SMOOTHING INTERVAL ESTIMATION USING

CORRELATION FUNCTION TYPE FOR A RANDOM

PROCESS IN REAL TIME

Dmitry Bychkov, Mark Polyak

Saint-Petersburg State University of Aerospace Instrumentation

Saint-Petersburg, 2009

Telemetry information

)(),(

max TnTHnZ - measure of process oscillativity

where:

n( H,T ) – number of crossovers of the H level in time interval T;

nmax( T ) – number of extremums in time interval T;

Z-coefficient

Graph of Z- coefficient for two types (sampling frequency 100Hz).

Graph of average values of Z- coefficient (sampling frequency 100Hz).

RESULTS

Graph of n as a function of Fc

dFTn

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

Fc, Hz

n, p

ts

=0.1

=5.0

Fd = 50 Hz

Fd = 100 Hz

1 6 8 10 11 12 13 14 15 16 16 17 18 18 19 20 20 21 21 22 22 23 23 24 24 25 … 36 362 3 4 5 6 7 7 8 8 9 9 10 10 11 11 11 12 12 12 13 13 13 14 14 14 15 … 23 233 2 3 4 4 5 5 6 6 6 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 … 44 444 2 2 3 3 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 7 8 8 8 8 8 … 34 34

5 1 2 2 3 3 3 3 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 7 7 7 … 28 28

6 1 1 2 2 2 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 … 24 247 1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 5 5 … 34 34

8 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 … 30 30

9 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 … 27 27

10 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 … 24 24

11 0 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 … 22 31

12 0 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 … 28 28

13 0 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 … 26 26

14 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 … 24 25

15 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 … 23 23

16 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 … 22 28

17 0 0 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 … 26 26

18 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 … 25 25

19 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 … 23 23

20 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 … 22 27

21 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 … 26 26

22 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 … 25 25

23 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 … 24 24

24 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 … 23 23

25 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 … 22 260,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 2,1 2,2 2,3 2,4 2,5 … 4,9 5

Static table

Fc

α

(Example for the first type of random process with γ = 50 Hz)

Practical example

Thank you for your attention!