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above: unemployment rate / nyt 2.6.09 "economy shed 598k jobs in january"

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. ..below.. .

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figures from:

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as. rybakov / wavelet decomposition and fractal analysis for joint measurements of laser signal delay and amplitude

avtomatika i vychislitel'naya tekhnika [automatic control & computer sciences] 2001

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a regression algorithm is considered for balancing out the effects of echo signal amplitude

spread on the error in range measurement to artificial satellites

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noise excursions can be filtered out in

nonstationary sequences of lidar measurements

by means of a procedure

for multiple-scale

wavelet

decomposition

the stationarity indicator

for the multiple-scale components is

provided by the fractal

dimensions

.

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above: reflected-signal amplitude distribution @photocell output in locating a reflector on a satellite

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multiscale processes are associated with fat-tailed distributions

eg the contributions of processes up and down the

fractal scaling hierarchy

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above: multiscale decomposition of a sequence of delays in the daubechies-4 wavelet basis

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above: decomposition in the haar wavelet basis

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the small scale [high frequency] are very similar no matter what the wavelet basis used

might as well use the simpler haar "lens"

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of a chaotic scaling regime

in the data

it is natural to ask if the dynamics are

deterministically chaotic

or not

however if all we know

is the time series

then we will not be able to distinguish further

between noisy chaos and

noise induced chaos

.

.

. . .

. ..since we're talking satellites.. .