Median Filtering Algorithms for Multichannel Detectors and their

influence on Thunderstorm Peaks in Cosmic Ray Data

Armen HovhannisyanArmen HovhannisyanAlikhanyan Physics Institute, ArmeniaAlikhanyan Physics Institute, Armenia

ASEC MonitorsASEC Monitors

Aragats Neutron Monitor Data

Different Kinds of Errors1 Spike

2 Slow Drift

3 Abrupt change of mean

Algorithm 1 – Moving Median Filter(MMF)• Moving window width – L; L=2I+1, where I is number of detections to the left and

to the right of the filtering (smoothing) measurement;• Maximal possible value – Pmax• Minimal possible value – Pmin• Maximal value of window width – Lmax

Algorithm Description1 Select time series from database with N elements;2 Start smoothing from the (I+1)th measurement of time time series – Vi , i=I+1;3 Calculate the median value Mi,L;4 Validate the median value: Mi,L ɛ (Pmin;Pmax) if not, enlarge L by 2, and after

checking L<=Lmax go to 2;5 ELSE go to STOP and report operator about data failure;6 Substitute selected measurment by median value Mi,L →Vi;7 Move to next i+1 element of time series;9 If i+1<=N THEN GO TO 210 ELSE STOP, ask operator where to write smoothed time series.

Algorithm 2(3) – Median filter for multichannel measurements

• Let's suppose that we have M channels of one monitor, and several of them have been down for some period.

• , where ni are mean values of each channel, Sum is the sum of means of all channels (1)

• ,where Med is median of all working channels at same minute, (2)

• Fi are coefficients of each channel. These coefficients are the relation of total median value of all channels for same minute and the i-th channel mean.

• For each minute of corrupted period of corrupted channel we calculate Med value(which is median of working channels), and then calculate value for that minute using equation (2).

SumMnF i

i*

MedFV ii *

Combination of 2 Algorithms• We have some date to start the smoothing, for that beginning

we calculate and coefficients and write them to a file• Then we take 1 day data and start smoothing all channels

with constant and not big I.e. (10 minute) window.• If some channels have been not corrected by 1 algorithm,

second one turns on, it reads the means and algorithms from files we have created

• After correcting with 2 algorithm , if everithing is ok, we calculate again means and coefficients for corrected data and write them to a the same file.

• If second algorithm didn't corrected the data (which means that all or nearly all channels have been corrupted) send an e-mail to operator.

• Take next Period and do 2-5 again.

in iF

Atmospheric Pressure, Nor-Amberd Station, Period – 6 Months

Atmospheric Pressure - Corrected

Aragats Neutron Monitor, MAY 2008 – after filtering

Correction of the AMMM time series, >5 Gev Muons

Correction of the ARNM time series

Simulation of Data For NANM

Simulation of Spoiled Timeserie

The Same Timeserie After Correction

CR Intensity Modulation during 23th solar cycle, Measured by NANM

Comparison of Corrected Data of NANM with Alma-Ata Data

Day-to-day changes of the channel coefficients of Aragats

Neutron Monitor

Neutron Monitors used in the “coherence” test

Neutron MonitorNeutron Monitor Altitude,mAltitude,m Rigidity,GVRigidity,GV TypeType

Alma AtaAlma Ata 33403340 6.696.69 18NM6418NM64

RomeRome 6060 6.326.32 17NM6417NM64

AragatsAragats 32003200 7.147.14 18NM6418NM64

Nor-AmberdNor-Amberd 20002000 7.147.14 18NM6418NM64

MoscowMoscow 200200 2.462.46 24NM6424NM64

OuluOulu 00 0.810.81 9NM649NM64

AthensAthens 4040 8.728.72 3NM643NM64

Pressure Corrected Data from NMDB

Pressure Corrected and Median Smoothed Data from NMDB

Equalizing coefficients of the NMDB facilities

Enhancements associated with thunderstorms

21 May 2009, AMMM

25000

26000

2700028000

29000

30000

3100032000

33000

34000

16:19 16:36 16:52 17:09 17:26 17:43 18:00UT

Inte

nsity

[par

ticle

s/m

in m

sq]

Types of Algorithms

Algorithm1 – Spike RemovalAlgorithm1 – Spike Removal

Algorithm2 – Correction of EACH Algorithm2 – Correction of EACH channel by coefficientschannel by coefficients

Algorithm3 – Getting WEGHTED Algorithm3 – Getting WEGHTED TimeSerie using data of all channels TimeSerie using data of all channels and coefficientsand coefficients

Filtering with Algorithm 1 and 2Window=60 minutes

Filtering with Algorithm 1 and 2Window=20 minutes

Filtering with Algorithm 3

Filtering with Algorithm 1 and 2Window=60 minutes

Filtering with Algorithm 3

Conclusions• We use this method for online and offline filtering of ASEC

data. The program is online filtering the data of Nor-Amberd and Aragats Neutron Monitors, and soon it’ll be implemented it to other monitors. Also the corrected data is being transferred to NMDB.

• Changing Parameters of different algorithms it is possible not to oversmooth enhancements associated with lightning events.

• Besides the filtering, this programme also provides an automatic alerting system in case of malfunctioning of some of 280 detecting channels.