Multi-Target Tracking with Phased Arrays : application to sonar bathymetry reconstruction

148 Pages·2017·7.99 MB·English

by  Augustin Alexandru Saucan

Multi-Target Tracking with Phased Arrays: application
to sonar bathymetry reconstruction
Augustin Alexandru Saucan
To cite this version:
Augustin Alexandru Saucan. Multi-Target Tracking with Phased Arrays: application to sonar
bathymetry reconstruction. Signal and Image processing. Télécom Bretagne; Université de Bretagne
Occidentale, 2015. English. ￿NNT: ￿. ￿tel-01272734￿
HAL Id: tel-01272734
https://hal.science/tel-01272734
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N◦ d’ordre : 2015telb0379
Sous le sceau de l’Universit´e Europ´eenne de Bretagne
T´el´ecom Bretagne
´
En accr´editation conjointe avec l’Ecole Doctorale – Sicma
Multi-target Tracking with Phased
Arrays: application to sonar
bathymetry reconstruction
Th`ese de Doctorat
Mention : STIC – Sciences et Technologies de l’Information et de la Communication
Augustin-Alexandru SAUCAN
Pr´esent´ee par
D´epartement : Image et traitement de l’information
Laboratoire : Lab-STICC Poˆle : Connaissance Information Decision
Souˆtenu le 01 D´ecembre 2015 devant la Commission d’Examen compos´ee de :
M. Philippe Vanheeghe - Professeur Ecole Centrale Lille (President)
Mme. Sylvie Marcos - Directrice de recherche CNRS SUPELEC (Rapporteur)
M. J´eroˆme Mars - Professeur INP Grenoble (Rapporteur)
M. Ba-Ngu Vo - Professeur Curtin University, Australie (Examinateur)
M. Jean-Marc Le Caillec - Professeur Telecom Bretagne (Directeur)
M. Thierry Chonavel - Professeur Telecom Bretagne (Examinateur)
M. Christophe Sintes - Directeur d’´etudes Telecom Bretagne (Examinateur)
M. Philippe Pouliguen - Ing´enieur de recherche DGA (Examinateur)
M. Dominique Fattaccioli - Ing´enieur de recherche DGA (Invit´e)
Mme. Myriam Chabah - Ing´enieur Thales Underwater Systems (Invit´ee)

Contents
Abbreviations and nomenclature vii
Acknowledgements x
R´esum´e 1
Contexte . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Les principaux d´efis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Objectifs et r´ealisations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Plan d´etaill´e de la th`ese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
I Introduction 13
II Sonar echo tracking: a data-association approach 19
II.1 Introduction: Objectives and challenges . . . . . . . . . . . . . . . . . . . . . . . 19
II.2 Underwater environment and pre-processing module . . . . . . . . . . . . . . . . 22
II.3 Post-processing module: the NNIPDA-UKF filter . . . . . . . . . . . . . . . . . 25
II.3.1 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
II.3.2 Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
II.3.3 Trajectory quality measure . . . . . . . . . . . . . . . . . . . . . . . . . . 30
II.4 Geometrical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
II.5 Results of NNIPDA-UKF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
II.5.1 Simulated data results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
II.5.2 Real data results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
II.6 Chapter conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
IIISonar echo tracking: an intensity function approach 45
III.1 Point-process formalism for target tracking . . . . . . . . . . . . . . . . . . . . . 45
III.2 Point-process theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
III.2.1 Preliminary definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
III.2.2 A probability measure for PP . . . . . . . . . . . . . . . . . . . . . . . . 50
III.2.3 RFS and set integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
III.2.4 Moment measures of point processes . . . . . . . . . . . . . . . . . . . . 51
III.3 Examples of finite point processes . . . . . . . . . . . . . . . . . . . . . . . . . . 52
III.3.1 Independent and identically distributed cluster (iidc) . . . . . . . . . . . 52
III.3.2 Poisson process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
III.4 Error metrics for multi-target tracking . . . . . . . . . . . . . . . . . . . . . . . 53
III.5 The PHD filter for TWS systems . . . . . . . . . . . . . . . . . . . . . . . . . . 54
III.5.1 TWS-PHD prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
III.5.2 TWS-PHD update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
i
Contents
III.6 TBD-PHD filter for phased arrays: a Gaussian
point-target case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
III.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
III.6.2 Array signal and marked multi-target process . . . . . . . . . . . . . . . 59
III.6.3 Approximate PHD filter for marked multi-target process . . . . . . . . . 60
III.6.4 Results on simulated phased-array data . . . . . . . . . . . . . . . . . . . 63
III.7 Chapter conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
IVSonar echo tracking: the case of extended and impulsive targets 67
IV.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
IV.2 Impulsive Sonar-signal distributions . . . . . . . . . . . . . . . . . . . . . . . . . 69
IV.2.1 The SIRV model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
IV.2.2 The joint-SIRV model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
IV.3 Phased-array signal and multi-target formalism . . . . . . . . . . . . . . . . . . 73
IV.3.1 Extended and impulsive target model . . . . . . . . . . . . . . . . . . . . 74
IV.3.2 Marked process for extended and impulsive target signals . . . . . . . . . 75
IV.4 Phased-array TBD-CPHD filter . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
IV.4.1 Phased-array TBD-CPHD prediction . . . . . . . . . . . . . . . . . . . . 77
IV.4.2 Phased-array TBD-CPHD intensity update . . . . . . . . . . . . . . . . . 78
IV.4.3 Phased-array TBD-CPHD cardinality update . . . . . . . . . . . . . . . 80
IV.4.4 TBD-CPHD Monte Carlo Implementation . . . . . . . . . . . . . . . . . 81
IV.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
IV.5.1 Tracking results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
IV.5.2 Angular resolution analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 91
IV.6 Real sonar data results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
IV.7 Chapter conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
V Conclusions and perspectives 95
A Integrated PDAF (IPDAF) 111
B Observation noise covariance estimation 117
C Model validation 119
D Proof of p-value |H ∼ U(0,1) 121
0
E Quadratic and Gaussian equalities 123
F On the distribution of random sums 125
G Array narrow-band condition 127
H Statistical analysis of sonar signals 129
ii
List of Figures
1 Principedel’imageriesous-marineparsonar: a)G´eom´etriedelafauch´eed’´emission
et le signal r´etrodiffus´e. b) Antenne r´eceptrice du sonar avec DOA du signal
r´etrodiffus´e. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
II.1 Underwater scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
II.2 Angular spectrum showing multiple echoes impinging the sonar array. . . . . . . 24
II.3 Flowchart showcasing the different stages of the proposed algorithm. . . . . . . . 27
II.4 Imaging geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
II.5 a) Capon spectrogram with DOA observations (♦) and the perfect FHB tra-
jectory (red curve). b) Only the DOA observations (♦) and the perfect FHB
trajectory (red curve). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
II.6 a) Receiver operating curves for Box-Pierce and Ljung-Box tests. b) Noisy tra-
jectory generated with FHB model. MSE of raw observation sequence(before fil-
tering). MSE after filtering with the correct FHB model and an incorrect slopped
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
ˆ
II.7 NN-IMM-PDA-UKF echo separation: a) θ overlay-ed on the Capon spectro-
t|t
gram. b) Bottom FHB and RW model probabilities µ . c)/d) Bottom/sea-
t|t
surface trajectory existence probability ν Eq. (A.17). . . . . . . . . . . . . . . 36
t|t
II.8 Side-scan (amplitude) image of 200 adjacent ping lines. b) Trajectory existence
probabilities for the 200 ping lines. . . . . . . . . . . . . . . . . . . . . . . . . . 37
II.9 Man-made object scenario: a) NN-IMM-IPDA-UKF estimates overlayed on the
MUSIC pseudo-spectrogram. b) Pole VO and RW model probabilities. c) Pole
trajectory existence probability ν , Eq. (A.17). . . . . . . . . . . . . . . . . . . 38
t|t
II.10 Trajectoryloss:a)TrackingwithonlytheRWmodel.b)Poletrajectoryexistence
probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
II.11 Man-made object reconstruction comparison: a) Interferometry b) MUSIC c)
NN-IMM-IPDA-UKF. Figure d) shows an image of the foam-filled fender, which
is mounted on top of the pole (courtesy of EdgeTech). Notice the partial submer-
sion of the fender, which makes it visible in the reconstructed sonar bathymetry
of figure c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
II.12 TurningnotchofPortEverglades,FortLauderdale,FL(GPScoordinates26.074920,
−80.115201). Courtesy of Google Maps, date 14.11.2013. The canal is called
Stranahan River. Note the encircled survey area and the turning piling. Large
container ships are turned inside this turning notch, with the help of the turning
piling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
II.13 Pole/pilling diameter inference. The bathymetry points comprising the main
body of the pole are projected onto the plane of the along-track and ground-
range axis. Note the fitted circle, corresponding to the inferred diameter and
center, and the projected points. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
II.14 a) Bathymetry reconstruction with the proposed filtering algorithm. b) Predom-
inant models (geometrical segmentation). c) Side-scan image (signal amplitude). 41
iii
List of Figures
II.15 GoF p−value histogram of ping lines composing the bathymetry in fig. II.14: a)
Box-Pierce test b) Ljung-Box test . . . . . . . . . . . . . . . . . . . . . . . . . . 42
II.16 GoF p−value histogram for RW model only: a) Box-Pierce test b) Ljung-Box test 42
III.1 Logarithm of estimated intensity function, for the proposed TBD-PHD filter. . . 63
III.2 DBSCAN clustering results: a) for the proposed TBD-PHD filter b) for the ref-
erence phased-array TWS-PHD. . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
IV.1 Pseudo-algorithm for one iteration for the proposed auxiliary SMC-CPHD filter
for array processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
IV.2 Pseudo-algorithm of the proposed clustering method. . . . . . . . . . . . . . . . 86
IV.3 Different PHD filter intensities and clustering results. . . . . . . . . . . . . . . . 87
IV.4 Box and whiskers plot of the OSPA error (order 2 and cut-off 10), as a function
of time. On each box, the central mark is the median, the edges of the box are
the 25th and 75th percentiles, the whiskers extend to the most extreme data
points not considered outliers, and outliers are plotted individually. . . . . . . . 88
IV.5 Cardinal histograms for different filtering methods at SNR 5dB. Ground truth
cardinality is represented by the red line. . . . . . . . . . . . . . . . . . . . . . . 90
IV.6 Angular resolution analysis with closely spaced targets scenario: stationary case
→ upper row, non-stationary case → bottom row. . . . . . . . . . . . . . . . . 91
IV.7 DOA estimates as the instantaneous maxima (a) of the Capon spectrogram an
the CA-CPHD filter results (b), overlaid on the CAPON spectrogram. . . . . . 92
IV.8 CA-CPHD filter centroid DOA estimates for a multiple echo scenario. . . . . . . 93
G.1 The narrow-band condition as a function of the DOA θ. The array axis coincides
withtheabscissaaxis.Thecolorrepresentstheconditionnumber Dsin(θ)B,which
c
has to be much smaller than 1 for the narrow-band condition to hold. . . . . . . 127
H.1 QQ plot for far range: a) H hypotheses are the Gaussian (blue) and the Laplace
0
(red)distributions,b)H hypothesesaretheGaussian(blue)andK-distributions
0
(red). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
H.2 QQplotfornearrange:a)H hypothesesaretheGaussian(blue)andtheLaplace
0
(red)distributions,b)H hypothesesaretheGaussian(blue)andK-distributions
0
(red). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
H.3 p−value histograms for different tests. . . . . . . . . . . . . . . . . . . . . . . . 132
iv
List of Tables
II.1 Type I error of different tests, evaluated from 1000 trials. . . . . . . . . . . . . . 34
III.1 Average OSPA error over 1000 Monte Carlo runs. . . . . . . . . . . . . . . . . . 64
IV.1 Average OSPA error of various filters computed over 400 runs. . . . . . . . . . . 89
IV.2 Average time duration of one iteration of various filters. . . . . . . . . . . . . . . 90
IV.3 Average OSPA error computed over 400 runs. . . . . . . . . . . . . . . . . . . . 92
H.1 Statistical test results: percentage of tests that accept the H distribution. . . . 131
0
v
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