ECE 538638 Statistical Signal Processing ece.pdx.edu

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ECE 538638 Statistical Signal Processing ece.pdx.edu Powered By Docstoc
					ECE 538/638: Statistical Signal Processing
ece.pdx.edu/~ssp



                                                                                                                                        Overview
                                                                                           STATISTICAL SIGNAL PROCESSING

            Temperature coupling in arctic ground
                                                                                         ece.pdx.edu/~ssp



                             Estimation of time delay
                                                                                        • Project Goals
            STATISTICAL SIGNAL PROCESSING
          ece.pdx.edu/~ssp                                                              • Importance
                                                                                        • Methodology
                                    Reto Töngi                                                 Concept
                                                                                               Data collection
                             Statistical Signal Processing                                     Used Technique
                                        Fall 2005
                                                                                        • Results
                                Portland State University
                                                                                        • Conclusion
                                                               E LECTRICAL & COMPUTER                                                  E LECTRICAL & COMPUTER
                                                               E NGINEERING                                                            E NGINEERING




                                                            Project goals                                                         Importance
            STATISTICAL SIGNAL PROCESSING                                                  STATISTICAL SIGNAL PROCESSING
          ece.pdx.edu/~ssp                                                               ece.pdx.edu/~ssp




         • Estimation of the speed that air temperature                                 Geology
           penetrates into soil up to 1 m of depth.                                     • Use of subsurface temperature propagation speed to
                                                                                          time past events
                                                                                        • Investigate stability issues with permafrost
         • Are frequency oscillation’s in upper surface                                 Biology
           layers visible?                                                              • Ecosystem of rough environment
                                                                                        Curiosity
         • Existence of temperature cycles other than                                   • How useful are the learned tools in such an
           the known seasonal cycles?                                                     environment

                                                               E LECTRICAL & COMPUTER                                                  E LECTRICAL & COMPUTER
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                                                                 Concept                                                                 Concept
            STATISTICAL SIGNAL PROCESSING                                                  STATISTICAL SIGNAL PROCESSING
          ece.pdx.edu/~ssp                                                               ece.pdx.edu/~ssp



         • Thermal flow from Air onto Earth’s surface                                   • Each Ground layer is modeled with a separate time
                                                                                          delay function.
                                                                                                    TAir(t)      TAir(t)     TAir(t)


                                                                                                    h1(t)
                                                                                                                  h2(t)
                                                                                                                              h3(t)

                                                                                                 TSoil1(t)     TSoil2(t)   TSoil3(t)
                                                               E LECTRICAL & COMPUTER                                                  E LECTRICAL & COMPUTER
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Portland State University                                                                                                                                       1
ECE 538/638: Statistical Signal Processing
ece.pdx.edu/~ssp



                                                                                            Data collection                                                                                                                                                                                                                          Data collection
            STATISTICAL SIGNAL PROCESSING                                                                                               STATISTICAL SIGNAL PROCESSING
          ece.pdx.edu/~ssp                                                                                                            ece.pdx.edu/~ssp



         • Data collected from 3 areas with 14 sites                                                                                 • Air temperature recorded 1.6 m above ground
         • North Slope, Ivotuk, Council                                                                                              • Sampled every 10 min, averaged from 12 pm-12 pm
                                                                                                                                                                                                                           Air temperature 1.6 m above Ground, NorthSlope
                                                                                                                                                                                                  20


                                                                                                                                                                                                  10


                                                                                                                                                                                                    0




                                                                                                                                                                              Temperature [°C]
                                                                                                                                                                                                 −10


                                                                                                                                                                                                 −20


                                                                                                                                                                                                 −30


         Data comes form:                                                                                                                                                                        −40

         NSIDC National Snow and Ice
           Data Center                                                                                                                                                                           −50
                                                                                                                                                                                                   200             400                    600     800      1000     1200     1400                                                              1600           1800
                                                                                                                                                                                                                                             Time in days since 1/1/1997 [day]
                                                                                                            E LECTRICAL & COMPUTER                                                                                                                                                                                                                              E LECTRICAL & COMPUTER
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                                                                                            Data collection                                                                                                                                                                                                                   Used Technique
            STATISTICAL SIGNAL PROCESSING                                                                                               STATISTICAL SIGNAL PROCESSING
          ece.pdx.edu/~ssp                                                                                                            ece.pdx.edu/~ssp



         • Soil temperatures in different depth, North                                                                               • Time delay estimation using lag of normalized
           Slope Westdock                              Soil temperature, North Slope westdock
                                                                                                                                       cross- covariance                                                                                                                1
                                                                                                                                                                                                                                                                                           cross−correlation Air− Soil−temperature, Council woods

                                                                                                                                                                                                                                                                                                                                                                                                   0m
                                          15
                                                                                                                                                                                                                                                                     0.8                                                                                                                           −0.15 m
                                                                                                  −0.05 m
                                                                                                                                                                                                                                                                                                                                                                                                   −0.3 m
                                                                                                  −0.15 m
                                          10                                                                                                                                                                                                                         0.6                                                                                                                           −0.45 m
                                                                                                  −0.2 m
                                                                                                                                                                                                                                                                                                                                                                                                   −0.65 m
                                                                                                  −0.3 m
                                                                                                                                                                                                                                                                     0.4                                                                                                                           max corr
                                           5                                                      −0.4 m
                                                                                                                                                                                                                                                                                                                                                                                                   max corr
                                                                                                  −0.5 m
                                                                                                  −0.7 m                                                                                                                                                             0.2
                      Temperature [°C]




                                           0                                                      −0.8 m



                                                                                                                                                                                                                                                             ρ(l)
                                                                                                                                                                                                                                                                        0
                                         −5
                                                                                                                                                                                                                                                                    −0.2

                                         −10                                                                                                                                                                                                                        −0.4

                                                                                                                                                                                                                                                                    −0.6
                                         −15

                                                                                                                                                                                                                                                                    −0.8
                                         −20
                                                                                                                                                                                                                                                                      −1
                                                                                                                                                                                                                                                                      −400            −300                           −200            −100             0              100              200          300        400
                                         −25                                                                                                                                                                                                                                                                                                      lag [day]
                                           200   400   600     800      1000     1200     1400   1600   1800
                                                          Time in days since 1/1/1997 [day]

                                                                                                            E LECTRICAL & COMPUTER                                                                                                                                                                                                                              E LECTRICAL & COMPUTER
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                                                                                        Used Technique                                                                                                                                                                                         Results Time delay
            STATISTICAL SIGNAL PROCESSING                                                                                               STATISTICAL SIGNAL PROCESSING
          ece.pdx.edu/~ssp                                                                                                            ece.pdx.edu/~ssp
                                                                                                                                                                                                  Temperature lag in Soil, Council                                                                                                            Temperature lag in Soil, Ivotuk
                                                                                                                                                                                                                                                                                                                     70
                                                                                                                                                              70

         • The Power Spectrum Estimated with Blackman-Tukey                                                                                                   60
                                                                                                                                                                             mean temerature delay
                                                                                                                                                                             upper 95% confidence band
                                                                                                                                                                             lower 95% confidence band
                                                                                                                                                                                                                                                                                                                     60
                                                                                                                                                                                                                                                                                                                                    mean temperature delay
                                                                                                                                                                                                                                                                                                                                    upper 95% confidence band
                                                                                                                                                                                                                                                                                                                                    lower 95% confidence band


           method                                                                                                                                             50
                                                                                                                                                                                                                                                                                                                     50
                                                                                                                                                                                                                                                                                                  time delay [day]
                                                                                                                                           time delay [day]




                                                                                                                                                                                                                                                                                                                     40


         • Auto-covariance chosen over Auto-correlation to remove
                                                                                                                                                              40


                                                                                                                                                                                                                                                                                                                     30
                                                                                                                                                              30


           delta function at frequency 0.                                                                                                                     20
                                                                                                                                                                                                                                                                                                                     20




         • Bartlett window length 365 samples
                                                                                                                                                                                                                                                                                                                     10
                                                                                                                                                              10


                                                                                                                                                                                                                                                                                                                      0
                                                                                                                                                               0                                                                                                                                                          0   0.1      0.2     0.3      0.4     0.5    0.6      0.7    0.8   0.9
                                                                                                                                                                   0   0.1           0.2            0.3     0.4     0.5    0.6                      0.7      0.8     0.9


               0.01 1/day, 26dB side lobe
                                                                                                                                                                                                                                                                                                                                                      sensor depth [m]
                                                                                                                                                                                                          sensor depth [m]

                                                                                                                                                                                                                                                                            Temperature lag in Soil, North Slope
                                                                                                                                                                                                                                                    80
                                                                                                                                                                                                                                                                    mean temperature delay
                                                                                                                                                                                                                                                    70              upper 95% confidence band
                                                                                                                                                                                                                                                                    lower 95% confidence band
                                                                                                                                                                                                                                                    60



                                                           N −1                                                                                                                                                                                     50
                                                                                                                                                                                                                                 time delay [day]




                                         Rx (k ) = ∑ γˆx (n) w(n)e − j ( 2π / N ) kn
                                         ˆ                                                                                                                                                                                                          40


                                                                                                                                                                                                                                                    30


                                                                                                                                                                                                                                                    20

                                                            n =0                                                                                                                                                                                    10


                                                                                                                                                                                                                                                     0
                                                                                                                                                                                                                                                         0    0.1     0.2       0.3     0.4     0.5    0.6                     0.7      0.8     0.9
                                                                                                                                                                                                                                                                                      sensor depth [m]



                                                                                                            E LECTRICAL & COMPUTER                                                                                                                                                                                                                              E LECTRICAL & COMPUTER
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Portland State University                                                                                                                                                                                                                                                                                                                                                                                           2
ECE 538/638: Statistical Signal Processing
ece.pdx.edu/~ssp



                                                                                                         Result Time delay                                                                                                                                       Results PSD
            STATISTICAL SIGNAL PROCESSING                                                                                                                               STATISTICAL SIGNAL PROCESSING
          ece.pdx.edu/~ssp                                                                                                                                       ece.pdx.edu/~ssp



         • Average lag of temperature flow over all sites                                                                                                        • Estimated Power Spectrum average
                                                                                                                                                                                                                  PSD of air temperature, average over all locations
                                                                             Temperature lag in Soil, average over all locations
                                                                                                                                                                                                                                                     mean power spectrum
                                                            80
                                                                                                                                                                                                   70                                                upper 95% confidence band
                                                                             mean temperature delay                                                                                                                                                  lower 95% confidence band
                                                            70               upper 95% confidence band
                                                                             lower 95% confidence band                                                                                             60

                                                            60
                                                                                                                                                                                                   50
                                                            50
                                         time delay [day]




                                                                                                                                                                                             PSD
                                                                                                                                                                                                   40
                                                            40
                                                                                                                                                                                                   30
                                                            30
                                                                                                                                                                                                   20
                                                            20
                                                                                                                                                                                                   10
                                                            10

                                                                                                                                                                                                        0      0.01          0.02         0.03       0.04     0.05      0.06
                                                             0                                                                                                                                                                      cycles per day [1/day]
                                                                 0     0.1      0.2     0.3     0.4     0.5    0.6       0.7       0.8   0.9
                                                                                              sensor depth [m]

                                                                                                                                     E LECTRICAL & COMPUTER                                                                                                             E LECTRICAL & COMPUTER
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                                                                                                                                   Result PSD                                                                                                                        Result PSD
            STATISTICAL SIGNAL PROCESSING                                                                                                                               STATISTICAL SIGNAL PROCESSING
          ece.pdx.edu/~ssp                                                                                                                                       ece.pdx.edu/~ssp



         • Simulated annual cycle, side lobe attenuation                                                                                                         • Air PSD Council (frequency period ~28 days)
           only 26 dB !!!                                              simulated annual cycle
                                                                                                                                                                                            PSD of air temperature, Council

                                                                                                                                                                        30                                            mean power spectrum
                          90                                                                          calculated PSD                                                                                                  upper 95% confidence band
                                                                                                                                                                                                                      lower 95% confidence band
                          80                                                                                                                                            25

                          70
                                                                                                                                                                        20
                          60
                                                                                                                                                                  PSD




                          50                                                                                                                                            15
                    PSD




                                                                                                                                                                                                                                                                     0.03     0.04
                          40
                                                                                                                                                                        10                                                                                            cycles per day
                          30
                                                                                                                                         0.01      0.02
                          20                                                                                                                         cycles pe           5

                          10
                                                                                                                                                                         0
                                                                                                                                                                              0.01   0.02          0.03     0.04      0.05      0.06       0.07     0.08
                               0       0.01                          0.02        0.03         0.04          0.05                                                                                    cycles per day [1/day]
                                                                       cycles per day [1/day]

                                                                                                                                     E LECTRICAL & COMPUTER                                                                                                             E LECTRICAL & COMPUTER
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                                                                                                                                   Result PSD                                                                                                                        Conclusion
            STATISTICAL SIGNAL PROCESSING                                                                                                                               STATISTICAL SIGNAL PROCESSING
          ece.pdx.edu/~ssp                                                                                                                                       ece.pdx.edu/~ssp



         • Are there frequency oscillation in upper surface
                                                                                                                                                                 Methods applied
           layers visible? How accurate?
                    18
                                                             PSD of Soil temperature, Council                                                                    • Time delay estimation using cross-covariance
                    16
                                                                                       −0.1m
                                                                                       upper 95% confidence band
                                                                                       lower 95% confidence band
                                                                                                                                                                   lag seems to work
                    14
                                                                                                                                                                 • PSD estimation using Blackman-Tukey has too
                    12
                                                                                                                                                                   much side lobe amplitude with known
                    10
                                                                                                                                                                   dominant cycle
              PSD




                      8

                      6
                                                                                                                            0.03                0.04                         Filtering the data before
                      4                                                                                                                        cycles p                      Using Welch-Bartlett method
                      2


                               0.01   0.02                  0.03      0.04 0.05 0.06          0.07   0.08    0.09
                                                                     cycles per day [1/day]

                                                                                                                                     E LECTRICAL & COMPUTER                                                                                                             E LECTRICAL & COMPUTER
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Portland State University                                                                                                                                                                                                                                                                        3
ECE 538/638: Statistical Signal Processing
ece.pdx.edu/~ssp



                                                Conclusion                                                                                                Visual Inspection
            STATISTICAL SIGNAL PROCESSING                                        STATISTICAL SIGNAL PROCESSING
          ece.pdx.edu/~ssp                                                ece.pdx.edu/~ssp



                                                                          • Nonlinearity around 0°C!
                                                                                                             Soil temperature, North Slope westdock
                                                                                                15

         Result interpretation                                                                  10
                                                                                                                                                        −0.05 m
                                                                                                                                                        −0.15 m
                                                                                                                                                        −0.2 m

         • In general the soil seems to delay the
                                                                                                                                                        −0.3 m
                                                                                                 5                                                      −0.4 m
                                                                                                                                                        −0.5 m

           temperature linear with the depth                                                                                                            −0.7 m




                                                                            Temperature [°C]
                                                                                                 0                                                      −0.8 m



         • Caution has to be paid around 0°C. (Water                                           −5



           freezing temperature)                                                               −10


                                                                                               −15


                                                                                               −20


                                                                                               −25
                                                                                                 200   400   600     800      1000     1200     1400   1600   1800
                                                                                                                Time in days since 1/1/1997 [day]

                                                 E LECTRICAL & COMPUTER                                                                                              E LECTRICAL & COMPUTER
                                                 E NGINEERING                                                                                                        E NGINEERING




                                                Conclusion                                                                                                           Questions
            STATISTICAL SIGNAL PROCESSING                                        STATISTICAL SIGNAL PROCESSING
          ece.pdx.edu/~ssp                                                ece.pdx.edu/~ssp




         Result interpretation
         • There are sub-cycles visible in some of the Air
           temperature spectrums
         • Only on the highest layer of the soil are the air
           sub-cycles visible



                                                 E LECTRICAL & COMPUTER                                                                                              E LECTRICAL & COMPUTER
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Portland State University                                                                                                                                                                     4

				
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