I think no one will be able to answer this.........

1 view (last 30 days)
How to get the noise component in a GPS time series applying MLE technique. The paper I have followed is http://onlinelibrary.wiley.com/doi/10.1029/1998JB900033/pdf. I having the time series data. The time series is attached. The first column is the time column, second is the signal and third is the standard deviation
<pre> 2004.00136 9.52602 0.00167
2004.00410 9.52649 0.00163
2004.00683 9.52660 0.00162
2004.00956 9.52682 0.00162
2004.01229 9.52638 0.00165
2004.01503 9.52665 0.00167
2004.01776 9.52728 0.00163
2004.02049 9.52750 0.00162
2004.02322 9.52809 0.00161
2004.02595 9.52774 0.00164
2004.02869 9.52838 0.00164
2004.03142 9.53009 0.00159
2004.03415 9.52968 0.00161
2004.03688 9.52793 0.00161
2004.03962 9.52739 0.00162
2004.04235 9.52801 0.00162
2004.04508 9.52890 0.00161
2004.04781 9.52899 0.00161
2004.05054 9.52808 0.00162
2004.05328 9.52920 0.00162
2004.05601 9.52847 0.00162
2004.05874 9.52863 0.00161
2004.06147 9.52853 0.00166
2004.06421 9.52906 0.00166
2004.06694 9.52805 0.00172
2004.06967 9.52941 0.00167
2004.07240 9.53081 0.00165
2004.07513 9.52914 0.00166
2004.07787 9.52952 0.00162
2004.08060 9.52988 0.00169
2004.08333 9.52935 0.00176
2004.08606 9.52930 0.00170
2004.08880 9.52990 0.00165
2004.09153 9.52938 0.00165
2004.09426 9.52956 0.00165
2004.09699 9.52935 0.00165
2004.09972 9.52938 0.00165
2004.10246 9.52864 0.00171
2004.10519 9.52894 0.00166
2004.10792 9.52956 0.00166
2004.11065 9.53003 0.00164
2004.11339 9.53020 0.00163
2004.11612 9.52975 0.00163
2004.11885 9.53000 0.00164
2004.12158 9.52942 0.00166
2004.12432 9.52940 0.00167
2004.12705 9.52931 0.00168
2004.12978 9.52998 0.00163
2004.13251 9.52995 0.00163
2004.13524 9.53029 0.00165
2004.13798 9.53065 0.00166
2004.14071 9.53059 0.00165
2004.14344 9.53094 0.00167
2004.14617 9.53070 0.00167
2004.14891 9.53063 0.00165
2004.15164 9.53078 0.00170
2004.15437 9.53184 0.00168
2004.15710 9.53110 0.00170
2004.15983 9.53164 0.00168
2004.16257 9.53094 0.00168
2004.16530 9.53164 0.00167
2004.16803 9.53174 0.00167
2004.17076 9.53181 0.00167
2004.17350 9.53188 0.00167
2004.17623 9.53197 0.00167
2004.17896 9.53233 0.00167
2004.18169 9.53174 0.00166
2004.18442 9.53281 0.00168
2004.18716 9.53325 0.00172
2004.18989 9.53282 0.00167
2004.19262 9.53160 0.00166
2004.19535 9.53186 0.00166
2004.19809 9.53272 0.00172
2004.20082 9.53249 0.00168
2004.20355 9.53244 0.00163
2004.20628 9.53191 0.00164
2004.20901 9.53309 0.00167
2004.21175 9.53366 0.00166
2004.21448 9.53266 0.00165
2004.21721 9.53289 0.00167
2004.21994 9.53256 0.00171
2004.22268 9.53326 0.00171
2004.22541 9.53343 0.00172
2004.22814 9.53464 0.00177
2004.23087 9.53462 0.00178
2004.23360 9.53360 0.00173
2004.23634 9.53443 0.00171
2004.23907 9.53486 0.00174
2004.24180 9.53447 0.00183
2004.24453 9.53291 0.00179
2004.24727 9.53448 0.00179
2004.25000 9.53375 0.00178
2004.25273 9.53428 0.00180
2004.25546 9.53520 0.00179
2004.25819 9.53441 0.00178
2004.26093 9.53476 0.00175
2004.26366 9.53565 0.00174
2004.26639 9.53481 0.00176
2004.26912 9.53538 0.00165
2004.27186 9.53638 0.00170
2004.27459 9.53648 0.00174
2004.27732 9.53628 0.00172
2004.28005 9.53575 0.00170
2004.28278 9.53575 0.00172
2004.28552 9.53609 0.00173
2004.28825 9.53543 0.00175
2004.29098 9.53448 0.00172
2004.29371 9.53628 0.00183
2004.29645 9.53487 0.00172
2004.29918 9.53619 0.00167
2004.30191 9.53616 0.00172
2004.30464 9.53646 0.00176
2004.30738 9.53695 0.00183
2004.32104 9.53747 0.00185
2004.32377 9.53789 0.00175
2004.32650 9.53781 0.00180
2004.32923 9.53757 0.00174
2004.33197 9.53797 0.00174
2004.33470 9.53741 0.00178
2004.33743 9.53686 0.00174
2004.34016 9.53771 0.00177
2004.34289 9.53779 0.00172
2004.34563 9.53725 0.00178
2004.34836 9.53754 0.00174
2004.35109 9.53732 0.00169
2004.35382 9.53809 0.00179
2004.35656 9.53796 0.00173
2004.35929 9.53834 0.00179
2004.36202 9.53738 0.00178
2004.36475 9.53865 0.00185
2004.36748 9.53743 0.00174
2004.37022 9.53800 0.00179
2004.37295 9.53866 0.00174
2004.37568 9.53839 0.00179
2004.37841 9.53823 0.00173
2004.38115 9.53782 0.00171
2004.38388 9.53826 0.00170
2004.38661 9.53867 0.00174
2004.38934 9.53892 0.00174
2004.39207 9.53967 0.00178
2004.39481 9.53943 0.00179
2004.39754 9.53919 0.00177
2004.40027 9.53941 0.00175
2004.40847 9.54066 0.00178
2004.41120 9.53967 0.00174
2004.41393 9.54036 0.00182
2004.41666 9.54074 0.00184
2004.41940 9.54067 0.00174
2004.42213 9.54118 0.00177
2004.42486 9.54115 0.00179
2004.42759 9.54158 0.00179
2004.43033 9.54085 0.00171
2004.43306 9.54154 0.00170
2004.43579 9.54079 0.00169
2004.43852 9.54019 0.00169
2004.44125 9.54087 0.00172
2004.44399 9.54107 0.00174
2004.44672 9.54154 0.00179
2004.44945 9.54170 0.00188
2004.45218 9.54135 0.00181
2004.45492 9.54130 0.00178
2004.45765 9.54228 0.00177
2004.46038 9.54151 0.00175
2004.46311 9.54206 0.00175
2004.46585 9.54200 0.00172
2004.46858 9.54231 0.00169
2004.47131 9.54332 0.00176
2004.47404 9.54314 0.00171
2004.47677 9.54179 0.00168
2004.47951 9.54183 0.00174
2004.48224 9.54254 0.00175
2004.48497 9.54365 0.00183
2004.49317 9.54239 0.00180
2004.49590 9.54300 0.00176
2004.49863 9.54332 0.00176
2004.50136 9.54276 0.00171
2004.50410 9.54343 0.00174
2004.50683 9.54315 0.00172
2004.50956 9.54297 0.00172
2004.51229 9.54305 0.00169
2004.51503 9.54270 0.00178
2004.51776 9.54279 0.00182
2004.52049 9.54294 0.00179
2004.52322 9.54362 0.00173
2004.52595 9.54264 0.00176
2004.52869 9.54317 0.00174
2004.53142 9.54373 0.00174
2004.53415 9.54332 0.00176
2004.53688 9.54354 0.00173
2004.53962 9.54345 0.00174
2004.54235 9.54483 0.00170
2004.54508 9.54562 0.00170
2004.54781 9.54497 0.00171
2004.55054 9.54576 0.00170
2004.55328 9.54534 0.00170
2004.55601 9.54514 0.00173
2004.55874 9.54633 0.00176
2004.56147 9.54605 0.00171
2004.56421 9.54622 0.00176
2004.56694 9.54683 0.00171
2004.56967 9.54594 0.00175
2004.57240 9.54646 0.00176
2004.57513 9.54647 0.00176
2004.57787 9.54670 0.00172
2004.58060 9.54666 0.00169
2004.58333 9.54628 0.00175
2004.58606 9.54583 0.00176
2004.58880 9.54627 0.00173
2004.59153 9.54652 0.00170
2004.59426 9.54590 0.00170
2004.59699 9.54640 0.00174
2004.59972 9.54644 0.00168
2004.60246 9.54633 0.00169
2004.60519 9.54689 0.00175
2004.60792 9.54662 0.00174
2004.61065 9.54730 0.00171
2004.61339 9.54688 0.00173
2004.61612 9.54792 0.00178
2004.61885 9.54783 0.00175
2004.62158 9.54729 0.00176
2004.62432 9.54871 0.00172
2004.62705 9.54734 0.00171
2004.62978 9.54841 0.00172
2004.63251 9.54835 0.00170
2004.63524 9.54789 0.00174
2004.63798 9.54852 0.00171
2004.64071 9.54783 0.00169
2004.64344 9.54882 0.00170
2004.64617 9.54836 0.00171
2004.65164 9.54866 0.00173
2004.65437 9.54872 0.00166
2004.65710 9.54923 0.00166
2004.65983 9.54923 0.00168
2004.66257 9.54889 0.00170
2004.66530 9.54957 0.00170
2004.66803 9.54889 0.00171
2004.67076 9.54917 0.00168
2004.67350 9.54936 0.00172
2004.67623 9.54931 0.00169
2004.67896 9.54945 0.00173
2004.68169 9.55012 0.00171
2004.68442 9.55014 0.00170
2004.68989 9.55064 0.00171
2004.69262 9.55106 0.00174
2004.69535 9.55007 0.00172
2004.69809 9.55052 0.00171
2004.70082 9.55001 0.00172
2004.70355 9.55088 0.00181
2004.70901 9.55141 0.00177
2004.71175 9.55155 0.00174
2004.71448 9.55209 0.00173
2004.71721 9.55148 0.00179
2004.71994 9.55249 0.00177
2004.72268 9.55166 0.00176
2004.72541 9.55289 0.00170
2004.72814 9.55217 0.00175
2004.73087 9.55295 0.00172
2004.73360 9.55350 0.00171
2004.73634 9.55264 0.00176
2004.73907 9.55289 0.00177
2004.74180 9.55259 0.00168
2004.74453 9.55319 0.00173
2004.74727 9.55352 0.00177
2004.75000 9.55278 0.00174
2004.75273 9.55406 0.00176
2004.75546 9.55381 0.00171
2004.75819 9.55488 0.00169
2004.76093 9.55370 0.00172
2004.76366 9.55441 0.00172
2004.76639 9.55619 0.00170
2004.76912 9.55445 0.00173
2004.77186 9.55482 0.00174
2004.77459 9.55425 0.00171
2004.77732 9.55485 0.00177
2004.78005 9.55372 0.00178
2004.78278 9.55394 0.00176
2004.78552 9.55485 0.00182
2004.78825 9.55449 0.00178
2004.79098 9.55536 0.00170
2004.79371 9.55630 0.00168
2004.79645 9.55619 0.00168
2004.79918 9.55550 0.00171
2004.80191 9.55606 0.00173
2004.80464 9.55566 0.00174
2004.80738 9.55564 0.00176
2004.81011 9.55541 0.00178
2004.81284 9.55614 0.00173
2004.81557 9.55580 0.00173
2004.81830 9.55654 0.00169
2004.82104 9.55671 0.00172
2004.82377 9.55626 0.00172
2004.82650 9.55673 0.00168
2004.82923 9.55673 0.00167
2004.83197 9.55655 0.00182
2004.84836 9.55779 0.00169
2004.85109 9.55689 0.00166
2004.85382 9.55716 0.00164
2004.85656 9.55664 0.00172
2004.85929 9.55706 0.00168
2004.86202 9.55802 0.00167
2004.86475 9.55797 0.00169
2004.86748 9.55855 0.00170
2004.87022 9.55835 0.00167
2004.87295 9.55864 0.00162
2004.87568 9.55886 0.00165
2004.87841 9.55872 0.00166
2004.88115 9.55865 0.00165
2004.88388 9.55793 0.00165
2004.88661 9.55826 0.00170
2004.88934 9.55844 0.00165
2004.89207 9.55832 0.00162
2004.89481 9.55766 0.00166
2004.89754 9.55830 0.00165
2004.90027 9.55916 0.00166
2004.90300 9.55936 0.00168
2004.90574 9.55869 0.00165
2004.90847 9.55921 0.00165
2004.91120 9.55985 0.00160
2004.91393 9.56013 0.00160
2004.91666 9.56058 0.00161
2004.91940 9.55994 0.00163
2004.92213 9.56045 0.00164
2004.92486 9.56065 0.00165
2004.92759 9.55968 0.00162
2004.93033 9.55981 0.00163
2004.93306 9.56039 0.00162
2004.93579 9.55980 0.00167
2004.93852 9.55964 0.00162
2004.94125 9.56013 0.00165
2004.94399 9.56044 0.00165
2004.94672 9.55992 0.00168
2004.94945 9.56005 0.00166
2004.95218 9.56098 0.00164
2004.95492 9.56017 0.00164
2004.95765 9.56061 0.00163
2004.96038 9.56129 0.00164
2004.96311 9.56007 0.00162
2004.96585 9.55909 0.00162
2004.96858 9.55985 0.00161
2004.97131 9.56043 0.00164
2004.97404 9.56280 0.00163
2004.97677 9.56250 0.00161
2004.97951 9.56218 0.00164
2004.98224 9.56183 0.00165
2004.98497 9.56154 0.00163
2004.98770 9.56176 0.00163
2004.99044 9.56283 0.00163
2004.99317 9.56225 0.00166
2004.99590 9.56140 0.00164
2005.00137 9.56151 0.00164
2005.00411 9.56197 0.00167
2005.00685 9.56123 0.00164
2005.00959 9.56173 0.00161
2005.01233 9.56194 0.00166
2005.01507 9.56208 0.00164
2005.01781 9.56277 0.00163
2005.02055 9.56414 0.00160
2005.02329 9.56424 0.00162
2005.02603 9.56431 0.00159
2005.02877 9.56354 0.00160
2005.03150 9.56349 0.00162
2005.03424 9.56339 0.00160
2005.03698 9.56296 0.00160
2005.03972 9.56352 0.00163
2005.04246 9.56307 0.00161
2005.04520 9.56281 0.00164
2005.04794 9.56364 0.00163
2005.05068 9.56381 0.00165
2005.05342 9.56335 0.00166
2005.05616 9.56334 0.00165
2005.05890 9.56296 0.00160
2005.06164 9.56291 0.00165
2005.06438 9.56331 0.00162
2005.06712 9.56362 0.00163
2005.06986 9.56400 0.00172
2005.07260 9.56412 0.00173
2005.07534 9.56455 0.00170
2005.07808 9.56495 0.00168
2005.08082 9.56503 0.00167
2005.08356 9.56476 0.00171
2005.08630 9.56458 0.00171
2005.08904 9.56401 0.00170
2005.09178 9.56413 0.00166
2005.09452 9.56473 0.00161
2005.09726 9.56588 0.00163
2005.10000 9.56483 0.00164
2005.10274 9.56483 0.00161
2005.10548 9.56445 0.00165
2005.10822 9.56477 0.00161
2005.11096 9.56576 0.00162
2005.11370 9.56588 0.00162
2005.11644 9.56471 0.00165
2005.11918 9.56543 0.00165
2005.12192 9.56515 0.00162
2005.12466 9.56544 0.00164
2005.12740 9.56623 0.00163
2005.13014 9.56703 0.00169
2005.13287 9.56684 0.00164
2005.13561 9.56642 0.00174
2005.14109 9.56601 0.00178
2005.14383 9.56601 0.00167
2005.14657 9.56607 0.00171
2005.14931 9.56763 0.00164
2005.15205 9.56722 0.00164
2005.15479 9.56631 0.00165
2005.15753 9.56652 0.00162
2005.16027 9.56606 0.00161
2005.16301 9.56778 0.00170
2005.16575 9.56615 0.00163
2005.16849 9.56599 0.00165
2005.17123 9.56628 0.00165
2005.17397 9.56678 0.00166
2005.17671 9.56729 0.00170
2005.17945 9.56674 0.00167
2005.18219 9.56680 0.00167
2005.18493 9.56756 0.00171
2005.18767 9.56717 0.00173
2005.19041 9.56828 0.00181
2005.19315 9.56715 0.00174
2005.19589 9.56727 0.00175
2005.19863 9.56834 0.00171
2005.20137 9.56800 0.00171
2005.20411 9.56794 0.00167
2005.20685 9.56823 0.00167
2005.20959 9.56776 0.00166
2005.21233 9.56852 0.00165
2005.21507 9.56872 0.00167
2005.21781 9.56880 0.00167
2005.22055 9.56925 0.00170
2005.22329 9.56930 0.00175
2005.22603 9.56758 0.00167
2005.22877 9.56885 0.00170
2005.23150 9.56884 0.00168
2005.23424 9.56980 0.00166
2005.23698 9.56976 0.00173
2005.23972 9.56934 0.00167
2005.24246 9.57018 0.00171
2005.24520 9.56957 0.00179
2005.24794 9.56987 0.00179
2005.25068 9.57006 0.00169
2005.25342 9.56992 0.00178
2005.25616 9.57018 0.00176
2005.25890 9.57076 0.00166
2005.26164 9.57051 0.00174
2005.26438 9.57040 0.00180
2005.26712 9.57078 0.00179
2005.28630 9.57214 0.00184
2005.28904 9.57179 0.00175
2005.29178 9.57187 0.00174
2005.29452 9.57163 0.00174
2005.29726 9.57248 0.00183
2005.30274 9.57195 0.00185
2005.30548 9.57158 0.00176
2005.30822 9.57261 0.00182
2005.31644 9.57206 0.00181
2005.31918 9.57195 0.00176
2005.32192 9.57170 0.00179
2005.32466 9.57247 0.00179
2005.32740 9.57176 0.00172
2005.33014 9.57243 0.00175
2005.33287 9.57188 0.00179
2005.33561 9.57266 0.00185
2005.36027 9.57376 0.00182
2005.36301 9.57453 0.00184
2005.37397 9.57394 0.00179
2005.37671 9.57437 0.00179
2005.37945 9.57472 0.00175
2005.38219 9.57513 0.00179
2005.38493 9.57483 0.00181
2005.38767 9.57519 0.00181
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2005.39315 9.57556 0.00174
2005.39589 9.57529 0.00181
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2005.40137 9.57686 0.00182
2005.40411 9.57556 0.00181
2005.40685 9.57667 0.00179
2005.40959 9.57589 0.00172
2005.41233 9.57580 0.00178
2005.41507 9.57534 0.00174
2005.41781 9.57566 0.00172
2005.42055 9.57589 0.00175
2005.42329 9.57570 0.00183
2005.42603 9.57514 0.00180
2005.42877 9.57675 0.00173
2005.43150 9.57704 0.00172
2005.43424 9.57656 0.00177
2005.43698 9.57661 0.00180
2005.43972 9.57645 0.00174
2005.44246 9.57636 0.00172
2005.44520 9.57642 0.00169
2005.44794 9.57731 0.00181
2005.45342 9.57606 0.00180
2005.45616 9.57677 0.00176
2005.45890 9.57709 0.00172
2005.46164 9.57717 0.00176
2005.46438 9.57676 0.00176
2005.46712 9.57760 0.00172
2005.46986 9.57795 0.00170
2005.47260 9.57801 0.00172
2005.47534 9.57737 0.00177
2005.47808 9.57861 0.00177
2005.48082 9.57749 0.00175
2005.48356 9.57778 0.00178
2005.48630 9.57792 0.00183
2005.50000 9.57762 0.00181
2005.50274 9.57853 0.00174
2005.50548 9.57939 0.00178
2005.50822 9.57832 0.00173
2005.51096 9.57894 0.00178
2005.51370 9.57951 0.00176
2005.51644 9.57915 0.00178
2005.51918 9.57848 0.00170
2005.52192 9.57903 0.00176
2005.52466 9.57899 0.00172
2005.52740 9.57985 0.00172
2005.53014 9.57932 0.00177
2005.53287 9.58057 0.00177
2005.53561 9.58036 0.00176
2005.53835 9.58010 0.00171
2005.54109 9.57996 0.00171
2005.54383 9.58046 0.00172
2005.54657 9.58067 0.00173
2005.54931 9.58017 0.00171
2005.55205 9.58088 0.00172
2005.55479 9.58029 0.00173
2005.55753 9.58120 0.00174
2005.56027 9.58046 0.00175
2005.56301 9.58086 0.00175
2005.56575 9.58030 0.00173
2005.56849 9.58075 0.00177
2005.57123 9.58119 0.00174
2005.57397 9.58184 0.00175
2005.57671 9.58166 0.00175
2005.57945 9.58154 0.00174
2005.58219 9.58183 0.00174
2005.58493 9.58204 0.00178
2005.58767 9.58170 0.00175
2005.59041 9.58202 0.00175
2005.59315 9.58218 0.00184
2005.59589 9.58158 0.00170
2005.59863 9.58117 0.00172
2005.60137 9.58133 0.00172
2005.60411 9.58178 0.00176
2005.60685 9.58304 0.00178
2005.60959 9.58302 0.00177
2005.61233 9.58366 0.00174
2005.61507 9.58483 0.00184
2005.61781 9.58437 0.00179
2005.62055 9.58351 0.00173
2005.62329 9.58324 0.00170
2005.62603 9.58414 0.00170
2005.62877 9.58380 0.00170
2005.63150 9.58312 0.00169
2005.63424 9.58320 0.00167
2005.63698 9.58277 0.00179
2005.63972 9.58348 0.00174
2005.64246 9.58328 0.00180
2005.64520 9.58297 0.00171
2005.64794 9.58330 0.00173
2005.65068 9.58370 0.00172
2005.65342 9.58437 0.00177
2005.65616 9.58416 0.00184
2005.65890 9.58408 0.00179
2005.66164 9.58447 0.00176
2005.66438 9.58416 0.00174
2005.66712 9.58499 0.00177
2005.66986 9.58488 0.00182
2005.67260 9.58428 0.00178
2005.67534 9.58580 0.00178
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2009.82603 9.73396 0.00168
2009.82877 9.73319
  5 Comments

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Accepted Answer

Greg Heath
Greg Heath on 23 Jan 2014
Edited: Greg Heath on 23 Jan 2014
Your question is ill-defined:
You have not presented enough info.
1. Is the middle column the noisy signal?
2. Is the noise supposed to be
a. additive?
b. zero-mean?
c. constant variance?
d. Gaussian distributed?
If so, how was the variance measured? In particular, how many points were used to estimate each tabulated value?
  7 Comments
Chris Martin
Chris Martin on 24 Jan 2014
Edited: Chris Martin on 24 Jan 2014
Give me your mail id so that I can send you the paper

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