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Keywords = multi-path geolocation

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17 pages, 4499 KiB  
Article
GM(1,1)-Based Weighted K-Nearest Neighbor Algorithm for Indoor Localization
by Lai Xiang, Ying Xu, Jianhui Cui, Yang Liu, Ruozhou Wang and Guofeng Li
Remote Sens. 2023, 15(15), 3706; https://doi.org/10.3390/rs15153706 - 25 Jul 2023
Cited by 2 | Viewed by 1247
Abstract
Along with the IoT technology, the importance of indoor positioning is increasing, but the accuracy of the traditional fingerprint positioning algorithm is negatively affected by the complex indoor environment. This issue of low indoor spatial geolocation localization accuracy when the signal is collected [...] Read more.
Along with the IoT technology, the importance of indoor positioning is increasing, but the accuracy of the traditional fingerprint positioning algorithm is negatively affected by the complex indoor environment. This issue of low indoor spatial geolocation localization accuracy when the signal is collected away from the present stage occurs due to the signal instability of the iBeacon in the traditional fingerprint localization algorithm, which generates a variety of factors such as object blocking and reflection, multipath effect, etc., as well as the scarcity of reference fingerprint data points. In response, this study proposes an inverse distance-weighted optimization WKNN algorithm for indoor localization based on the GM(1,1) model. By implementing GM(1,1) model pre-process leveling, the original fingerprint library was reconstructed into a large-capacity fingerprint database using the inverse distance-weighted interpolation method. The local inverse distance-weighted interpolation was used for interpolation, combined with the WKNN algorithm to complete the coordinate solution in real time. This effectively solved the issue of low localization accuracy caused by the large fluctuation of the received signal strength (RSS) sampling measurement data and the existence of few reference fingerprint datapoints in the fingerprint database. The results show that this algorithm reduced the average positioning error by 5.9% compared with ordinary kriging (OK) interpolation leveling and reduced the average positioning error by 18.2% compared with the indoor spatial location accuracy of the original fingerprint database, which can effectively improve the positioning accuracy and provide technical support for indoor location and navigation services. Full article
(This article belongs to the Special Issue Remote Sensing in Urban Positioning and Navigation)
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<p>Technology route.</p>
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<p>Schematic diagram of the offline fingerprint database after interpolation.</p>
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<p>The relationship between the RSS and the distance. Time periods (<b>a</b>) 9:00−11:00 AM; (<b>b</b>) 15:00−17:00 PM; (<b>c</b>) 19:00−21:00 PM.</p>
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<p>The relationship between the RSS and the distance. Time periods (<b>a</b>) 9:00−11:00 AM; (<b>b</b>) 15:00−17:00 PM; (<b>c</b>) 19:00−21:00 PM.</p>
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<p>Schematic diagram of the experimental site in building A.</p>
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<p>Schematic diagram of the experimental site in building B.</p>
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<p>RMSE of the three pretreatment methods.</p>
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<p>(<b>A</b>): CDF comparison graph under WKNN matching location algorithm. (<b>B</b>): CDF comparison graph under WKNN matching location algorithm. Note: GM(1,1): original fingerprint database; GM(1,1) + IDW: fingerprint database optimization algorithm based on GM(1,1) and IDW interpolation; GM(1,1) + OK: fingerprint database optimization algorithm based on GM(1,1) and OK interpolation. The same parameters are shown below.</p>
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<p>Comparison of the mean error, RMSE, and maximum error.</p>
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<p>Building A: trajectory diagrams of different algorithms. (<b>a</b>) GM(1,1); (<b>b</b>) GM(1,1) + IDW; (<b>c</b>) GM(1,1) + OK; (<b>d</b>) comparison of trajectories.</p>
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<p>Building B: trajectory diagrams of different algorithms. (<b>a</b>) GM(1,1); (<b>b</b>) GM(1,1) + IDW; (<b>c</b>) GM(1,1) + OK; (<b>d</b>) comparison of trajectories.</p>
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19 pages, 3010 KiB  
Article
Subgraph Learning for Topological Geolocalization with Graph Neural Networks
by Bing Zha and Alper Yilmaz
Sensors 2023, 23(11), 5098; https://doi.org/10.3390/s23115098 - 26 May 2023
Cited by 1 | Viewed by 2005
Abstract
One of the challenges of spatial cognition, such as self-localization and navigation, is to develop an efficient learning approach capable of mimicking human ability. This paper proposes a novel approach for topological geolocalization on the map using motion trajectory and graph neural networks. [...] Read more.
One of the challenges of spatial cognition, such as self-localization and navigation, is to develop an efficient learning approach capable of mimicking human ability. This paper proposes a novel approach for topological geolocalization on the map using motion trajectory and graph neural networks. Specifically, our learning method learns an embedding of the motion trajectory encoded as a path subgraph where the node and edge represent turning direction and relative distance information by training a graph neural network. We formulate the subgraph learning as a multi-class classification problem in which the output node IDs are interpreted as the object’s location on the map. After training using three map datasets with small, medium, and large sizes, the node localization tests on simulated trajectories generated from the map show 93.61%, 95.33%, and 87.50% accuracy, respectively. We also demonstrate similar accuracy for our approach on actual trajectories generated by visual-inertial odometry. The key benefits of our approach are as follows: (1) we take advantage of the powerful graph-modeling ability of neural graph networks, (2) it only requires a map in the form of a 2D graph, and (3) it only requires an affordable sensor that generates relative motion trajectory. Full article
(This article belongs to the Section Navigation and Positioning)
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<p>Key Idea: A graph representation of a map is composed of places and their connections on which an object navigates from one place to another. Additionally, object navigation is usually guided by instructions including turns made and distances traversed, based on which a motion trajectory is formed. We are inspired by this observation to generate a possible set of such trajectories and their respective node locations to be used as a dataset to train a graph neural network. The testing in this setup is a path subgraph that is fed into a trained model that in turn outputs the object’s node location on the map.</p>
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<p>Illustration of the proposed method to achieve topological localization. A forward pass consists of (<b>a</b>) acquisition of raw trajectory from visual or/and inertial data source; (<b>b</b>) construction of a trajectory graph or augmented trajectory graph by identifying significant turnings in raw trajectories. The augmented trajectory graph encodes both the turns and the distances by inserting virtual nodes; (<b>c</b>) each subgraph embedding is obtained by training a graph neural network; and (<b>d</b>) classification of subgraph embedding to generate a node label that indicates the final location of the learned map. Note that the training and inference share an identical pipeline except for the subgraph embedding part.</p>
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<p>Encode original trajectory into subgraph using two different representations: filtered trajectory graph encodes turning information, and augmented trajectory graph encodes both turning and distance information.</p>
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<p>Egocentric coordinate system for angle computation and quantization into discrete angle representation. The illustrated figure uses 20 bins.</p>
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<p>Illustration of embedding trajectory subgraph with a graph neural network layer and a fully connected layer. The GNN layer is used to embed each node’s attribute and integrate it into a single subgraph embedding by graph pooling operation. The fully connected layer and softmax layer serves as a classifier intended to classify subgraph embedding into node space <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>i</mi> </msub> <mo>∈</mo> <mi mathvariant="script">E</mi> <mo>=</mo> <mrow> <msub> <mi>v</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>v</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <msub> <mi>v</mi> <mi>n</mi> </msub> </mrow> </mrow> </semantics></math>.</p>
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<p>Map graphs: from the top row to the bottom row are small, medium-sized, and larger maps.</p>
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<p>Three ways to collect real trajectory data for testing: the left and medium ones are used for collecting trajectories through visual-inertial odometry in the small- and medium-sized map; the last one uses Google Maps to collect trajectory data in the large-sized map.</p>
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<p>Training performance on the original, filtered, and augmented dataset for different numbers of layers in GNN. The first row is for the small-sized map where the best accuracies are reported to be 99.1%, 83.0%, and 94.0%, respectively; the second row is for the medium-sized map where the best accuracies are 98.9%, 82.7%, and 96.1%, respectively; and the bottom row is for the large-sized map, where best accuracies are 96.1%, 51.0%, and 87.5%, respectively.</p>
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<p>Testing results on real trajectories generated using visual-inertial odometry.</p>
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<p>Testing results on real trajectories generated using visual-inertial odometry.</p>
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<p>Testing results on real trajectories generated using visual-inertial odometry.</p>
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24 pages, 25145 KiB  
Article
High-Frequency Channel Modeling Based on the Multi-Source Ionospheric Assimilation Model
by Mingjie Lv, Chen Zhou, Tongxin Liu, Jiandong Qiao, Wei Qiao, Chen Li, Junming Wang and Jianhua Zhu
Remote Sens. 2022, 14(17), 4133; https://doi.org/10.3390/rs14174133 - 23 Aug 2022
Viewed by 1688
Abstract
In this paper, we explored how to more accurately predict the quality of high-frequency links and how to better research and improve the capabilities of high-frequency communication, reconnaissance, and positioning systems. Based on the background electron density generated by the ionospheric assimilation model [...] Read more.
In this paper, we explored how to more accurately predict the quality of high-frequency links and how to better research and improve the capabilities of high-frequency communication, reconnaissance, and positioning systems. Based on the background electron density generated by the ionospheric assimilation model and 3D ray-tracing technology, more realistic and accurate high-frequency channel parameters with physical meanings were obtained. On this basis, a complete high-frequency channel model that can be used for simulation and prediction was constructed. First, the ionospheric assimilation model, the high-frequency channel model, and the method used for calculating the parameters of the high-frequency channel model based on the background electron density generated by the multi-source ionospheric assimilation model are introduced. Then, the HF oblique sounding experiment and experimental data processing are introduced. Finally, the modeling and simulation of the high-frequency channel are compared with the HF oblique sounding experimental results. The simulation results showed that the modeling results of the high-frequency channel based on the multi-source ionospheric assimilation model proposed in this paper were similar to the HF oblique sounding experimental results. The average deviation of the difference between the simulation results and the experimental ones of the group path, the group path broadening, and the Doppler frequency shift are 29.2200 km, 17.3456 km, and 0.2121 Hz, respectively. The group delay, Doppler frequency shift, and delay broadening results calculated by the high-frequency channel model simulation were relatively accurate and could be used in high-frequency channel quality reporting and prediction, high-frequency reconnaissance and geolocation, and high-frequency radar frequency selection and positioning, etc. Full article
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<p>Site distribution of the experimental scheme.</p>
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<p>21 October 2020, data processing results of Leshan station. The redder the color in the figure, the stronger the received signal energy. The color bar only represents the relative size of the value. The time the data were received was 00:00 LT (<b>upper left</b>), 10:00 LT (<b>upper right</b>), 12:00 LT (<b>middle left</b>), 14:00 LT (<b>middle right</b>), 16: 00 LT (<b>lower left</b>), and 20:00 LT (<b>lower right</b>). If elliptic-like bright spots appear in the figure, it means that the receiver can receive signals reflected from the ionosphere. Generally speaking, the elliptic-like bright spot with the smaller ordinate is reflected through the E layer (in which the group paths are about 1100 km), and the elliptic-like bright spot with larger ordinate is reflected through the F layer (in which the group paths are about 1200–1300 km). There is no elliptic-like bright spot in the upper left and lower right panels, which indicates that the Wuhan receiver cannot receive the HF signals transmitted from Leshan station at these two moments (as mentioned above, the signals with a frequency of 10.8 MHz were unable to obtain a good oblique measurement reception effect at night).</p>
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<p>22 October 2020, data processing results of Leshan station. Refer to the captions in <a href="#remotesensing-14-04133-f002" class="html-fig">Figure 2</a> for the receiving time and other descriptions of each panel. The difference from <a href="#remotesensing-14-04133-f002" class="html-fig">Figure 2</a> is that at 20:00 LT (bottom right) the Wuhan receiver can still receive the HF signals from the Leshan station.</p>
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<p>23 October 2020, data processing results of Leshan station. Refer to the captions in <a href="#remotesensing-14-04133-f002" class="html-fig">Figure 2</a> for the receiving time and other descriptions of each panel.</p>
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<p>21 October 2020, data processing results of Daofu station. Refer to the captions in <a href="#remotesensing-14-04133-f002" class="html-fig">Figure 2</a> for the receiving time and other descriptions of each panel. Because the ground distance between Wuhan and Daofu is greater, the SNR of this figure is lower and the quality of the HF channel is also worse compared to <a href="#remotesensing-14-04133-f002" class="html-fig">Figure 2</a>. The group paths of the HF signals reflected by the E layer are about 1350 km, and the group paths of the HF signals reflected by the F layer are about 1400 km.</p>
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<p>22 October 2020, data processing results of Daofu station. Refer to the captions in <a href="#remotesensing-14-04133-f002" class="html-fig">Figure 2</a> for the receiving time and other descriptions of each panel.</p>
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<p>23 October 2020, data processing results of Daofu station. Refer to the captions in <a href="#remotesensing-14-04133-f002" class="html-fig">Figure 2</a> for the receiving time and other descriptions of each panel.</p>
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<p>The relationship between the Doppler shift of the two HF links with time. The left panel represents the Daofu–Wuhan link, and the right panel represents the Leshan–Wuhan link. The blue circles represent the results of the Doppler shift interpretation, and the red lines represents the average value of the Doppler shift. The average Doppler shifts of the Leshan–Wuhan link and the Daofu–Wuhan link are 0.0733 Hz and 0.0714 Hz.</p>
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<p>3D directive gain of the antenna in the experiment. The left figure is a three-wire antenna, and the right figure is an inverted V antenna.</p>
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<p>21 October 2020, modeling and simulation results of the HF channel at Leshan station. The redder the color in the figure, the stronger the received energy. The color bar’s unit is <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>B</mi> <mrow> <mo>(</mo> <mrow> <mrow> <mrow> <mn>1</mn> <mi>μ</mi> <mi>V</mi> </mrow> <mo>/</mo> <mi>m</mi> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>. The time in the picture is 00:00 LT (<b>upper left</b>), 10:00 LT (<b>upper right</b>), 12:00 LT (<b>middle left</b>), 14:00 LT (<b>middle right</b>), 16: 00 LT (<b>lower left</b>), and 20:00 LT (<b>lower right</b>). The group paths of the HF signals reflected by the E layer are about 1100 km, and the group paths of the HF signals reflected by the F layer are about 1200 km, which was close to the HF oblique sounding experimental results. In addition, the Wuhan receiver was also unable to receive the HF signals transmitted from Leshan station at 00:00 LT (<b>upper left</b>) and 20:00 LT (<b>lower right</b>) compared to <a href="#remotesensing-14-04133-f002" class="html-fig">Figure 2</a>.</p>
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<p>22 October 2020, modeling and simulation results of the HF channel at Leshan station. Refer to the captions in <a href="#remotesensing-14-04133-f010" class="html-fig">Figure 10</a> for the receiving time and other descriptions of each panel.</p>
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<p>23 October 2020, modeling and simulation results of the HF channel at Leshan station. Refer to the captions in <a href="#remotesensing-14-04133-f010" class="html-fig">Figure 10</a> for the receiving time and other descriptions of each panel.</p>
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<p>21 October 2020. The modeling and simulation results of the HF channel at Daofu station. Refer to the captions in <a href="#remotesensing-14-04133-f010" class="html-fig">Figure 10</a> for the receiving time and other descriptions of each panel. The group paths of the HF signals reflected by the E layer are about 1350 km, and the group paths of the HF signals reflected by the F layer are about 1400 km, which was close to the HF oblique sounding experimental results. In addition, the Wuhan receiver was also unable to receive the HF signals transmitted from Daofu station at 00:00 LT (<b>upper left</b>) and 20:00 LT (<b>lower right</b>) compared to <a href="#remotesensing-14-04133-f005" class="html-fig">Figure 5</a>.</p>
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<p>22 October 2020, modeling and simulation results of the HF channel at Daofu station. Refer to the captions in <a href="#remotesensing-14-04133-f010" class="html-fig">Figure 10</a> for the receiving time and other descriptions of each panel.</p>
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<p>23 October 2020, the modeling and simulation results of the HF channel at Daofu station. Refer to the captions in <a href="#remotesensing-14-04133-f010" class="html-fig">Figure 10</a> for the receiving time and other descriptions of each panel.</p>
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11 pages, 2642 KiB  
Article
Decimeter-Level Geolocation Accuracy Updated by a Parametric Tropospheric Model with GF-3
by Wentao Wang, Jiayin Liu and Xiaolan Qiu
Sensors 2018, 18(7), 2197; https://doi.org/10.3390/s18072197 - 8 Jul 2018
Cited by 8 | Viewed by 3917
Abstract
GaoFen-3 (GF-3) is a multi-polarization C-band synthetic aperture radar (SAR) satellite in China with a resolution of up to 1 m. Up to now, the geolocation accuracy of GF-3 could be improved to 3 m. According to the current study, there still exist [...] Read more.
GaoFen-3 (GF-3) is a multi-polarization C-band synthetic aperture radar (SAR) satellite in China with a resolution of up to 1 m. Up to now, the geolocation accuracy of GF-3 could be improved to 3 m. According to the current study, there still exist meter-level geolocation residuals caused by atmospheric path delay after compensating with a static tropospheric model. In this paper, we compensate the residuals with the sophisticated tropospheric model based on real meteorological data. The experimental results show that the tropospheric model has an accuracy on the millimeter level, which can increase GF-3’s geolocation accuracy to several decimeters compared with the static tropospheric model. Full article
(This article belongs to the Special Issue First Experiences with Chinese Gaofen-3 SAR Sensor)
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<p>The propagation path of the signal in the atmosphere (disproportional schematic scheme).</p>
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<p>The zenith path delay (ZPD) variations at the BJFS International GNSS Service (IGS) station in 2016.</p>
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<p>(<b>a</b>) The IGS ZPD variations and ZTD variations of the three models in June; (<b>b</b>) The difference value (DIFF) between ZTD of three models and IGS ZPD in June. SAAS: the Saastamoinen model.</p>
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<p>(<b>a</b>) The IGS ZPD variations and ZTD variations of the three models in December; (<b>b</b>) The DIFF between ZTD of three models and IGS ZPD in December.</p>
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<p>(<b>a</b>) The DIFF between ZTD of three models and IGS ZPD in 2016 (<b>b</b>) The RMSE between ZTD of three models and IGS ZPD in 2016.</p>
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<p>(<b>a</b>) The URUM IGS ZPD variations and ZTD variations of the three models in December (<b>b</b>) The DIFF between ZTD of three models and the URUM IGS ZPD in December.</p>
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36 pages, 2614 KiB  
Article
Direct Position Determination of Unknown Signals in the Presence of Multipath Propagation
by Jianping Du, Ding Wang, Wanting Yu and Hongyi Yu
Sensors 2018, 18(3), 892; https://doi.org/10.3390/s18030892 - 17 Mar 2018
Cited by 9 | Viewed by 4403
Abstract
A novel geolocation architecture, termed “Multiple Transponders and Multiple Receivers for Multiple Emitters Positioning System (MTRE)” is proposed in this paper. Existing Direct Position Determination (DPD) methods take advantage of a rather simple channel assumption (line of sight channels with complex path attenuations) [...] Read more.
A novel geolocation architecture, termed “Multiple Transponders and Multiple Receivers for Multiple Emitters Positioning System (MTRE)” is proposed in this paper. Existing Direct Position Determination (DPD) methods take advantage of a rather simple channel assumption (line of sight channels with complex path attenuations) and a simplified MUltiple SIgnal Classification (MUSIC) algorithm cost function to avoid the high dimension searching. We point out that the simplified assumption and cost function reduce the positioning accuracy because of the singularity of the array manifold in a multi-path environment. We present a DPD model for unknown signals in the presence of Multi-path Propagation (MP-DPD) in this paper. MP-DPD adds non-negative real path attenuation constraints to avoid the mistake caused by the singularity of the array manifold. The Multi-path Propagation MUSIC (MP-MUSIC) method and the Active Set Algorithm (ASA) are designed to reduce the dimension of searching. A Multi-path Propagation Maximum Likelihood (MP-ML) method is proposed in addition to overcome the limitation of MP-MUSIC in the sense of a time-sensitive application. An iterative algorithm and an approach of initial value setting are given to make the MP-ML time consumption acceptable. Numerical results validate the performances improvement of MP-MUSIC and MP-ML. A closed form of the Cramér–Rao Lower Bound (CRLB) is derived as a benchmark to evaluate the performances of MP-MUSIC and MP-ML. Full article
(This article belongs to the Special Issue Sensor Fusion and Novel Technologies in Positioning and Navigation)
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<p>Multiple-path positioning problem with static transponders/receivers.</p>
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<p>Multiple-peak cost function of a frequency band signal and single peak cost function of a base band signal. (<b>a</b>) Cost function for a frequency band signal (<b>b</b>) Cost function for a base band signal.</p>
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<p>Layouts of the numerical examples. (<b>a</b>) Layout A (<b>b</b>) Layout B.</p>
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<p>Spatial spectrum of Signal Subspace Projection (SSP)-MUSIC and Noise Subspace Projection (NSP)-MUSIC in a single path scenario. (<b>a</b>) SSP-MUSIC (<b>b</b>) NSP-MUSIC.</p>
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<p>Spatial spectrum in baseband signal positioning. (<b>a</b>) Spatial spectrum of SSP-MUSIC and NSP-MUSIC (<b>b</b>) Spatial spectrum of Multi-path Propagation (MP)-MUSIC.</p>
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<p>Spatial spectrum when a transponder is close to the anther. (<b>a</b>) Spatial spectrum of SSP-MUSIC and NSP-MUSIC (<b>b</b>) Spatial spectrum of MP-MUSIC.</p>
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<p>Spatial spectrum for a single antenna of each receiving array. (<b>a</b>) Spatial spectrum of SSP-MUSIC and NSP-MUSIC (<b>b</b>) Spatial spectrum of MP-MUSIC.</p>
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<p>Spatial spectrum in a general scenario. (<b>a</b>) Spatial spectrum of SSP-MUSIC and NSP-MUSIC (<b>b</b>) Spatial spectrum of MP-MUSIC.</p>
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<p>Performance of MP-MUSIC-Active Set Algorithm (ASA) and MP-MUSIC-Interior Point Algorithm (IPA).</p>
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<p>Performances of MP-MUSIC and MP-ML (<math display="inline"> <semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>16</mn> <mo>,</mo> <mi>J</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math>).</p>
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<p>Performance of MP-ML and MP-MUSIC with different <math display="inline"> <semantics> <mrow> <mi>J</mi> <mo>,</mo> <mi>K</mi> </mrow> </semantics> </math> combinations.</p>
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<p>Performances of MP-MUSIC and MP-ML with different numbers of snapshots.</p>
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<p>Time consumptions and RMSE of different numbers of emitters. (<b>a</b>) Time consumptions of MP-MUSIC and MP-ML (<b>b</b>) RMSE of MP-MUSIC and MP-ML.</p>
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<p>Positioning accuracies and time consumptions of MP-ML.</p>
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<p>MP-ML and CRLB of different numbers of receivers (<math display="inline"> <semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics> </math>).</p>
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<p>MP-ML and CRLB of different numbers of emitters (<math display="inline"> <semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>1024</mn> <mo>,</mo> <mi>J</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math>).</p>
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<p>Two paths with the same delay.</p>
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