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Synthetic-Aperture Radar image based positioning in GPS-denied environments using Deep Cosine Similarity Neural Networks

  • * Corresponding author: Maciej Rysz

    * Corresponding author: Maciej Rysz 
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  • Navigating unmanned aerial vehicles in precarious environments is of great importance. It is necessary to rely on alternative information processing techniques to attain spatial information that is required for navigation in such settings. This paper introduces a novel deep learning-based approach for navigating that exclusively relies on synthetic aperture radar (SAR) images. The proposed method utilizes deep neural networks (DNNs) for image matching, retrieval, and registration. To this end, we introduce Deep Cosine Similarity Neural Networks (DCSNNs) for mapping SAR images to a global descriptive feature vector. We also introduce a fine-tuning algorithm for DCSNNs, and DCSNNs are used to generate a database of feature vectors for SAR images that span a geographic area of interest, which, in turn, are compared against a feature vector of an inquiry image. Images similar to the inquiry are retrieved from the database by using a scalable distance measure between the feature vector outputs of DCSNN. Methods for reranking the retrieved SAR images that are used to update position coordinates of an inquiry SAR image by estimating from the best retrieved SAR image are also introduced. Numerical experiments comparing with baselines on the Polarimetric SAR (PolSAR) images are presented.

    Mathematics Subject Classification: Primary: 68T07, 68U10; Secondary: 65D18.


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  • Figure 1.  Overview of the system for SAR aided navigating by SAR image representation, matching and registration

    Figure 2.  Example of a patch graph. (a) a SAR map from the UAVSAR dataset (b) patches extracted from the SAR map and its associated graph (c) visualization of the adjacency matrix. White cells show zero edge values whereas black cells show nonzero values

    Figure 3.  Overview of Product Quantization (PQ) with DCSNN

    Figure 4.  Comparison between keypoints generated by (a) SAR-SIFT and (b) SIFT

    Figure 5.  (a) SAR-SIFT based keypoints on two adjacent SAR patches (b) image matching of the keypoints via RANSAC

    Figure 6.  PolSAR data from UAVSAR dataset for our experiments. (From left) VVVV(R), HVHV(G), HHHH(B) channels, and total RGB image. Best viewed in color. (a) PolSAR map for Hayward Fault Zone in California, US. (b) PolSAR map for Yukon–Kuskokwim Delta in Alaska, US

    Figure 7.  Precision recall curves on Hayward Fault Zone (Top rows) and Yukon–Kuskokwim Delta (Bottom rows) PolSAR maps. From left column, the feature length is $ 24 $, $ 48 $, $ 96 $, and $ 120 $. AlexNet is used as a backbone

    Figure 8.  Examples of the retrieved SAR patches before and after reranking processes. First column represents examples of inquiry SAR patches. The first two rows ((a) and (b)) are from Hayward Fault Zone PolSAR and the later two rows ((c) and (d)) are from Yukon-Kuskokwim Delta PolSAR data. Having green box indicates it is correctly retrieved, whereas having red box indicates that it is incorrectly retrieved

    Table 1.  Descriptions of the PolSAR map from UAVSAR [1]

    Region (Dataset Name) Usage Acquired Date Pixel Size (Height×Width) #Patches
    Hayward Fault Zone Training Oct 9, 2018 $23506\times3300$ 6440
    Test May 30, 2019 $23476\times3300$ 6412
    Yukon–Kuskokwim Delta Training Aug 28, 2018 $19066\times3300$ 5180
    Test Sep 17, 2019 $19148\times3300$ 5208
     | Show Table
    DownLoad: CSV

    Table 2.  Mean average precision (mAP) results of DCSNN and binary hashing methods before reranking on Hayward Fault Zone PolSAR map

    Methods Feature length $l$ AlexNet [21] VGG-11 [40]
    Pretrained (BH) $l=24$ 0.0478 0.0313
    $l=48$ 0.0761 0.0522
    $l=96$ 0.1547 0.1200
    $l=120$ 0.1566 0.1219
    Pretrained (PQ+AQD) $l=24$ 0.2332 0.1706
    $l=48$ 0.3208 0.2055
    $l=96$ 0.3231 0.2676
    $l=120$ 0.3856 0.3161
    DHN [50] $l=24$ 0.1182 0.1255
    $l=48$ 0.1642 0.1693
    $l=96$ 0.2274 0.2153
    $l=120$ 0.3202 0.2449
    DPSH [23] $l=24$ 0.0895 0.1220
    $l=48$ 0.2825 0.2632
    $l=96$ 0.4545 0.4005
    $l=120$ 0.5213 0.4334
    DHNN-L2 [24] $l=24$ 0.0451 0.1147
    $l=48$ 0.0683 0.1291
    $l=96$ 0.2044 0.1329
    $l=120$ 0.2190 0.1304
    DCSNN (ours) $l=24$ 0.2519 0.4889
    $l=48$ 0.6145 0.6301
    $l=96$ 0.6481 0.5783
    $l=120$ 0.6813 0.5819
     | Show Table
    DownLoad: CSV

    Table 3.  mAP results of the DCSNN and binary hashing methods before reranking on Yukon–Kuskokwim Delta PolSAR map

    Methods Feature length $l$ AlexNet [21] VGG-11 [40]
    Pretrained (BH) $l=24$ 0.0566 0.0396
    $l=48$ 0.1048 0.0550
    $l=96$ 0.1927 0.1227
    $l=120$ 0.2196 0.1174
    Pretrained (PQ+AQD) $l=24$ 0.2684 0.1736
    $l=48$ 0.3580 0.2091
    $l=96$ 0.3718 0.2579
    $l=120$ 0.4184 0.2690
    DHN [50] $l=24$ 0.1219 0.1610
    $l=48$ 0.2072 0.1910
    $l=96$ 0.2715 0.2447
    $l=120$ 0.3627 0.2239
    DPSH [23] $l=24$ 0.1347 0.1170
    $l=48$ 0.2371 0.2516
    $l=96$ 0.3649 0.3281
    $l=120$ 0.4098 0.3331
    DHNN-L2 [24] $l=24$ 0.0621 0.1132
    $l=48$ 0.1556 0.1812
    $l=96$ 0.2916 0.3166
    $l=120$ 0.3227 0.2822
    DCSNN (ours) $l=24$ 0.4393 0.4324
    $l=48$ 0.5424 0.5196
    $l=96$ 0.5734 0.4913
    $l=120$ 0.5996 0.4831
     | Show Table
    DownLoad: CSV

    Table 4.  mAP values before and after reranking with SAR-SIFT or SIFT on Hayward Fault Zone PolSAR map

    CNN backbone Feature length $l$ Before reranking After reranking (SAR-SIFT/SIFT)
    AlexNet [21] $l=24$ 0.2519 0.4074/0.3533
    $l=48$ 0.6145 0.7394/0.6850
    $l=96$ 0.6481 0.7548/0.6998
    $l=120$ 0.6813 0.7760/0.7252
    VGG-11 [40] $l=24$ 0.4889 0.6512/0.5813
    $l=48$ 0.6301 0.7540/0.6923
    $l=96$ 0.5783 0.6799/0.6231
    $l=120$ 0.5819 0.6787/0.6216
     | Show Table
    DownLoad: CSV

    Table 5.  mAP values of the DCSNN before and after reranking with SAR-SIFT or SIFT on Yukon–Kuskokwim Delta PolSAR map

    CNN backbone Feature length $l$ Before reranking After reranking (SAR-SIFT/SIFT)
    AlexNet [21] $l=24$ 0.4393 0.5831/0.5965
    $l=48$ 0.5424 0.6591/0.6693
    $l=96$ 0.5734 0.6782/0.6888
    $l=120$ 0.5996 0.7021/0.7123
    VGG-11 [40] $l=24$ 0.4324 0.5909/0.6030
    $l=48$ 0.5196 0.6418/0.6521
    $l=96$ 0.4913 0.5939/0.6036
    $l=120$ 0.4831 0.5840/0.5940
     | Show Table
    DownLoad: CSV

    Table 6.  Positioning accuracy examples

    Inquiry SAR Patch Actual Coordinates [$deg$] Estimated Coordinates [$deg$] Error [$m$]
    Fig. 8(a) 38.0625, -122.2733 38.0625, -122.2734 5.7288
    Fig. 8(b) 37.9836, -122.3599 37.9836, -122.3600 5.7347
    Fig. 8(c) 61.0926, -164.1878 61.0926, -164.1879 4.2529
    Fig. 8(d) 61.0808, -164.1208 61.0808, -164.1208 5.0970
     | Show Table
    DownLoad: CSV

    Table 7.  Mean and standard deviation of positioning error results

    Data Name Success Cases Ratio [%] Distance Error [$m$]
    Hayward Fault Zone 98.50 4.9635$\pm$0.1755
    Yukon–Kuskokwim Delta 97.70 4.9522$\pm$0.4038
     | Show Table
    DownLoad: CSV
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