Singularity-Free Lie Group Integration and Geometrically Consistent Evaluation of Multibody System Models Described in Terms of Standard Absolute Coordinates

Abstract A classical approach to the multibody systems (MBS) modeling is to use absolute coordinates, i.e., a set of (possibly redundant) coordinates that describe the absolute position and orientation of the individual bodies with respect to an inertial frame (IFR). A well-known problem for the time integration of the equations of motion (EOM) is the lack of a singularity-free parameterization of spatial motions, which is usually tackled by using unit quaternions. Lie group integration methods were proposed as an alternative approach to the singularity-free time integration. At the same time, Lie group formulations of EOM naturally respect the geometry of spatial motions during integration. Lie group integration methods, operating directly on the configuration space Lie group, are incompatible with standard formulations of the EOM, and cannot be implemented in existing MBS simulation codes without a major restructuring. The contribution of this paper is twofold: (1) A framework for interfacing Lie group integrators to standard EOM formulations is presented. It allows describing MBS in terms of various absolute coordinates and at the same using Lie group integration schemes. (2) A method for consistently incorporating the geometry of rigid body motions into the evaluation of EOM in absolute coordinates integrated with standard vector space integration schemes. The direct product group SO(3)×ℝ3 and the semidirect product group SE(3) are used for representing rigid body motions. The key element is the local-global transitions (LGT) transition map, which facilitates the update of (global) absolute coordinates in terms of the (local) coordinates on the Lie group. This LGT map is specific to the absolute coordinates, the local coordinates on the Lie group, and the Lie group used to represent rigid body configurations.

Реконструкция тенденций в расположении палеолитических поселений в рамках городской агломерации

With the use of available archival materials, the density and types of Palaeolithic settlements of the chosen urban agglomeration have been reconstructed. Considering the character of this study and availability of archival documents, the city of Brno, presently the second biggest city in the Czech Republic in terms of density of population, was selected. The discovered sites with evidence of Palaeolithic settlement were located using absolute coordinates and visualised using the ArcGis software. The research showed that even the present urban agglomeration holds relevant information on the original settlements and that it is possible to predict other potential locations with Palaeolithic finds.

Астрометрия и геодезия как одна наука. История и предназначение звездных каталогов

According to the resolution of the International Astronomical Union, since 1999 the main reference for spherical coordinates has become the international celestial reference frame ICRF, compiled from observations of quasars and point-like radio galaxies. This decision abolishes the observations necessary for compiling the traditional spherical coordinate system represented by the fundamental catalogs of the FK series. It is useful to recall the principles of astronomers of the 18th–20th centuries who had organized the determination of the absolute coordinates of stars at the state observatories, required for compiling the next fundamental catalog. This will allow natural scientists who study movements by measured coordinates of celestial objects, firstly astronomers and geodesists, to compare the opportunities provided by optical fundamental catalogs and the reference system of radio coordinates for solving the problems of their branch of science. Let us turn to historical experience, which shows that the establishment of main optical coordinate systems was not a volitional decision but was affirmed in the process of searching for the most effective method for solving both fundamental problems and satisfying current needs of each historical era.

Phase measuring deflectometry based on calibration of the entrance pupil center of the camera lens.

A camera calibration method for phase measuring deflectometry (PMD) based on the entrance pupil center (EPC) of the camera lens is proposed. In our method, the position of the entrance pupil of the camera lens is first measured; next the absolute coordinates of the EPC are calibrated by using a reference flat and an external stop that is mounted in front of the camera lens; then the EPC as the camera coordinates is used for PMD. The feasibility of the proposed method is verified by simulation. The surface shapes of a planar optical element and a planar window glass are separately measured in our experiments, and a subwavelength accuracy level is achieved. Meanwhile, the effects of the camera lens with different aperture settings on captured images are investigated (including exposure time, image contrast, and measurement accuracy). The experimental results show that the exposure time required declines with the decrease in the f-number, and the measurement accuracy is higher than others when the f-numbers are changed from f/5.6 to f/11.

Miniaturization of a coherent monocular structured illumination system for future combination with digital holography

Holographic and 3D-measurement processes are an often-used tool in industry, medicine, and scientific applications. While small deviations of objects can be visualized by holographic means with high accuracy, optical systems with active structured illumination are a reliable source of absolute 3D-information in these fields. The combination of digital holography with structured illumination allows to simultaneously measure deformations and absolute 3D coordinates but also requires coherent light and has already been demonstrated in principle with a stereo camera setup. Multi-camera systems are limited to certain setup sizes given by the volume and distance of the detectors. Reducing the system to a one-camera (monocular) setup reduces space and acquisition costs. By using a multi-aperture illumination source an extremely high projection rate could be realized and reduced to a monocular approach with a novel voxel-calibration technique, while the projection system itself still requires a large amount of space. In this paper we present a miniaturized, monocular 3D-measurement system that works with repeatable, coherent speckles, generated by a fiber-coupled laser whose light was distributed by a fiber-switch to a diffuser plate connected with a measurement-head, also including a camera. By addressing different fibers through the switch, varying but repeatable patterns are generated. The size of the device (diameter < 3 cm) is now mainly limited by the volume of the camera. A first 3D-reconstruction of an object and an outlook for a combination of this system with digital holography is given, allowing absolute 3D-coordinates and relative deviations of object points to be measured simultaneously.

A Spatial Geometric Nonlinearity Spline Beam Element With Nodal Parameters Containing Strains

Many slender robs in engineering can be abstracted as Euler-Bernoulli beams. When analyzing their dynamic behavior, it is necessary to establish the dynamic model of the flexible multi-body systems. Geometric nonlinear elements with absolute nodal coordinates solved a large number of dynamic problems of flexible beams, but it still faces such problems as shear locking, discontinuity of nodal stress and low computational efficiency. In this paper, based on the theory of large deformation beam’s virtual power equation, the functional formula between displacements and rotation angles located at the nodes were established, which can satisfy the deformation coupling relationships and the generalized strains that can describe geometric nonlinear effects in this case were derived. Some parameters of boundary nodes were replaced by axial strain and sectional curvature to obtain a more accurate and concise constraint method for applying external forces. In order to improve the numerical efficiency and stability of the system’s motion equations, a model smoothing method was used to filter out high frequencies from the model. The rationality and effectiveness of the proposed unit were verified.

Feasibility of Using Electrooculography-Based Eye-Trackers for Neuromarketing Applications

Eye-tracking has been increasingly utilized in neuromarketing applications to quantitatively investigate consumers’ subliminal attention and preferences. Eye-tracking technology in neuromarketing has been developed mainly using camera-based methods; however, camera-based eye-trackers are generally expensive for some customers, hindering widespread use of eye-tracking technology. Electrooculography (EOG)-based eye-tracking could be a promising alternative because it can be implemented at a relatively lower cost even less than 100 USD; however, EOG-based eye-tracking has not yet been employed in neuromarketing applications. In this study, we developed a method to estimate the absolute coordinates of eye-gaze from EOG and investigated its reliability over time. The EOG signals were acquired in three separate experimental sessions: calibration, instructed eye-tracking test, and free eye-tracking test sessions. A linear regression model was constructed using the calibration data to estimate the absolute coordinates on the screen. The reconstructed eye-gaze results were visualized in the form of a heat map to be applied to practical neuromarketing scenarios. The results of the instructed eye-tracker test session revealed that the reliability of the eye-tracking results gradually decreased over time but did not drop drastically for up to 8 s. Moreover, the results of the neuromarketing test session analyzed with 6-s-EOG-data revealed clear gender differences among the heat maps of six advertisement pictures, coinciding with previous camera-based study results. Our results suggest that the proposed EOG-based eye-tracker has great potential to be utilized in practical neuromarketing applications.

Vehicle Positioning Based on Optical Camera Communication in V2I Environments

Demand for precise vehicle positioning (VP) increases as autonomous vehicles have recently been drawing attention. This paper proposes a scheme for positioning vehicles on the move based on optical camera communication (OCC) technology in the vehicle-to-infrastructure (V2I) environment. Light-emitting diode (LED) streetlights and vehicle cameras are used as transmitters and receivers respectively. Regions of streetlights are detected and traced by examining images that are obtained from cameras of vehicles. Then, a scheme for analyzing visible light data extracted from the images is proposed. The proposed vehicle positioning scheme uses information on angles between vectors that are formed under the collinearity conditions between the absolute coordinates of at least three received streetlights, and the coordinates of an image sensor. The experiments are performed under stationary state and moving state at a speed of 5 and 20 km/h. To verify the reliability of the proposed scheme, a comparison is made between the actual and estimated location of the camera in the stationary state. In addition, the path of a moving vehicle and the estimated path of the vehicle are compared to check the performance of the scheme. The performance of the proposed technique is analyzed and experimental demonstration confirms that the proposed OCC-based VP scheme achieves positioning accuracy of under 1 m.

Bending, buckling, and free vibration analysis of multi-span beams

In this paper, the modified segmented rod method (MSRM) will be used for bending, buckling, and free vibration analysis of multi-span beams. Since there is MSRM for a one-span beam in literature, slight corrections will enable the application of this method to the case of multi-span beams. The motivation for this research lies in the fact that there are engineering objects that must be modeled as multi-span beams, such as bridges. The proposed MSRM uses the absolute coordinates of the rigid segments, so the introduction of different boundary conditions as well as the loads can be done easily. The effectiveness of the MSRM was tested through numerical examples where the comparison with current results from the available literature was done.

Evaluation of vestibular function in children with purulent media otitis by computer stabilometry

The aim of the research – assessment of vestibular function in children with acute purulent otitis media by computer static stabilometry compared with typically developed children of the same age.&#x0D; Materials and methods: 22 children with purulent otitis media aged 4 to 7 years and 30 practically healthy peers were examined by static stabilometry on the device “MPFI stabilograph 1” (Kharkiv, Ukraine). Indicators of variation and shape of the pressure center distribution, spectral-correlation indicators of stabilograms, as well as integral indicators of stability (length, velocity and angle of postural oscillations) were taken into account and the equilibrium functions of the two sensory states (open and closed eyes) are calculated in the StabiliS software.&#x0D; Results: purulent otitis media causes posterior displacement of the absolute coordinates of the pressure center. In the state with closed eyes, children with purulent otitis differ from their healthy coevals by 14 of 24 stabilometric parameters, including stabilogram length, speed, angle and amplitude of oscillations, giving way to them in the stability of equilibrium. Children with purulent otitis media are more sensitive to the visual canal of postural control than their coevals. Involvement of visual afferents in postural control significantly improves balance maintenance in children with purulent otitis by reducing deviations of postural oscillations, which is reflected in the probable changes of 9 out of 24 stabilometric parameters compared to control.&#x0D; Conclusions: In preschool age, purulent otitis media leads to latent vestibular dysfunction, which is manifested by a violation of the stability of the vertical posture in a state with closed eyes and is compensated by visual-vestibulo-proprioceptive integration in the process of postural control.

A Comparison of Fresh Pork Colour Measurements by Using Four Commercial Handheld Devices.

The objective of this study was to evaluate the performance of different low-cost instruments to measure pork colour in comparison to Minolta spectrophotometers and industry subjective standards. Canadian pork colour standards and commercial meat (252 loin chops and 46 tenderloins) were measured using two Minolta (CM 700D) spectrophotometers, four Nix sensors (two Nix Pro II and two Nix QC), and four Spectro devices (two Spectro 1 and two Spectro 1 Pro). Using Bland-Altman plots, all hand-held devices revealed similar performance on colour coordinates, except for the Nix Pro II, which had more variability on a* value, and Spectro 1 Pro on b* value, when compared to Minolta measurements. Low RSD values (< 5%) were obtained from repeated measurements on Canadian colour standards. The trend of colour coordinates on colour scores (0–6) were similar for all four commercial instruments, except for a* from Nix Pro and b* from Spectro 1. The correlation coefficients between subjective standards and colour coordinates from the Nix and Spectro devices were slightly higher than the Minolta spectrophotometers. Even though Nix and Spectro 1 series instruments generated different absolute colour coordinate values on meat samples, these pocket-size instruments presented great reliability to measure pork surface colour. However, operational limitations of the instruments, such as the internal calibration time between samples for the Spectro 1 series, should also be considered.

Method for the Coordination of Referencing of Autonomous Underwater Vehicles to Man-Made Objects Using Stereo Images

The use of an autonomous underwater vehicle (AUV) to inspect underwater industrial infrastructure requires the precise, coordinated movement of the AUV relative to subsea objects. One significant underwater infrastructure system is the subsea production system (SPS), which includes wells for oil and gas production, located on the seabed. The present paper suggests a method for the accurate navigation of AUVs in a distributed SPS to coordinate space using video information. This method is based on the object recognition and computation of the AUV coordinate references to SPS objects. Stable high accuracy during the continuous movement of the AUV in SPS space is realized through the regular updating of the coordinate references to SPS objects. Stereo images, a predefined geometric SPS model, and measurements of the absolute coordinates of a limited number of feature points of objects are used as initial data. The matrix of AUV coordinate references to the SPS object coordinate system is computed using 3D object points matched with the model. The effectiveness of the proposed method is estimated based on the results of computational experiments with virtual scenes generated in the simulator for AUV, and with real data obtained by the Karmin2 stereo camera (Nerian Vision, Stuttgart, Germany) in laboratory conditions.

Failure Detection in Eucalyptus Plantation Based on UAV Images

The information of the locations and numbers of failures is crucial to precise management of new afforestation, especially during seedling replanting in young forests. In practice, foresters are more accustomed to determining the locations of failures according to their rows than based on their geographical coordinates. The relative locations of failures are more difficult to collect than the absolute geographic coordinates which are available from an orthoimage. This paper develops a novel methodology for obtaining the relative locations of failures in rows and counting the number of failures in each row. The methodology contains two parts: (1) the interpretation of the direction angle of seedlings rows on an unmanned aerial vehicle (UAV) orthoimage based on the probability statistical theory (called the grid-variance (GV) method); (2) the recognition of the centerline of each seedling rows using K-means and the approach to counting failures in each row based on the distribution of canopy pixels near the centerline of each seedling row (called the centerline (CL) method). The experimental results showed that the GV method can accurately interpret the direction angle of rows (45°) in an orthoimage and the CL method can quickly and accurately obtain the numbers and relative locations of failures in rows. The failure detection rates in the two experimental areas were 91.8% and 95%, respectively. These research findings can provide technical support for the precise cultivation of planted seedling forests.

Discontinuous dynamics of an asymmetric 2-DOF friction oscillator with elastic and rigid impacts

• An asymmetric 2 DOF oscillator with elastic and rigid impacts is investigated. • Negative feedback forces and nonlinear spring of cubic term are considered. • Switching conditions of motion at separation boundaries are explored. • Several typical motions are simulated numerically by MATLAB software. In this paper, by using flow switching theory of discontinuous dynamical systems , the discontinuous dynamic behavior of a 2-DOF (two-degree-of-freedom) friction oscillator with elastic impact and rigid impact on different sides is investigated. For the 2-DOF friction oscillator, when the direction of object’s velocity changes, the negative feedback works and the inequality of maximum static friction force and kinetic friction force leads to the existence of flow barriers. In addition, the elastic impact and rigid impact can change motion states of object, resulting in the discontinuity of this 2-DOF system. Considering the multiple motion states of object and better analyzing the equation of object’s motion, the phase space of each object is divided into different motion domains and boundaries in relative and absolute coordinates by means of the discontinuities resulted from the friction and impact. Moreover, because the elastic impact exists in a time period, there will be a variety of motion behaviors coexisting, such as elastic and rigid impacts occur simultaneously. With that in mind, in absolute coordinate system, the phase space of the system is divided in six cases according to whether there are stick motion and stuck motion. Based on flow switching theory, the switching conditions at discontinuous boundaries for all possible motions are given by using G-functions, and it should be noted that the vanishing conditions of the sliding motion become more complicated due to the existence of flow barriers at speed boundaries. Through defining the switching sets on separation boundaries, the mapping structures are further introduced to demonstrate the global dynamic behavior and periodic motions. For a better understanding of the object’s motion and the switching criteria at separation boundaries, the numerical simulation method is used to demonstrate several typical motions such as passable motion, sliding motion, grazing motion, stick motion (elastic impact), rigid impact and periodic motions etc. The results obtained have reference value for the optimization design and noise control of mechanical systems with gap couplings and negative feedbacks.

Automatic Road Marking Extraction and Vectorization from Vehicle-Borne Laser Scanning Data

Automatic driving technology is becoming one of the main areas of development for future intelligent transportation systems. The high-precision map, which is an important supplement of the on-board sensors during shielding or limited observation distance, provides a priori information for high-precision positioning and path planning in automatic driving. The position and semantic information of the road markings, such as absolute coordinates of the solid lines and dashed lines, are the basic components of the high-precision map. In this paper, we study the automatic extraction and vectorization of road markings. Firstly, scan lines are extracted from the vehicle-borne laser point cloud data, and the pavement is extracted from scan lines according to the geometric mutation at the road boundary. On this basis, the pavement point clouds are transformed into raster images with a certain resolution by using the method of inverse distance weighted interpolation. An adaptive threshold segmentation algorithm is used to convert raster images into binary images. Followed by the adaptive threshold segmentation is the Euclidean clustering method, which is used to extract road markings point clouds from the binary image. Solid lines are detected by feature attribute filtering. All of the solid lines and guidelines in the sample data are correctly identified. The deep learning network framework PointNet++ is used for semantic recognition of the remaining road markings, including dashed lines, guidelines and arrows. Finally, the vectorization of the identified solid lines and dashed lines is carried out based on a line segmentation self-growth algorithm. The vectorization of the identified guidelines is carried out according to an alpha shape algorithm. Point cloud data from four experimental areas are used for road marking extraction and identification. The F-scores of the identification of dashed lines, guidelines, straight arrows and right turn arrows are 0.97, 0.66, 0.84 and 1, respectively.

Multi-vehicle cooperative positioning based on edge-computed multidimensional scaling

As the basis of location-based services (LBS), positioning is one of the most essential parts in intelligent transportation systems (ITS). Although global positioning system (GPS) has been widely used in vehicle positioning, it can not achieve lane level positioning accuracy. Motivated by the mature ranging technologies such as radar and ultra-wideband (UWB), several cooperative positioning (CP) methods have been proposed to enhance the accuracy and robustness of GPS. In this paper, we proposed a two-stage CP algorithm that combines multidimensional scaling (MDS) and Procrustes analysis for vehicles with GPS information. Specifically, the optimized MDS based on the scaling by majorizing a complicated function (SMACOF) algorithm is first proposed to get the relative coordinates of vehicles which can tackle measurements of different error distributions, then Procrustes analysis is carried out to transform the relative coordinates of vehicles to their absolute coordinates based on GPS information. All the computations are performed at the mobile edge computing node (MECN) for the request of ultra-reliable and low latency communications (URLLC). Simulation results validate that the proposed algorithm can greatly improve the positioning accuracy and robustness for vehicles.

Inner‐Core Wind Field in a Concentric Eyewall Replacement of Typhoon Trami (2018): A Quantitative Analysis Based on the Himawari‐8 Satellite

AbstractDynamics of rapid changes of intensity and structure in an eyewall replacement cycle of tropical cyclones remain an open question. To clarify the dynamics of the inner eyewall decaying, a quantitative estimation of inner‐core wind fields based on highly frequent observation images with 2.5‐min temporal resolution in the Himawari‐8 satellite is applied to Typhoon Trami (2018) which had a clear concentric eyewall structure. A high tangential wind of 50 m s−1 is estimated at a radius of 30 km, which is located in the inner edge of the inner eyewall, during an active stage of the inner eyewall. During the decaying stage of the inner eyewall, the estimated tangential wind rapidly decreases to about 20 m s−1 at a radius of 24 km. The satellite‐based tangential winds are validated with dropsondes around the inner core by an aircraft. Vorticity field retrieved by the satellite‐based tangential winds during the decaying stage exhibits a rapid decrease in an outer part of the eye and the inner eyewall, and a slow decrease near the storm center. Examination on an absolute angular momentum coordinate indicates that the rapidly slow‐down rotation in the outer edge of the eye and inner eyewall is faster than a slow‐down rotation explained by surface friction. It suggests that asymmetric eddies transport angular momentum across the moat in the inner eyewall dissipation. This study is the first examination of dynamical contributions of asymmetric eddies to the inner‐eyewall dissipation based on satellite‐estimated tangential winds.

3D source tracking and error detection in HDR using two independent scintillator dosimetry systems.

The aim of this study is to perform three-dimensional (3D) source position reconstruction by combining in vivo dosimetry measurements from two independent detector systems. Time-resolved dosimetry was performed in a water phantom during HDR brachytherapy irradiation with Ir source using two detector systems. The first was based on three plastic scintillator detectors and the second on a single inorganic crystal (CsI:Tl). Brachytherapy treatments were simulated in water under TG-43U1 conditions, including a HDR prostate plan. Treatment needles were placed in distances covering a range of source movement of 120mm around the detectors. The distance from each dwell position to each scintillator was determined based on the measured dose rates. The three distances given by the mPSD were recalculated to a position along the catheter (z) and a distance radially away from the mPSD (xy) for each dwell position (a circumference around the mPSD). The source x, y, and z coordinates were derived from the intersection of the mPSD's circumference with the sphere around the ISD based on the distance to this detector. We evaluated the accuracy of the source position reconstruction as a function of the distance to the source, the most likely location for detector positioning within a prostate volume, as well as the capacity to detect positioning errors. Approximately 4000 source dwell positions were tracked for eight different HDR plans. An intersection of the mPSD torus and the ISD sphere was observed in 77.2% of the dwell positions, assuming no uncertainty in the dose rate determined distance. This increased to 100% if 1σ search regions were added. However, only 73(96)% of the expected dwell positions were found within the intersection band for 1(2) σ uncertainties. The agreement between the source's reconstructed and expected positions was within 3mm for a range of distances to the source up to 50mm. The experiments on a HDR prostate plan, showed that by having at least one of the detectors located in the middle of the prostate volume, reduces the measurement deviations considerably compared to scenarios where the detectors were located outside of the prostate volume. The analysis showed a detection probability that, in most cases, is far from the random detection threshold. Errors of 1(2)mm can be detected in ranges of 5-25 (25-50)mm from the source, with a true detection probability rate higher than 80%, while the false probability rate is kept below 20%. By combining two detector responses, we enabled the determination of the absolute source coordinates. The combination of the mPSD and the ISD in vivo dosimetry constitutes a promising alternative for real-time 3D source tracking in HDR brachytherapy.

Distributed localization algorithm for wireless sensor networks using range lookup and subregion stitching

One of the ways in which localization algorithms in wireless sensor networks (WSNs) have been categorized is whether they are range-based or range-free. Range-based algorithms use expensive hardware to measure one or more physical quantities and, in turn, use them to localize nodes with greater precision. In contrast, range-free algorithms use coarse-grained quantities like connectivity to localize nodes with limited precision. A middle way between these two approaches can be called a partial range-based approach that can utilize the existing received signal strength indicator (RSSI) readings from sensor nodes to improve the already existing coarse-grained localization methods. Another important consideration in WSNs is that a distributed localization algorithm is more computationally feasible as compared to its centralized counterpart. Keeping these two considerations in mind, a distributed localization algorithm is proposed here which falls in the aforementioned partial range-based category. The proposed algorithm called RangeLookup-MDS first creates subregions using connectivity information only. This is followed by the collection of RSSI readings from individual sensor nodes that are used to perform range lookup for inter-node distance estimates in a lookup table. After that, relative localization in every subregion is performed using multidimensional scaling, and then the relative maps are stitched together to create a consistent (but relative) coordinate system. The algorithm also has the capability to compute absolute coordinates in two-dimensional if the stitching step is executed with at least three non-collinear anchor nodes with known locations. Simulation results on uniform as well as irregular networks of various sizes show that the proposed algorithm provides improved localization accuracy and reduces localization error up to 25% in comparison to a previous partial range-based localization algorithm.

Distributed and Collaborative Localization for Swarming UAVs

In recent years, unmanned aerial vehicles (UAVs), especially swarming UAVs are widely deployed in a variety of Internet-of-Things (IoT) scenarios. Since UAVs’ positions are essential for their collaboration, high-precision localization for swarming UAVs has attracted a lot of attention. Although the global positioning system (GPS) receiver has been widely integrated in UAV, it is not accurate enough and is prone to accidental or deliberate interferences. In this article, we propose a distributed and collaborative localization method for swarming UAVs that combines super multidimensional scaling (SMDS) and patch dividing/merging with GPS information. Specifically, the SMDS is first used to get the relative coordinates of the UAVs in each patch, then we merge relative map patches into a global map and transform the relative coordinates of the UAVs to their absolute coordinates. Furthermore, we propose a low-complexity algorithm that greatly reduces the computational complexity of SMDS with a large number of UAVs. Simulation results validate that with accurate enough angle measurements, the proposed SMDS localization algorithm outperforms the other MDS-based collaborative localization algorithms and can greatly improve the localization accuracy and robustness of swarming UAVs.