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17 pages, 4838 KiB  
Article
Improved Detection of Multi-Class Bad Traffic Signs Using Ensemble and Test Time Augmentation Based on Yolov5 Models
by Ibrahim Yahaya Garta, Shao-Kuo Tai and Rung-Ching Chen
Appl. Sci. 2024, 14(18), 8200; https://doi.org/10.3390/app14188200 - 12 Sep 2024
Viewed by 626
Abstract
Various factors such as natural disasters, vandalism, weather, and environmental conditions can affect the physical state of traffic signs. The proposed model aims to improve detection of traffic signs affected by partial occlusion as a result of overgrown vegetation, displaced signs (those knocked [...] Read more.
Various factors such as natural disasters, vandalism, weather, and environmental conditions can affect the physical state of traffic signs. The proposed model aims to improve detection of traffic signs affected by partial occlusion as a result of overgrown vegetation, displaced signs (those knocked down, bent), perforated signs (those damaged with holes), faded signs (color degradation), rusted signs (corroded surface), and de-faced signs (placing graffiti, etc., by vandals). This research aims to improve the detection of bad traffic signs using three approaches. In the first approach, Spiral Pooling Pyramid-Fast (SPPF) and C3TR modules are introduced to the architecture of Yolov5 models. SPPF helps provide a multi-scale representation of the input feature map by pooling at different scales, which is useful in improving the quality of feature maps and detecting bad traffic signs of various sizes and perspectives. The C3TR module uses convolutional layers to enhance local feature extraction and transformers to boost understanding of the global context. Secondly, we use predictions of Yolov5 as base models to implement a mean ensemble to improve performance. Thirdly, test time augmentation (TTA) is applied at test time by using scaling and flipping to improve accuracy. Some signs are generated using stable diffusion techniques to augment certain classes. We test the proposed models on the CCTSDB2021, TT100K, GTSDB, and GTSRD datasets to ensure generalization and use k-fold cross-validation to further evaluate the performance of the models. The proposed models outperform other state-of-the-art models in comparison. Full article
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<p>Sample images representing all the classes in the dataset: (<b>a</b>) occluded; (<b>b</b>) displaced; (<b>c</b>) faded; (<b>d</b>) perforated; (<b>e</b>) good; (<b>f</b>) rusted; (<b>g</b>) defaced.</p>
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<p>Structure of the Yolov5 model.</p>
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<p>Structures of C3 and C3TR modules.</p>
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<p>Flowchart of the proposed ensemble model.</p>
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<p>Flowchart of the proposed test time augmentation.</p>
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<p>Comparison of accuracy of all classes for base and improved models.</p>
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<p>Precision–recall curve of the mean ensemble.</p>
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<p>F1 score of the TTA model.</p>
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<p>Graph showing mAP@50 of the proposed models.</p>
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<p>Detection results on some public datasets: (<b>a</b>) Detection results on the GTSRD by TTA; (<b>b</b>) detection results on the TT100K test image by mean ensemble; (<b>c</b>) detection result showing misclassification and detection of good traffic signs on GTSRD image by improved Yolov5m; (<b>d</b>) detection result by improved Yolov5s on CCTSDB2021; (<b>e</b>) misdetection by Yolov5s on CCTSDB2021 as rusted traffic sign and correctly detect good traffic sign; (<b>f</b>) detection result by Yolov5m on GTSDB dataset.</p>
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17 pages, 3227 KiB  
Article
Combined Cubature Kalman and Smooth Variable Structure Filtering Based on Multi-Kernel Maximum Correntropy Criterion for the Fully Submerged Hydrofoil Craft
by Hongmin Niu and Sheng Liu
Appl. Sci. 2024, 14(9), 3952; https://doi.org/10.3390/app14093952 - 6 May 2024
Viewed by 1054
Abstract
This paper introduces a novel filter algorithm termed as an MKMC-CSVSF which combined square-root cubature Kalman (SR-CKF) and smooth variable structure filtering (SVSF) under multi-kernel maximum correntropy criterion (MKMC) for accurately estimating the state of the fully submerged hydrofoil craft (FSHC) under the [...] Read more.
This paper introduces a novel filter algorithm termed as an MKMC-CSVSF which combined square-root cubature Kalman (SR-CKF) and smooth variable structure filtering (SVSF) under multi-kernel maximum correntropy criterion (MKMC) for accurately estimating the state of the fully submerged hydrofoil craft (FSHC) under the influence of uncertainties and multivariate heavy-tailed non-Gaussian noises. By leveraging the precision of the SR-CKF and the robustness of the SVSF against system uncertainties, the MKMC-CSVSF integrates these two methods by introducing a time-varying smooth boundary layer along with multiple fading factors. Furthermore, the MKMC is introduced for the adjustment of kernel bandwidths across different channels to align with the specific noise characteristics of each channel. A fuzzy rule is devised to identify the appropriate kernel bandwidths to ensure filter accuracy without undue complexity. The precision and robustness of state estimation in the face of heavy-tailed non-Gaussian noises are improved by modifying the SR-CKF and the SVSF using a fixed-point approach based on the MKMC. The experimental results validate the efficacy of this algorithm. Full article
(This article belongs to the Section Marine Science and Engineering)
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<p>The state trajectory of the CSVSF.</p>
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<p>The estimation of heave motion of the FSHC.</p>
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<p>The estimation error of heave motion of the FSHC.</p>
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<p>The estimation of heave velocity of the FSHC.</p>
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<p>The estimation error of heave velocity of the FSHC.</p>
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<p>The estimation of pitch angle of the FSHC.</p>
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<p>The estimation error of pitch angle of the FSHC.</p>
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<p>The estimation of pitch angle velocity of the FSHC.</p>
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<p>The estimation error of pitch angle velocity of the FSHC.</p>
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<p>The RMSE of heave motion of the FSHC.</p>
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<p>The RMSE of heave velocity of the FSHC.</p>
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<p>The RMSE of pitch angle of the FSHC.</p>
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<p>The RMSE of pitch angle velocity of the FSHC.</p>
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14 pages, 2336 KiB  
Article
Physical Layer Security Performance of Multi-User Mixed Radio-Frequency/Free-Space-Optics System Based on Optimal User Interference
by Zihe Shen, Yi Wang and Jiamin Wu
Sensors 2023, 23(14), 6523; https://doi.org/10.3390/s23146523 - 19 Jul 2023
Cited by 1 | Viewed by 1206
Abstract
This paper presents research on the physical layer security performance of a multi-user mixed RF/FSO system based on optimal user interference. In this system model, the RF link experiences Rayleigh fading, and the FSO link follows the Fischer–Snedecor F distribution. The system adopts [...] Read more.
This paper presents research on the physical layer security performance of a multi-user mixed RF/FSO system based on optimal user interference. In this system model, the RF link experiences Rayleigh fading, and the FSO link follows the Fischer–Snedecor F distribution. The system adopts a double-hop-decode-and-forward (DF) relay scheme. We also consider the effect of directivity errors in the FSO link and assume the presence of an illegal eavesdropper with a single antenna near the RF link. The source node controls the energy collection and information forwarding using a multi-user structure based on simultaneous wireless information and power transfer (SWIPT). We select the optimal user to jam the eavesdropper’s communication. We derive closed-form expressions for the mixed RF/FSO communication system’s secrecy outage probability (SOP) and average secrecy capacity (ASC). Monte Carlo simulations are performed to verify the accuracy of these expressions. By formulating and simulating the simulation system, the impact of various important factors on the mixed system’s physical layer security (PLS) is analyzed. The analysis indicates that increasing the number of antennas and interference signal-to-noise ratio (SNR) of the optimal user, the time allocation factor and energy conversion efficiency, and the improvement in the quality of atmospheric channels with improved weather will significantly enhance this system’s PLS. Full article
(This article belongs to the Section Communications)
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<p>A multi-user mixed RF/FSO system based on optimal user interference.</p>
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<p>Time slot switching (TS) protocol for SWIPT.</p>
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<p>Simulation of the SOP and the Instantaneous SNR of RF link for the RF/FSO system with the optimal user’s different numbers of interference antennas <math display="inline"><semantics><mrow><msub><mi>N</mi><mi>J</mi></msub></mrow></semantics></math>.</p>
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<p>Simulation of the SOP and the instantaneous SNR of the RF link of the RF/FSO system under different interference SNR <math display="inline"><semantics><mrow><msub><mi>λ</mi><mrow><mi>J</mi><mi>E</mi></mrow></msub></mrow></semantics></math> of the optimal user.</p>
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<p>Simulation of the security outage probability and the instantaneous signal-to-noise ratio of the RF link in RF/FSO system under different energy conversion efficiency <math display="inline"><semantics><mi>η</mi></semantics></math> of the optimal user.</p>
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<p>Simulation of the average secrecy capacity and the instantaneous SNR of RF link in RF/FSO system when the optimal user uses different time allocation factors <math display="inline"><semantics><mi>ρ</mi></semantics></math>.</p>
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<p>Simulation of the average secrecy capacity and the instantaneous SNR of the RF link of the RF/FSO system under different interference SNRS <math display="inline"><semantics><mrow><msub><mi>λ</mi><mrow><mi>J</mi><mi>E</mi></mrow></msub></mrow></semantics></math> of the optimal user.</p>
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<p>Simulation of the ASC of the RF/FSO system with different turbulence factors a, b and the instantaneous SNR <math display="inline"><semantics><mrow><msub><mi>λ</mi><mrow><mi>R</mi><mi>D</mi></mrow></msub></mrow></semantics></math> of the FSO link under optimal user interference.</p>
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32 pages, 1171 KiB  
Article
Exploiting User Clustering and Fixed Power Allocation for Multi-Antenna UAV-Assisted IoT Systems
by Sang Quang Nguyen, Anh-Tu Le, Chi-Bao Le, Phu Tran Tin and Yong-Hwa Kim
Sensors 2023, 23(12), 5537; https://doi.org/10.3390/s23125537 - 13 Jun 2023
Cited by 5 | Viewed by 1447
Abstract
Internet of Things (IoT) systems cooperative with unmanned aerial vehicles (UAVs) have been put into use for more than ten years, from transportation to military surveillance, and they have been shown to be worthy of inclusion in the next wireless protocols. Therefore, this [...] Read more.
Internet of Things (IoT) systems cooperative with unmanned aerial vehicles (UAVs) have been put into use for more than ten years, from transportation to military surveillance, and they have been shown to be worthy of inclusion in the next wireless protocols. Therefore, this paper studies user clustering and the fixed power allocation approach by placing multi-antenna UAV-mounted relays for extended coverage areas and achieving improved performance for IoT devices. In particular, the system enables UAV-mounted relays with multiple antennas together with non-orthogonal multiple access (NOMA) to provide a potential way to enhance transmission reliability. We presented two cases of multi-antenna UAVs such as maximum ratio transmission and the best selection to highlight the benefits of the antenna-selections approach with low-cost design. In addition, the base station managed its IoT devices in practical scenarios with and without direct links. For two cases, we derive closed-form expressions of outage probability (OP) and closed-form approximation ergodic capacity (EC) generated for both devices in the main scenario. The outage and ergodic capacity performances in some scenarios are compared to confirm the benefits of the considered system. The number of antennas was found to have a crucial impact on the performances. The simulation results show that the OP for both users strongly decreases when the signal-to-noise ratio (SNR), number of antennas, and fading severity factor of Nakagami-m fading increase. The proposed scheme outperforms the orthogonal multiple access (OMA) scheme in outage performance for two users. The analytical results match Monte Carlo simulations to confirm the exactness of the derived expressions. Full article
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<p>Multi-antenna UAV-aided IoT network.</p>
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<p>Separated antenna selection for UAV-aided IoT network.</p>
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<p>The block diagram of the antenna selection for <a href="#sensors-23-05537-f002" class="html-fig">Figure 2</a>.</p>
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<p>Outage probability versus transmitting SNR of two users with direct link.</p>
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<p>The outage probability versus SNR and different values of <span class="html-italic">m</span>, with <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> with direct link.</p>
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<p>The outage probability versus <math display="inline"><semantics> <msub> <mi>a</mi> <mn>2</mn> </msub> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> (dB), <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> and different values of <span class="html-italic">N</span> with direct link.</p>
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<p>The outage probability with/without direct link versus <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msub> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> (dB) and <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p>
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<p>Comparison of outage probability between OMA and NOMA versus SNR with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> with direct link.</p>
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<p>The ergodic capacity versus SNR and different values of <span class="html-italic">N</span>, with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> with direct link.</p>
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<p>Outage comparison between <a href="#sensors-23-05537-f001" class="html-fig">Figure 1</a> and <a href="#sensors-23-05537-f002" class="html-fig">Figure 2</a>, with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p>
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<p>Ergodic capacity between <a href="#sensors-23-05537-f001" class="html-fig">Figure 1</a> and <a href="#sensors-23-05537-f002" class="html-fig">Figure 2</a> with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p>
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<p>The ergodic capacity versus <span class="html-italic">N</span> with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> with direct link.</p>
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21 pages, 29512 KiB  
Article
Pedestrian Smartphone Navigation Based on Weighted Graph Factor Optimization Utilizing GPS/BDS Multi-Constellation
by Chen Chen, Jianliang Zhu, Yuming Bo, Yuwei Chen, Changhui Jiang, Jianxin Jia, Zhiyong Duan, Mika Karjalainen and Juha Hyyppä
Remote Sens. 2023, 15(10), 2506; https://doi.org/10.3390/rs15102506 - 10 May 2023
Cited by 5 | Viewed by 2359
Abstract
Many studies have focused on the smartphone-based global navigation satellite system (GNSS) for its portability. However, complex urban environments, such as urban canyons and tunnels, can easily interfere with GNSS signal qualities. Current smartphone-based positioning technologies using the GNSS signal still pose great [...] Read more.
Many studies have focused on the smartphone-based global navigation satellite system (GNSS) for its portability. However, complex urban environments, such as urban canyons and tunnels, can easily interfere with GNSS signal qualities. Current smartphone-based positioning technologies using the GNSS signal still pose great challenges. Since the last satellite of the BeiDou navigation system (BDS) was successfully launched on 23 June 2020, it is possible to use a low-cost Android device to realize the localization based on the BDS signals worldwide. This research focuses on smartphone-based outdoor pedestrian navigation utilizing the GPS/BDS multi-constellation system. To improve the localization accuracy, we proposed the Weighted Factor Graph Optimization localization model (W-FGO). In this paper, firstly, we evaluate the signal qualities of the BDS via the data collected by the static experiment. Then, we structure the cost function based on the pseudo-range and the time series data for the traditional Factor Graph Optimization (FGO). Finally, we design the weight model based on the signal quality of each satellite and the time fading factor to further improve the localization accuracy of the conventional FGO method. An Android smartphone is utilized to collect the GNSS data for the evaluation and the localization. The experiment results demonstrate the superior performance of the proposed method. Full article
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<p>The placement of the smartphone and surrounding environments of the static experiment. (<b>a</b>) The placement of the Huawei Mate40 Pro. (<b>b</b>) The environment of the experiment.</p>
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<p>The sky plot of the observed BDS satellites. The gray circles indicate different elevating angle from 0° to 90°. The gray lindicate different azimuth angle from 0° to 360°. N, E, S, and W means the north, east, south, and west, respectively. The format of time is GPS time.</p>
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<p>The visibility of BDS satellites. The format of time is GPS time.</p>
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<p>The tracked satellites’ number of different constellations with elevation angles above 10° during the static experiment. (<b>a</b>) The number of tracked satellites for BDS. (<b>b</b>) The number of tracked satellites for Galileo. (<b>c</b>) The number of tracked satellites for GPS. (<b>d</b>) The number of tracked satellites for GLONASS. The format of time is GPS time.</p>
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<p>The factor graph of GPS/BDS positioning with the constraints of the pseudo-range, the velocity, and the height.</p>
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<p>Receiver pseudo-range residuals (PR) against the satellite <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>/</mo> <mi>N</mi> <mn>0</mn> </mrow> </semantics></math> for the selected BDS satellites.</p>
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<p>The kinematic pedestrian experiments in urban areas. (<b>a</b>) The experimental box. (<b>b</b>) The example of kinematic pedestrian experiments.</p>
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<p>Trajectories of ground tests drawn by Google Earth Pro.</p>
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<p>The horizontal positioning errors for test 1∼test 4 based on the LSM methods.</p>
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<p>The horizontal positioning errors for test 1∼test 4 between the GPS/BDS-based LSM, EKF, FGO, and W-FGO.</p>
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<p>Cumulative distribution functions (CDF) of horizontal positioning errors for test 1∼test 4.</p>
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<p>Boxplots of horizontal positioning errors for test 1∼test 4.</p>
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14 pages, 3178 KiB  
Article
Design and Analysis of a Multi−Carrier Orthogonal Double Bit Rate Differential Chaotic Shift Keying Communication System
by Tao Sui, Yongxin Feng, Bo Qian, Fang Liu, Qiang Jiang and Xiao Li
Electronics 2023, 12(8), 1785; https://doi.org/10.3390/electronics12081785 - 10 Apr 2023
Cited by 2 | Viewed by 1191
Abstract
A new multi−carrier orthogonal double bit rate differential chaotic shift keying (MC−ODBR−DCSK) communication system is presented in this paper. With two composite signals generated by an orthogonal chaotic signal generator as reference signals, 2M bits of information data are transmitted on M−channel [...] Read more.
A new multi−carrier orthogonal double bit rate differential chaotic shift keying (MC−ODBR−DCSK) communication system is presented in this paper. With two composite signals generated by an orthogonal chaotic signal generator as reference signals, 2M bits of information data are transmitted on M−channel subcarriers, improving transmission speed and energy efficiency. In addition, the receiver does not require a radio frequency (RF) delay circuit to demodulate the received data, which makes the system easier to implement. This paper analyzes Data−energy−to−Bit−energy Ratio (DBR) of the system. The bit error rate performance of the system is simulated to verify the impact of parameters such as chaotic maps, semi-spread spectrum factor, and sub-carrier number. At the same time, the bit error rate performance of the MC−ODBR−DCSK system is compared with traditional DCSK systems in Rician fading and additive Gaussian white noise (AWGN) channels. Full article
(This article belongs to the Section Microwave and Wireless Communications)
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<p>Time domain diagram. (<b>a</b>) Improved Logistic Map (<math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.40</mn> </mrow> </semantics></math>, <span class="html-italic">μ</span> = 2); (<b>b</b>) 2D-Logistic map (<math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.40</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.40</mn> </mrow> </semantics></math>, <span class="html-italic">r</span> = 1.19).</p>
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<p>Block diagram of OCG.</p>
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<p>Transmitter of MC-ODBR-DCSK.</p>
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<p>The signal structure of MC−ODBR−DCSK.</p>
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<p>Format of the signal transmitted in the MC−ODBR−DCSK system.</p>
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<p>Receiver of MC−ODBR−DCSK.</p>
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<p>Comparison of DBR of data subcarriers in different systems.</p>
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<p>BER performance curves of the system with different number of IFFT points.</p>
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<p>BER curves of the system with different chaos maps. (<b>a</b>) <span class="html-italic">β</span> = 100, <span class="html-italic">x</span><sub>0</sub> = 0.40; (<b>b</b>) <span class="html-italic">β</span> = 200, <span class="html-italic">x</span><sub>0</sub> = 0.40.</p>
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<p>BER curves of the system with different semi−spread spectrum factors.</p>
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<p>Relationship between semi−spread spectrum factor and bit error rate.</p>
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<p>Comparison of bit error rates of DCSK, ODBR−DCSK, SR−ODBR−DCSK, and MC−ODBR-DCSK systems in Gaussian and Rician channels.</p>
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<p>Relationship between semi−spread spectrum factor and bit error rate in Gaussian channel.</p>
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15 pages, 379 KiB  
Article
Performance Analysis of Wireless Communications with Nonlinear Energy Harvesting under Hardware Impairment and κ-μ Shadowed Fading
by Toi Le-Thanh and Khuong Ho-Van
Sensors 2023, 23(7), 3619; https://doi.org/10.3390/s23073619 - 30 Mar 2023
Cited by 6 | Viewed by 1734
Abstract
This paper improves energy efficiency and communications reliability for wireless transmission under κ-μ shadowed fading (i.e., integrating all channel impairments including path loss, shadowing, fading) and hardware impairment by employing a nonlinear energy harvester and multi-antenna power transmitter. To this end, [...] Read more.
This paper improves energy efficiency and communications reliability for wireless transmission under κ-μ shadowed fading (i.e., integrating all channel impairments including path loss, shadowing, fading) and hardware impairment by employing a nonlinear energy harvester and multi-antenna power transmitter. To this end, this paper provides explicit formulas for outage probability. Numerous results corroborate these formulas and expose that energy-harvesting nonlinearity, hardware impairment, and channel conditions drastically deteriorate system performance. Notwithstanding, energy-harvesting nonlinearity influences system performance more severely than hardware impairment. In addition, desired system performance is accomplished flexibly and possibly by choosing a cluster of specifications. Remarkably, the proposed communications scheme obtains the optimal performance with the appropriate selection of the time-splitting factor. Full article
(This article belongs to the Special Issue RF Energy Harvesting and Wireless Power Transfer for IoT)
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<p>Wireless communications with energy harvesting.</p>
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<p>OP versus <math display="inline"><semantics> <mover accent="true"> <mi>P</mi> <mo stretchy="false">¯</mo> </mover> </semantics></math>.</p>
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<p>OP versus the HWi degree <math display="inline"><semantics> <mi>ρ</mi> </semantics></math>.</p>
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<p>Parameters pertinent to harvested energy. (<b>a</b>) OP versus <math display="inline"><semantics> <mi>η</mi> </semantics></math>. (<b>b</b>) OP versus <math display="inline"><semantics> <mi>ι</mi> </semantics></math>.</p>
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<p>Effects of parameters <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>β</mi> <mo>,</mo> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) OP versus <math display="inline"><semantics> <mi>β</mi> </semantics></math>. (<b>b</b>) OP versus <math display="inline"><semantics> <msub> <mi>R</mi> <mn>0</mn> </msub> </semantics></math>.</p>
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<p>Shadowed fading parameters <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>μ</mi> <mo>,</mo> <mi>χ</mi> <mo>,</mo> <mi>κ</mi> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) OP versus <math display="inline"><semantics> <mi>χ</mi> </semantics></math>. (<b>b</b>) OP versus <math display="inline"><semantics> <mi>κ</mi> </semantics></math>.</p>
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18 pages, 5957 KiB  
Article
Adaptive Markov IMM Based Multiple Fading Factors Strong Tracking CKF for Maneuvering Hypersonic-Target Tracking
by Yalun Luo, Zhaoming Li, Yurong Liao, Haining Wang and Shuyan Ni
Appl. Sci. 2022, 12(20), 10395; https://doi.org/10.3390/app122010395 - 15 Oct 2022
Cited by 9 | Viewed by 1701
Abstract
Hypersonic targets have complex motion states and high maneuverability. The traditional interactive multi-model (IMM) has low tracking accuracy and a slow convergence speed. Therefore, this paper proposes a strong tracking cubature Kalman filter (CKF) adaptive interactive multi-model (AIMM) based on multiple fading factors. [...] Read more.
Hypersonic targets have complex motion states and high maneuverability. The traditional interactive multi-model (IMM) has low tracking accuracy and a slow convergence speed. Therefore, this paper proposes a strong tracking cubature Kalman filter (CKF) adaptive interactive multi-model (AIMM) based on multiple fading factors. Firstly, this paper analyzes the structure of the CKF algorithm, introduces the fading factor of the strong tracking algorithm into the covariance matrix of the time update and measurement update, and adjusts the filter gain online and in real time, which can reduce the decline infilter accuracy caused by model mismatch. Secondly, Singer model, “current” statistical (CS) model, and Jerk model are selected in the model set of IMM and introduced singular value decomposition (SVD) decomposition to solve the problem that Cholesky decomposition cannot be performed in the CKF due to the model dimension expansion. Last, an adaptive algorithm for the Markov matrix in the IMM is proposed. The transition probability was adaptively modified by the value of the model likelihood function to enhance the proportion of matching models. The simulation results show that the proposed algorithm enhanced the proportion of matching models in the IMM and improved the tracking accuracy by 16.51% and the convergence speed by 37.5%. Full article
(This article belongs to the Section Aerospace Science and Engineering)
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<p>Coordinate system relationship. <math display="inline"><semantics> <mrow> <mi>O</mi> </mrow> </semantics></math> is geo-center, <math display="inline"><semantics> <mrow> <mi>O</mi> <mo>−</mo> <mi>X</mi> <mi>Y</mi> <mi>Z</mi> </mrow> </semantics></math> is the geocentric earth fixed coordinate system, and <math display="inline"><semantics> <mrow> <mi>O</mi> <mo>−</mo> <mi>x</mi> <mi>y</mi> <mi>z</mi> </mrow> </semantics></math> is the aircraft position coordinate system.</p>
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<p>Target measurement in the radar observation coordinate system. The origin <math display="inline"><semantics> <mrow> <mi>O</mi> </mrow> </semantics></math> is the radar coordinate, the azimuth angle is <math display="inline"><semantics> <mi>e</mi> </semantics></math>, the elevation angle is <math display="inline"><semantics> <mi>a</mi> </semantics></math>, and the relative distance is <math display="inline"><semantics> <mi>r</mi> </semantics></math>.</p>
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<p>The geocentric coordinate system and reference coordinate system of the radar station. The radar position <math display="inline"><semantics> <mi>R</mi> </semantics></math> is the origin of the coordinate system, and the <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>E</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>N</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>U</mi> </mrow> </semantics></math> axes point to the east, north, and sky directions perpendicular to each other.</p>
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<p>Computational steps of the interactive multi-model algorithm. Each filter is an independent model. The observation information is introduced, the target motion state is obtained by filtering, and finally the state fusion is carried out by weighting.</p>
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<p>HTV-2 trajectory. The blue track part shows the entire movement process of the hype-sonic target in a step jump process, and the red track part shows the radar observation period.</p>
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<p>Tradition target maneuver trajectory. The traditional target has two state changes during maneuver, and IMM-CKF and IMM-STCKF track it.</p>
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<p>RMSE of position (<b>a</b>) and velocity (<b>b</b>). The red line is RMSE of IMM-CKF, the blue line is RMSE of IMM-STCKF.</p>
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<p>Trajectory tracking of hypersonic target. (<b>a</b>) Hypersonic target strong maneuver phase; (<b>b</b>) X-axis trajectory tracking; (<b>c</b>) Y-axis trajectory tracking; (<b>d</b>) Z-axis trajectory tracking.</p>
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<p>Comparison of algorithm with reference [<a href="#B13-applsci-12-10395" class="html-bibr">13</a>]. (<b>a</b>) RMSE of position; (<b>b</b>) Change of trace value <math display="inline"><semantics> <mrow> <msub> <mstyle mathvariant="bold-italic"> <mi>K</mi> </mstyle> <mi>k</mi> </msub> </mrow> </semantics></math> of position gain matrix of Jerk model.</p>
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<p>Position RMSE of three algorithms: (<b>a</b>) RMSE of position in the x-axis direction; (<b>b</b>) RMSE of position in the y-axis direction; (<b>c</b>) RMSE of position in the z-axis direction; (<b>d</b>) RMSE of position.</p>
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<p>Velocity RMSE of three algorithms: (<b>a</b>) RMSE of velocity in the x-axis direction; the RMSE is about 400 m/s; (<b>b</b>) RMSE of velocity in the y-axis direction; (<b>c</b>) RMSE of velocity in the z-axis direction; (<b>d</b>) RMSE of velocity.</p>
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<p>Model probability: (<b>a</b>) IMM-CKF; (<b>b</b>) AIMM-STCKF.</p>
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15 pages, 5099 KiB  
Article
In-Motion Alignment Method of SINS Based on Improved Kalman Filter under Geographic Latitude Uncertainty
by Jin Sun, Qianqi Ye and Yue Lei
Remote Sens. 2022, 14(11), 2581; https://doi.org/10.3390/rs14112581 - 27 May 2022
Cited by 3 | Viewed by 2028
Abstract
To realize the in-motion alignment of the strapdown inertial navigation system (SINS) under the geographic latitude uncertainty, we propose a latitude estimation and in-motion alignment method based on the integral dynamic window and polynomial fitting (IDW-PF) and improved Kalman filter (IKF). First, the [...] Read more.
To realize the in-motion alignment of the strapdown inertial navigation system (SINS) under the geographic latitude uncertainty, we propose a latitude estimation and in-motion alignment method based on the integral dynamic window and polynomial fitting (IDW-PF) and improved Kalman filter (IKF). First, the integral dynamic window (IDW) is designed to smooth out the high-frequency line motion interference and accelerometer noise. Second, the specific force integral is performed for a cubic polynomial fitting (PF) with time as an independent variable to further suppress the line motion interference. Simultaneously, the latitude is estimated according to the geometric relationship between the angle of the gravitational acceleration vectors at different moments and the latitude. Finally, the IKF based on the multi-fading factor is designed for the in-motion alignment of SINS. A simulation experiment is conducted to verify the proposed latitude estimation and in-motion alignment method. The results indicate that the latitude can be estimated well by the method based on the IDW-PF; the mean and standard deviation of the estimated latitude can achieve −0.016° and 0.013° within 300 s. The trapezoidal maneuvering path is optimal when IKF is used, the pitch error is 0.0002°, the roll error is 0.0009° and the heading error is −0.0047° after the alignment ends at 900 s. Full article
(This article belongs to the Topic Multi-Sensor Integrated Navigation Systems)
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Graphical abstract

Graphical abstract
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<p>Geometric relationship diagram for the latitude estimation.</p>
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<p>Integral dynamic window algorithm diagram.</p>
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<p>Curves of latitude estimation error.</p>
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<p>Attitude error of in-motion alignment of uniform linear motion.</p>
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<p>Estimation values of IMU constant error (uniform linear motion).</p>
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<p>Circular maneuver path.</p>
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<p>Attitude error of in-motion alignment of circular maneuver.</p>
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<p>Estimation values of IMU constant error (circular maneuver).</p>
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<p>Trapezoidal maneuver path.</p>
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<p>Attitude error of in-motion alignment of trapezoidal maneuver.</p>
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<p>Estimation values of IMU constant error (trapezoidal maneuver).</p>
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<p>S-shaped maneuver path.</p>
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<p>Attitude error of in-motion alignment of s-shaped maneuver.</p>
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<p>Estimation values of IMU constant error (s-shaped maneuver).</p>
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13 pages, 1149 KiB  
Communication
Mitigating Wireless Channel Impairments in Seismic Data Transmission Using Deep Neural Networks
by Naveed Iqbal, Abdulmajid Lawal and Azzedine Zerguine
Sensors 2021, 21(18), 6105; https://doi.org/10.3390/s21186105 - 12 Sep 2021
Cited by 1 | Viewed by 1650
Abstract
The traditional cable-based geophone network is an inefficient way of seismic data transmission owing to the related cost and weight. The future of oil and gas exploration technology demands large-scale seismic acquisition, versatility, flexibility, scalability, and automation. On the one hand, a typical [...] Read more.
The traditional cable-based geophone network is an inefficient way of seismic data transmission owing to the related cost and weight. The future of oil and gas exploration technology demands large-scale seismic acquisition, versatility, flexibility, scalability, and automation. On the one hand, a typical seismic survey can pile up a massive amount of raw seismic data per day. On the other hand, the need for wireless seismic data transmission remains immense. Moving from pre-wired to wireless geophones faces major challenges given the enormous amount of data that needs to be transmitted from geophones to the on-site data collection center. The most important factor that has been ignored in the previous studies for the realization of wireless seismic data transmission is wireless channel effects. While transmitting the seismic data wirelessly, impairments like interference, multi-path fading, and channel noise need to be considered. Therefore, in this work, a novel amalgamation of blind channel identification and deep neural networks is proposed. As a geophone already is responsible for transmitting a tremendous amount of data under tight timing constraints, the proposed setup eschews sending any additional training signals for the purpose of mitigating the channel effects. Note that the deep neural network is trained only on synthetic seismic data without the need to use real data in the training process. Experiments show that the proposed method gives promising results when applied to the real/field data set. Full article
(This article belongs to the Section Sensor Networks)
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<p>Schematic diagram of the denoising method. Seven STDCT segments are fed to the deep convolutional neural network to get a clean STDCT segment.</p>
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<p>Deep convolutional neural network for SNR enhancement with convolutional (Conv) and LeakyRelu layers.</p>
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<p>Fully connected neural network for classification.</p>
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<p>Flow chart for SNR enhancement of seismic data set.</p>
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<p>MSE comparison of SSS method and modified updated estimation at SNR <math display="inline"><semantics> <mrow> <mo>=</mo> <mo>−</mo> <mn>5</mn> </mrow> </semantics></math> dB.</p>
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<p>SNR enhancement using deep convolutional neural network, SNR of the received data <math display="inline"><semantics> <mrow> <mi mathvariant="bold">y</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </semantics></math> versus SNR of the reconstructed traces after processing.</p>
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<p>Single trace SNR enhancement (SNR of received data is <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </semantics></math> dB). (<b>a</b>) Original trace. (<b>b</b>) Reconstructed trace after MLSE. (<b>c</b>) Reconstructed trace after SNR enhancement. On the right side: zoomed view of panels (<b>a</b>–<b>c</b>).</p>
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<p>SNR enhancement versus various values of window size <span class="html-italic">M</span> (SNR of the received data is <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </semantics></math> dB).</p>
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<p>Single trace SNR enhancement (SNR of received data is <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>8</mn> </mrow> </semantics></math> dB). (<b>a</b>) Original trace. (<b>b</b>) Reconstructed trace after MLSE. (<b>c</b>) Reconstructed trace after SNR enhancement.</p>
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<p>Single trace SNR enhancement (SNR of received data is <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>10</mn> </mrow> </semantics></math> dB). (<b>a</b>) Original trace. (<b>b</b>) Reconstructed trace after MLSE. (<b>c</b>) Reconstructed trace after SNR enhancement.</p>
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24 pages, 8348 KiB  
Article
A Deep Neural Network-Based Multi-Frequency Path Loss Prediction Model from 0.8 GHz to 70 GHz
by Chi Nguyen and Adnan Ahmad Cheema
Sensors 2021, 21(15), 5100; https://doi.org/10.3390/s21155100 - 28 Jul 2021
Cited by 26 | Viewed by 4095
Abstract
Large-scale fading models play an important role in estimating radio coverage, optimizing base station deployments and characterizing the radio environment to quantify the performance of wireless networks. In recent times, multi-frequency path loss models are attracting much interest due to their expected support [...] Read more.
Large-scale fading models play an important role in estimating radio coverage, optimizing base station deployments and characterizing the radio environment to quantify the performance of wireless networks. In recent times, multi-frequency path loss models are attracting much interest due to their expected support for both sub-6 GHz and higher frequency bands in future wireless networks. Traditionally, linear multi-frequency path loss models like the ABG model have been considered, however such models lack accuracy. The path loss model based on a deep learning approach is an alternative method to traditional linear path loss models to overcome the time-consuming path loss parameters predictions based on the large dataset at new frequencies and new scenarios. In this paper, we proposed a feed-forward deep neural network (DNN) model to predict path loss of 13 different frequencies from 0.8 GHz to 70 GHz simultaneously in an urban and suburban environment in a non-line-of-sight (NLOS) scenario. We investigated a broad range of possible values for hyperparameters to search for the best set of ones to obtain the optimal architecture of the proposed DNN model. The results show that the proposed DNN-based path loss model improved mean square error (MSE) by about 6 dB and achieved higher prediction accuracy R2 compared to the multi-frequency ABG path loss model. The paper applies the XGBoost algorithm to evaluate the importance of the features for the proposed model and the related impact on the path loss prediction. In addition, the effect of hyperparameters, including activation function, number of hidden neurons in each layer, optimization algorithm, regularization factor, batch size, learning rate, and momentum, on the performance of the proposed model in terms of prediction error and prediction accuracy are also investigated. Full article
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<p>The process of training path loss dataset with the proposed DNN model.</p>
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<p>Empirical path loss at an above rooftop in an urban high-rise environment.</p>
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<p>Empirical path loss at below rooftop in urban high-rise environment.</p>
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<p>Empirical path loss at below rooftop in an urban low-rise (suburban) environment.</p>
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<p>Block diagram of the processing data using proposed DNN model.</p>
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<p>Feature importance using XGBoost algorithm.</p>
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<p>Proposed fully connected DNN model.</p>
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<p>Loss of training and testing datasets according to epochs.</p>
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<p>Accuracy of training and testing datasets according to epochs.</p>
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<p>Path loss models and empirical data for low 5G band.</p>
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<p>Path loss models and empirical data for mid 5G band.</p>
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<p>Path loss models and empirical data for high 5G band.</p>
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<p>Comparison of loss with different learning rate.</p>
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<p>Comparison of accuracy with different learning rate.</p>
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<p>Comparison of loss with different optimizers.</p>
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<p>Comparison of accuracy with different optimizers.</p>
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<p>Comparison of loss with different activation functions.</p>
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<p>Comparison of accuracy with different activation functions.</p>
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<p>Comparison of loss with different regularization factor.</p>
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<p>Comparison of accuracy with different regularization factor.</p>
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<p>Comparison of loss with different the number of hidden units.</p>
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<p>Comparison of accuracy with different the number of hidden units.</p>
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15 pages, 2883 KiB  
Communication
Robust SCKF Filtering Method for MINS/GPS In-Motion Alignment
by Huanrui Zhang and Xiaoyue Zhang
Sensors 2021, 21(8), 2597; https://doi.org/10.3390/s21082597 - 7 Apr 2021
Cited by 3 | Viewed by 1853
Abstract
This paper presents a novel multiple strong tracking adaptive square-root cubature Kalman filter (MSTASCKF) based on the frame of the Sage–Husa filter, employing the multi-fading factor which could automatically adjust the Q value according to the rapidly changing noise in the flight process. [...] Read more.
This paper presents a novel multiple strong tracking adaptive square-root cubature Kalman filter (MSTASCKF) based on the frame of the Sage–Husa filter, employing the multi-fading factor which could automatically adjust the Q value according to the rapidly changing noise in the flight process. This filter can estimate the system noise in real-time during the filtering process and adjust the system noise variance matrix Q so that the filtering accuracy is not significantly reduced with the noise. At the same time, the residual error in the filtering process is used as a measure of the filtering effect, and a multiple fading factor is introduced to adjust the posterior error variance matrix in the filtering process, so that the residual error is always orthogonal and the stability of the filtering is maintained. Finally, a vibration test is designed which simulates the random noise of the short-range guided weapon in flight through the shaking table and adds the noise to the present simulation trajectory for semi-physical simulation. The simulation results show that the proposed filter can significantly reduce the attitude estimation error caused by random vibration. Full article
(This article belongs to the Section Physical Sensors)
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<p>The power spectrum density and frequency range of the vibration experiment.</p>
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<p>The experimental platform.</p>
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<p>The vibration experiment process.</p>
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<p>The vibration noise data of the vibration experiment of each axis.</p>
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<p>The real-time trajectory of the simulation. (<b>a</b>) The real-time attitude of the simulated trajectory. (<b>b</b>) The real-time velocity of the simulated trajectory in the direction of east, north, and up, respectively.</p>
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<p>The attitude error comparison between MSTASCKF and SCKF.</p>
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<p>The RMS of the attitude error of MSTASCKF and SCKF.</p>
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22 pages, 4160 KiB  
Article
LoRa Channel Characterization for Flexible and High Reliability Adaptive Data Rate in Multiple Gateways Networks
by Ulysse Coutaud, Martin Heusse and Bernard Tourancheau
Computers 2021, 10(4), 44; https://doi.org/10.3390/computers10040044 - 2 Apr 2021
Cited by 9 | Viewed by 4413
Abstract
We characterize the LoRa channel in terms of multi-path fading, loss burstiness, and assess the benefits of Forward Error Correction as well as the influence of frame length. We make these observations by synthesizing extensive experimental measurements realized with The Things Network in [...] Read more.
We characterize the LoRa channel in terms of multi-path fading, loss burstiness, and assess the benefits of Forward Error Correction as well as the influence of frame length. We make these observations by synthesizing extensive experimental measurements realized with The Things Network in a medium size city. We then propose to optimize the LoRaWAN Adaptive Data Rate algorithm based on this refined LoRa channel characterization and taking into account the LoRaWAN inherent macro-diversity from multi-gateway reception. Firstly, we propose ADRopt, which adjusts Spreading Factor and frame repetition number to maintain the communication below a target Packet Error Rate ceiling with optimized Time-On-Air. Secondly, we propose ADRIFECC, an extension of ADRopt in case an Inter-Frame Erasure Correction Code is available. The resulting protocol provides very high reliability even over low quality channels, with comparable Time on Air and similar downlink usage as the currently deployed mechanism. Simulations corroborate the analysis, both over a synthetic random wireless link and over replayed real-world packet transmission traces. Full article
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<p>LoRa CHIRPs for <math display="inline"><semantics> <mrow> <mi>SF</mi> <mo>∈</mo> <mo>[</mo> <mn>7</mn> <mo>.</mo> <mo>.</mo> <mn>12</mn> <mo>]</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>BW</mi> <mo>∈</mo> <mo>{</mo> <mn>125</mn> <mo>,</mo> <mn>250</mn> <mo>,</mo> <mn>500</mn> <mo>}</mo> <mspace width="0.166667em"/> <mi>kHz</mi> </mrow> </semantics></math> on the 868.5 MHz channel.</p>
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<p>LoRaWAN uplink frame structure.</p>
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<p>Time-On-Air by applicative bit (<span class="html-italic">ToA/b</span>) cost for 25 bytes applicative payload over a 125 kHz bandwidth for selected transmissions parameters.</p>
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<p>Experimental Setup.</p>
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<p>Distribution of the measured <span class="html-italic">SNR</span> of several LoRaWAN series of frames with <span class="html-italic">SF</span> 11 and 7, compared to an exponential distribution curve in red (manually centered), for several <math display="inline"><semantics> <msub> <mi mathvariant="italic">P</mi> <mi>Tx</mi> </msub> </semantics></math>. Yellow and black arrows mark each <span class="html-italic">SF</span> 11 and 7 demodulation floor (typical values from the documentation [<a href="#B1-computers-10-00044" class="html-bibr">1</a>]).</p>
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<p>Distribution of the measured <span class="html-italic">SNR</span> and <span class="html-italic">FER</span> as a function of the <span class="html-italic">CR</span> for selected series of frames.</p>
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<p>Comparison of the Frame Error Rate with <math display="inline"><semantics> <mrow> <mi mathvariant="italic">CR</mi> <mo>=</mo> <mfrac> <mn>4</mn> <mn>5</mn> </mfrac> </mrow> </semantics></math> against <math display="inline"><semantics> <mrow> <mi mathvariant="italic">CR</mi> <mo>=</mo> <mfrac> <mn>4</mn> <mn>6</mn> </mfrac> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="italic">CR</mi> <mo>=</mo> <mfrac> <mn>4</mn> <mn>7</mn> </mfrac> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="italic">CR</mi> <mo>=</mo> <mfrac> <mn>4</mn> <mn>8</mn> </mfrac> </mrow> </semantics></math>. The black curve is the computed <span class="html-italic">FER</span> gain expected for sensitivity gain over a Rayleigh channel.</p>
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<p>Distribution of the measured <span class="html-italic">SNR</span> and <span class="html-italic">FER</span> as a function of the number of symbols (<span class="html-italic">NS</span>) for selected series of frames.</p>
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<p>Comparison of the Frame Error Rate with <span class="html-italic">NS</span> = 48 against <span class="html-italic">NS</span> = 128 and <math display="inline"><semantics> <mrow> <mi mathvariant="italic">NS</mi> <mo>∈</mo> <mo>[</mo> <mn>296</mn> <mo>.</mo> <mo>.</mo> <mn>298</mn> <mo>]</mo> </mrow> </semantics></math>. The black curve is the computed <span class="html-italic">FER</span> gain expected for sensitivity gain over a Rayleigh channel.</p>
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<p><span class="html-italic">ToA/b</span> as a function of the application data payload length for <span class="html-italic">SF</span> 7 and 8 with <span class="html-italic">BW</span> = 125 kHz and <span class="html-italic">CR</span> = <math display="inline"><semantics> <mfrac> <mn>4</mn> <mn>5</mn> </mfrac> </semantics></math>.</p>
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<p>Dots marks the experimental proportion of frames lost in bursts of various sizes. The colored areas correspond to a simulated independent and identically distributed (iid) channel.</p>
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<p><span class="html-italic">DER</span> as a function of <math display="inline"><semantics> <mover> <mi mathvariant="italic">SNR</mi> <mo>¯</mo> </mover> </semantics></math> for the simulated series of frames with multiple GWs (99% confidences interval plots).</p>
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<p><span class="html-italic">ToA/b</span> as a function of <math display="inline"><semantics> <mover> <mi mathvariant="italic">SNR</mi> <mo>¯</mo> </mover> </semantics></math> for the simulated series of frames with multiple GWs (99% confidences interval plots).</p>
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<p><span class="html-italic">DER</span> as a function of <math display="inline"><semantics> <msub> <mi mathvariant="italic">P</mi> <mi>Tx</mi> </msub> </semantics></math>, for selected real world series of frames replays.</p>
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<p><span class="html-italic">ToA/b</span> as a function of <math display="inline"><semantics> <msub> <mi mathvariant="italic">P</mi> <mi>Tx</mi> </msub> </semantics></math>, for selected real world series of frames replays.</p>
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<p>Experimental <span class="html-italic">PER</span> against <span class="html-italic">FER</span> for several <math display="inline"><semantics> <msub> <mi mathvariant="italic">NB</mi> <mi>Trans</mi> </msub> </semantics></math>.</p>
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<p><span class="html-italic">DER</span> against <math display="inline"><semantics> <mover> <mi mathvariant="italic">SNR</mi> <mo>¯</mo> </mover> </semantics></math> for the simulated series of frames with a yellow dashed line to mark the 0.01 threshold (99% confidences interval plots).</p>
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<p><span class="html-italic">ToA/b</span> as a function of <math display="inline"><semantics> <mover> <mi mathvariant="italic">SNR</mi> <mo>¯</mo> </mover> </semantics></math> for the simulated series of frames with several GWs (99% confidences interval plots).</p>
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<p><span class="html-italic">DER</span> as a function of <math display="inline"><semantics> <msub> <mi mathvariant="italic">P</mi> <mi>Tx</mi> </msub> </semantics></math>, for selected real world series of frames replays.</p>
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<p><span class="html-italic">ToA/b</span> as a function of <math display="inline"><semantics> <msub> <mi mathvariant="italic">P</mi> <mi>Tx</mi> </msub> </semantics></math>, for selected real world series of frames replays.</p>
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17 pages, 1617 KiB  
Article
Strong Tracking PHD Filter Based on Variational Bayesian with Inaccurate Process and Measurement Noise Covariance
by Zhentao Hu, Linlin Yang, Yong Jin, Han Wang and Shibo Yang
Sensors 2021, 21(4), 1126; https://doi.org/10.3390/s21041126 - 5 Feb 2021
Cited by 2 | Viewed by 1861
Abstract
Assuming that the measurement and process noise covariances are known, the probability hypothesis density (PHD) filter is effective in real-time multi-target tracking; however, noise covariance is often unknown and time-varying for an actual scene. To solve this problem, a strong tracking PHD filter [...] Read more.
Assuming that the measurement and process noise covariances are known, the probability hypothesis density (PHD) filter is effective in real-time multi-target tracking; however, noise covariance is often unknown and time-varying for an actual scene. To solve this problem, a strong tracking PHD filter based on Variational Bayes (VB) approximation is proposed in this paper. The measurement noise covariance is described in the linear system by the inverse Wishart (IW) distribution. Then, the fading factor in the strong tracking principle uses the optimal measurement noise covariance at the previous moment to control the state prediction covariance in real-time. The Gaussian IW (GIW) joint distribution adopts the VB approximation to jointly return the measurement noise covariance and the target state covariance. The simulation results show that, compared with the traditional Gaussian mixture PHD (GM-PHD) and the VB-adaptive PHD, the proposed algorithm has higher tracking accuracy and stronger robustness in a more reasonable calculation time. Full article
(This article belongs to the Section Physical Sensors)
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<p>The flow chart of the proposed Gaussian inverse Wishart GIW-stPHD filter.</p>
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<p>The true trajectory of the target.</p>
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<p>The optimal sub-pattern assignment (OSPA) error in scene 1.</p>
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<p>Localisation error in scene 1.</p>
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<p>OSPA error in scene 2.</p>
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<p>Localisation error in scene 2.</p>
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<p>OSPA error in scene 3.</p>
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<p>Localisation error in scene 3.</p>
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<p>Cardinality error under different filtering.</p>
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<p>OSPA error.</p>
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<p>Localisation error.</p>
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23 pages, 3888 KiB  
Article
Multi-Fading Factor and Updated Monitoring Strategy Adaptive Kalman Filter-Based Variational Bayesian
by Chenghao Shan, Weidong Zhou, Yefeng Yang and Zihao Jiang
Sensors 2021, 21(1), 198; https://doi.org/10.3390/s21010198 - 30 Dec 2020
Cited by 12 | Viewed by 2547
Abstract
Aiming at the problem that the performance of adaptive Kalman filter estimation will be affected when the statistical characteristics of the process and measurement of the noise matrices are inaccurate and time-varying in the linear Gaussian state-space model, an algorithm of multi-fading factor [...] Read more.
Aiming at the problem that the performance of adaptive Kalman filter estimation will be affected when the statistical characteristics of the process and measurement of the noise matrices are inaccurate and time-varying in the linear Gaussian state-space model, an algorithm of multi-fading factor and an updated monitoring strategy adaptive Kalman filter-based variational Bayesian is proposed. Inverse Wishart distribution is selected as the measurement noise model and the system state vector and measurement noise covariance matrix are estimated with the variational Bayesian method. The process noise covariance matrix is estimated by the maximum a posteriori principle, and the updated monitoring strategy with adjustment factors is used to maintain the positive semi-definite of the updated matrix. The above optimal estimation results are introduced as time-varying parameters into the multiple fading factors to improve the estimation accuracy of the one-step state predicted covariance matrix. The application of the proposed algorithm in target tracking is simulated. The results show that compared with the current filters, the proposed filtering algorithm has better accuracy and convergence performance, and realizes the simultaneous estimation of inaccurate time-varying process and measurement noise covariance matrices. Full article
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Figure 1

Figure 1
<p>The flowchart of one time-step of the updated monitoring strategy based on maximum a posterior (MAP) for estimating the process noise covariance matrix (PNCM).</p>
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<p>True and estimated trajectories of the target.</p>
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<p>The root mean square errors (RMSEs) of the target position and velocity estimation.</p>
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<p>The root mean square errors (RMSEs) of the target position and velocity estimation.</p>
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<p>The SRNFN of PECM estimation.</p>
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<p>The square root of the normalized Frobenius norm (SRNFN) of the measurement noise covariance matrix (MNCM) estimation.</p>
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<p>The SRNFN of the PNCM estimation.</p>
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<p>The RMSEs of the position and velocity estimation in the case of <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>0.85</mn> <mo>,</mo> <mo> </mo> <mn>0.93</mn> <mo>,</mo> <mo> </mo> <mn>0.95</mn> <mo>,</mo> <mo> </mo> <mn>1</mn> <mo>−</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>4</mn> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p>
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<p>The RMSE of the position and velocity estimation in the case of μ = 0.65, 0.75, 0.85, 0.95, 1.0.</p>
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<p>The RMSE of the position and velocity estimation in the case of μ = 0.65, 0.75, 0.85, 0.95, 1.0.</p>
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<p>The RMSE of the position and velocity estimation in the case of <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.2</mn> <mo>,</mo> <mo> </mo> <mn>0.4</mn> <mo>,</mo> <mo> </mo> <mn>0.6</mn> <mo>,</mo> <mo> </mo> <mn>0.8</mn> <mo>,</mo> <mo> </mo> <mn>1.0</mn> </mrow> </semantics></math>.</p>
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<p>The RMSE of the position and velocity estimation in the case of <math display="inline"><semantics> <mrow> <mi>b</mi> <mo>=</mo> <mn>0.76</mn> <mo>,</mo> <mo> </mo> <mn>0.86</mn> <mo>,</mo> <mo> </mo> <mn>0.96</mn> <mo>,</mo> <mo> </mo> <mn>0.99</mn> </mrow> </semantics></math>.</p>
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<p>The ARMSEs of the position and velocity estimation under a combination of <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <mrow> <mi>σ</mi> <mo>,</mo> <mi>ε</mi> </mrow> <mo>)</mo> </mrow> <mo>∈</mo> <mrow> <mo>[</mo> <mrow> <mn>0.1</mn> <mo>,</mo> <mo> </mo> <mn>800</mn> </mrow> <mo>]</mo> </mrow> <mo>×</mo> <mrow> <mo>[</mo> <mrow> <mn>0.1</mn> <mo>,</mo> <mo> </mo> <mn>800</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics></math>.</p>
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