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

Seonho Park; Maciej Rysz; Kaitlin L. Fair; Panos M. Pardalos

doi:10.3934/ipi.2021013

Article Contents

2021, Volume 15, Issue 4: 763-785. Doi: 10.3934/ipi.2021013

This issue Previous Article A sampling type method in an electromagnetic waveguide Next Article Preconditioned Douglas-Rachford type primal-dual method for solving composite monotone inclusion problems with applications

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

1.
Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA
2.
Department of Information Systems and Analytics, Miami University, Oxford, OH 45056, USA
3.
Air Force Research Laboratory (AFRL/RWWI), Eglin Air Force Base, FL 32542, USA

^* Corresponding author: Maciej Rysz
^* Corresponding author: Maciej Rysz

Received: August 31, 2020

Revised: October 31, 2020

Early access: January 2021

Published: August 2021

Distribution A: Approved for public release, distribution is unlimited, 96TW-2020-0170

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Abstract

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.

Keywords:

Synthetic Aperture Radar (SAR),
polarimetric SAR (PolSAR),
Deep Cosine Similarity Neural Networks,
image graphs,
image retrieval,
image registration,
scale-invariant feature transform (SIFT),
SAR-SIFT,
remote sensing.

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

Citation:

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

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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

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

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

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

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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

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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

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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

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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
Hayward Fault Zone	Test	May 30, 2019	$23476\times3300$	6412
Yukon–Kuskokwim Delta	Training	Aug 28, 2018	$19066\times3300$	5180
Yukon–Kuskokwim Delta	Test	Sep 17, 2019	$19148\times3300$	5208

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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

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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

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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

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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

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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

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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

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