Various Signal Processing Techniques used on non-Stationary Acoustic Doppler Current Data. Volume I - XI

Document type: Researchreports
Author(s): Thomas L Lagö, Sven Olsson
Title: Various Signal Processing Techniques used on non-Stationary Acoustic Doppler Current Data. Volume I - XI
Series: Research Report
Year: 1999
Issue: 16
ISSN: 1103-1581
Organization: Blekinge Institute of Technology
Department: Department of Telecommunications and Signal Processing (Institutionen för telekommunikation och signalbehandling)
Department of Telecommunications and Signal Processing S-372 25 Ronneby
+46 455 780 00
Authors e-mail: tlago@pcb.com, sven.olsson@signal.se
Language: English
Abstract: Chapter 1 - Background, deals with the process of analyzing the backscattering
signal transmitted from an ultrasonic transducer, [5][28]. The narrowband
sinusoidal burst signal is Doppler-shifted due to the current, and this information
is converted into current, [14]. The traditional mathematical model for this
Doppler process is based on the assumption that the backscattering time signal is
Gaussian, due to the Rayleigh backscattering amplitude assumption with random
phase, [23][27]. This is based on the assumption that the backscattering is due to
many randomly distributed bubbles with about equal size. It is reasonable to
question whether this assumption holds for real life signals, [ 1][7][8]. Therefore,
this work has concentrated on looking at real life data, and has investigated
whether the Gaussian assumption holds for the background noise and the Doppler
signal received. It has been found that this is not generally the case.
Chapter 2 - Spectral Analysis of Data, provides analysis of the spectral content
in the data using tools with different properties. The reason is the difficulty in
distinguishing real spectral peaks in the data from peaks coming from variance in
the estimate, [2][3]. Therefore, 3D-plots have been generated of current data from
four locations around the world with very different environments. Also, a non-linear
filtering method named Multiple Peak Count Analysis, MPCA, has been
developed. This analysis is most important in understanding if there is more than
one Doppler signal component (current) active in the measurement cell analyzed.
Using these two methods, which use different foundations for the analysis, it is
possible to determine if, and often, how many, Doppler signals are active in one
cell. This compares to how many spectral peaks the data contains for each
observation interval.
Chapter 3 - Statistical Measures provides an analysis of the data using classical
statistical tools like histo.gram, normal probability plots, Chi-square tests and
variance analysis like ANOVA, ANalysis Of Variance, [2 1][26]. These tools helps
in understanding if it is possible to use a Gaussian approach for the signal model,
or if some other distribution could be better suited. Data from all four locations are
used in the analysis and key results are presented. In this chapter, analysis of the
background noise is also analyzed and presented using the above statistical
measures.
Chapter 4 - Higher Order Moments, provides a description of higher order
moments using skewness y, and kurtosis y2. These are important tools of the
statistical behavior of the data analysis. The .investigation of the higher order
moments for the time series of the three ADCMs, does not contradict the proposed
signal model. Furthermore, the real world signals converge very much to what can
be expected if this new model is adequate for this kind of signal. The conclusion
is, then, that the model holds for this test. The data is found not to obey the
Gaussian signal model in general. This is particularly true when the water is
troubled. A comparison with real data from four different locations presented
above has been performed and all data shows the same trends, the data cannot be
modeled using Gaussian statistical properties. The 3D plots presented earlier show
that there often are several current vectors active in a cell at the same time, and this
has a strong effect on the statistics for the time signal, which is quantified in this
chapter.
Chapter 5 - Comparison of Estimators, provides an extensive comparison
between the covariance method and the Symmiktos MethodTM. Simulated and real
data from all four locations have been used in the comparison. The comparison is
presented in several formats to make conclusions easier. It is clear that the
Symmiktos Method*M generates quite different results from those of the
covariance method. On simulated data, the Symmiktos MethodTM is much closer
to the simulated truth. However, in real life we don’t know the answer, so it is
impossible to be sure which estimator is more accurate. Based on the results from
the simulated signals and also noticing that the variance is lower when using the
Symmiktos Method M, plus adding the results from the signal model together, it
is fairly safe to argue that the Symmiktos Method*M is a more robust and accurate
method for Doppler frequency estimation on this type of data.
Chapter 6 - Estimator Programs, gives a brief background on the imple-mentation
of the main Matlab programs used in the calculations, and the most
important programs for understanding of the work, are listed. The programs listed
are not only the statistical programs but also the programs used for testing a new
signal model and comparing the covariance method with the Symmiktos Method.
Chapter 7 - Description of Used Data Sets, gives a brief background on the data
sets used in this research. Key data from the four locations is given as well as all
the background parameters to when and how the data was collected, as well as the
main observations made at the time of data collection. )

Chapter 8 - Summary and Conclusions, provides a summary of the key results
from the four different locations. Each method is commented individually and the
main effects are discussed.

Chapter 9 : References, lists all the references used.

Chapter 10 - Listing of Measurement Plots, lists all the plots. The plots consist
of about 2000 pages divided over 11 volumes.
Subject: Signal Processing\Hydro-Acoustics
Keywords: Doppler, Current, Estimation, Shte symmiktos method, ADCP, ADCM, Gaussian Backscattering Model, Acoustic Doppler, Doppler Profiler, MPCA
Note: This research report consists of eleven volumes. The content of each volume is described below, Volume I. l.Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch l -Page 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 1 -.Page 1 1.2 Short description of used data sets. . . . . . . . . . . . . . . . . Ch 1 - Page 3 1.3 List of notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch l -Page 5 1.4 Systembackground. ... . . . . . .. . . . . . . . . . . . . . . . . . Ch 1 -Page 7 2. Spectral Analysis of Data . . . . . . . . . . . . . . . . . . . ......... Ch 2 -Page 1 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 2 - Page 1 2.2 Used Data Set .... . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 2 -Page 3 2.3 Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 2 - Page 5 2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 2 - Page 5 2.3.2 Non-linear Pre-filtering of the Spectral Data . Ch 2 - Page 9 2.4 Multiple Peak Count Analysis, MPCA . . . . . . . . . . . . Ch 2 - Page 11 2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . Ch 2 - Page 11 2.4.2 Peak Detection . . . . . . . . . . . . . ... . . . . . . Ch 2 -Page 11 2.4.3 Difference equation . . . . . . . . . . . . . . . . . . . Ch 2 - Page 13 2.4.4 The Floor .........,............................................ Ch 2 -Page15 2.4.5 Double Peaks . . . . . . . . . . . . . . . . . . . . . . . . . Ch 2 - Page 15 2.4.6 Quantification . . . . . . . . . . . . . . . . . . . . . . . Ch 2 - Page 17 2.4.7 Results from the MPCA Calculation . . . . . . . Ch 2 - Page 19 2.5 3 D MPCA Plots of.Data . . . . . . . . . . . . . . . . . . . . . . . Ch 2 - Page 25 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 2-Page 45 3. Statistical Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 3 - Page 1 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 3 -Page 1 3.2 Used Data Sets . . . . . ...... .. . . . . . . . . . . . . . . . . . Ch3-Page3 3.3 ANOVA Tests . . . . . . . . . . . . . . ................. Ch3-Page5 3.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch3-Page5 3.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 3 - Page 8 3.4 Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 3 - Page 17 3.4.1 Background . . . . . . . .. . . . . . . . . . . . . . . . . . . . Ch 3 - Page 17 t 3.4.2 Several distributions or mixed signals . . . . . Ch 3 - Page 23 3.4.3 Results: Histograms . . . . . . . . . . . . . . . . . . . . Ch 3 - Page 25 3.5 Normal Probability Tests ........ ............. Ch 3 - Page 33 3.5.1 Background .......................... Ch 3 -Page 33 3.5.2 Results: Normal Probability Plots ... ..... Ch 3 - Page 35 3.6 Chi-2 Tests ................................. Ch 3 -Page 43 3.6.1 Background ........................... Ch 3 -Page 43 3.6.2 Results: Chi-2 Tests, 2-Dimensional ..... Ch 3 - Page 45 3.7 Chi-2 Tests, 3-Dimensional .................... Ch 3 - Page 53 3.7.1 Results: Chi-2 Tests, 3-Dimensional ....... Ch 3 - Page 53 3.8. Background Noise .............................. Ch 3 -Page 61 3.9 Summary ................................... Ch 3 -Page 67 3.10 Table of Contents ........................... Ch 3 -Page 71 4. Higher Order Moments ............................... Ch 4 - Page 1 4.1 Background ................................... Ch 4 - Page 1 4.2 Used Data Sets ................................ Ch 4 -Page 3 4.3 Theoretical Background ...... ................. Ch 4 - Page 5 4.4 Higher Order Moments for the Proposed Model ..... Ch 4 - Page 9 4.5 Comparison with Real World Signals ............ Ch 4 - Page 17 4.6 Results from Higher Order Moments .............. Ch 4 - Page 2 1 4.7 Summary ................................... Ch 4 - Page 29 5. Comparison of Estimators ............................. Ch 5 - Page 1 5.l Introduction.. ................................ Ch 5 - Page 1 5.2 Used Data Sets ............................... Ch 5 - Page 3 5.3 Comparisons Using Simulated Signals ............. Ch 5 - Page 5 5.4 Comparisons Using Real Life Data ............... Ch 5 - Page 9 5.5 Sumrnary ................................... Ch 5 - Page 19 6. Description of Matlab Programs ........................ Ch 6 - Page 1 6.1 Introduction .................................. . . Ch 6 - Page 1 HIST_D0P.m:. .......... :.. ....................... Ch 6 -Page 5 PL6_ADCM.m: .................................. Ch 6 - Page 6 SP3_ADCM.m: ................................... Ch 6 -Page 9 SPA_ADCM.m: ............................ Ch 6 - Page 11 SP4_ADCM,m: .................................. Ch 6 - Page 15 SP_ADCM.m: .................................. Ch 6 - Page 17 N0RMERA.m: ................................. Ch 6 - Page 18 PL8_ADCM.m: ................................. Ch 6 - Page 19 SP5_ADCM.m: ........... .. .......... .. Ch 6 - Page 22 SP_TEST.m: . . . . . . . . . . . . . . . . . . . . . . . . . :. . . . . . . . . Ch 6 - Page 24 P.m: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 6-Page 25 RD_ADCM.m: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 6 - Page 29 X300ADCM.m: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 6 -Page 32 PL4_ADCM.m: . . . . . . . . . . . . . . . .. . . . . . . . .. . . . . . . . Ch 6 - Page 33 S.m: ...:... . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . Ch 6 - Page 35 SP7_ADCM.m: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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Ch 6 - Page 153 adcm_cov.m: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 6 - Page 157 adcm_sym.m:...................................................................... Ch 6 - Page 159 7. Description of Used Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . Ch 7 - Page 1 7.1 Introduction.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 7 -Page 1 7.2 The Trubaduren Light House . . . . . . . . . . . . . . . . . . . . Ch 7 - Page 5 7.3 FIaden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 7 - Page 7 7.4 AImagrundet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 7 - Page 9 7.5 Ma-Wan ,Hongkong ........................... C h 7 - Page 11 7.6 DataFormat ... .............................. ........Ch 7 - Page 13 8. Summary and Conclusions ............................. Ch 8 - Page 1 8.1 Main reason for the work ......................... Ch 8 - Page 1 8.2 Key results ................................... Ch 8 - Page 3 8.3 Future work .: ................................. Ch 8 - Page 5 9. References .. . . . . . . . . . . . . . . . . . . . ... Ch 9 - Page l-2 10. Listing of Measurement Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ch 10 Time domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Pages 3D Spectrogram plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Pages Volume II. Normal probability plots, part 1 . . . . . . . . . . . . . . . . . . . . . . . . 254 Pages Volume III. Normal probability plots. part 2...................................................254 Pages Volume IV. Histogram plots,.part l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180Pages Volume V. Histogram plots, part 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Pages Volume VI. ANOVA plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Pages Gamma plots . . . . . . . . . . . . . . . . . . . . ‘ . . . . . . . . . . . . . . . . . . . . 32 Pages 3D Multiple Peak Count Analysis, MPCA . . . . . . . . . . . . . . . 134 Pages Volume VII. Multiple Peak Count Analysis, MPCA, part 1 ..............................192 Pages Volume VIII. Multiple Peak Count Analysis, MPCA, part 2 ..............................192 Pages Volume IX Multiple Peak Count Analysis, MPCA, part 3 ..............................192 Pages Volume X. Chi-2, 2D Plots.....................................................................................158 Pages Chi-w, 3D Plots......................................................................................58 Pages Volume XI. Comparison Covariance-Symmiktos..................................................133 Pages
URN: urn:nbn:se:bth-00127
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