Harmonic signal parameters estimation Supervisor: I.G. Prokopenko - - PowerPoint PPT Presentation

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Harmonic signal parameters estimation Supervisor: I.G. Prokopenko - - PowerPoint PPT Presentation

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National Aviation University Aviation radio-electronic complex department Bulgarian Academy of Sciences Institute of Information and Communication Technologies Advanced computing for Innovation Y.D. Chyrka Harmonic signal parameters estimation

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National Aviation University

Aviation radio-electronic complex department

Bulgarian Academy of Sciences

Institute of Information and Communication Technologies Advanced computing for Innovation

Y.D. Chyrka

Harmonic signal parameters estimation

Supervisor: I.G. Prokopenko

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Background

2

2005 2007 2009 2011 2013 Student in the NAU Study at the IMT Working as an engineer Working as a scientist Postgraduate student

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Outline

3

Publications:

4 International conferences (SMSDP-2010, SPS-2011, Automatics-2011, IRS-2012) (include 1 in Scopus) 1 International article (JET) (include 1 in Scopus) 5 Ukrainian conferences 3 Ukrainian articles 2 International conferences (SPS-2013, IRS-2013) (include 2 in Scopus) 1 International article (TKEA) 1 Ukrainian conference 3 International conferences (SPS-2009, SPS-2013, IRS-2013) (include 2 in Scopus) 2 Ukrainian conferences 1 Ukrainian article 1 Ukrainian conference 1 Ukrainian patent 2 Ukrainian conferences 1 Ukrainian patent

Total:

6 Scopus publications 9 International conferences 2 International articles 10 Ukrainian conferences 4 Ukrainian articles 2 Ukrainian patents

Harmonic signals parameters estimation Stochastic approach NonStochastic approach Synchronization systems Clusterization by

  • rdered statistics

EEG processing Local projects:

  • Radar simulation complex for laboratory works
  • Simulation modeling program for a production line

Signal Detection

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Scopus publications

4

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GOAL: to improve efficiency of parameters estimation on a limited observation interval.

d

  • b

/ 2 f T <

The additive model of counts sample:

i i i i

s u ξ η + + = ,

N i , 1 =

  • 1. The digitized harmonic signal:

( ) [ ]

1

1 cos ϕ γ ρ + − = i si ,

τ

ω γ f

d /

=

– the normalized frequency

  • 2. The white Gaussian noise:

i

η

  • 3. The correlated interference:

i

ξ , . 1 95 . ÷ =

c

r There is no any a priori information about signal, noise and interference parameters.

Goal and a signal model

5 Harmonic signal parameters estimation

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The recurrent form of a sinewave:

2 1 − − −

α =

i i i

s s s ,

N , i 3 =

, ) cos( 2 γ = α 1) Without interference The quadratic equation: 2 2

2

= − α − α B Step1 – (

) ( )

[ ]

( )

     + − + =

∑ ∑

− = − + − = − + − 2 1 1 1 2 1 2 2 1 1 1

2 / 2 ..., ,

N i i i i i N i i i i N

x x x x x x x x x B Step2 – 2

2 ) , ( 2 , 1

+ ± = α

− +

B B Step3 – normed frequency estimation:

( )

2 / arccos

∗ ∗

α = γ

( )

γ = α + cos 2

1

, 2 / π < γ < 2) With interference The quadratic equation:

2

= + α + α C B A Step 1:

( ) ( )( )

[ ]

∑

− = − − − − − − −

− + − − − − =

1 3 3 2 1 1 2 2 1 2 N i i i i i i i i i

x x x x x x x x A

( ) ( )

[ ]

∑

− = − − − − −

− + − − − =

1 3 2 3 2 1 2 1 2

2

N i i i i i i i

x x x x x x B

( )( ) ( )

[ ]

∑

− = − − − − − − − −

− + − − − + − − =

1 3 2 3 2 1 3 2 1 1 2

2

N i i i i i i i i i i i

x x x x x x x x x x C

Step 2:

( )

A AC B B 2 / 4

2 −

+ − = α Step 3:

( )

2 / arccos

∗ ∗

α = γ

,

γ cos 2 α1 =

, π γ < <

Frequency estimation

6 Harmonic signal parameters estimation

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Frequency estimation

7 Harmonic signal parameters estimation

Simulation parameters: N = 32 , dB 10 =

η S /P

P AR-est.:

( )

∑ ∑

− = − − = − − ∗

+ = α

1 1 2 1 1 2 1 2 AR N i i N i i i i

x / x x x

The normed shift of estimations The normed st. dev of estimations.

“k” – Our method; “а” – AR.

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Amplitude and initial phase estimation

8 Harmonic signal parameters estimation

1) Without interference

( )

       ϕ ρ = ϕ ρ = − = ϕ − + = ρ ⇒        γ = γ + γ γ γ = γ γ + γ

∑ ∑ ∑ ∑ ∑ ∑

− = − = − = − = − = − =

sin , cos arctan ) cos( ) ( cos ) sin( ) cos( ) sin( ) cos( ) sin( ) ( sin

* 2 2 * 1 1 2 1 1 1 1 2 y x x y y x N i i N i y N i x N i i N i y N i x

A A phase initial A A amplitude A A i x i A i i A i x i i A i A

2) With interference

( )

       = = = − = − + = ⇒          = ⋅ + + = + + = + +

∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑

− = − = − = − = − = − = − = − = − = − = − =

ξ ϕ ρ ϕ ρ ϕ ρ γ γ γ γ γ γ γ γ γ γ γ γ

z y x x y y x N i i z N i y N i x N i i N i z N i y N i x N i i N i z N i y N i x

A A A phase initial A A amplitude A A x N A i A i A i x i A i A i i A i x i A i i A i A , sin , cos arctan . ) cos( ) sin( ; ) cos( ) cos( ) ( cos ) sin( ) cos( ; ) sin( ) sin( ) cos( ) sin( ) ( sin

* 2 2 * 1 1 1 1 1 1 2 1 1 1 1 1 2

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Likelihood function analysis

9 Harmonic signal parameters estimation

∑

− =

ξ − ϕ + − = ξ ϕ Λ

1 2 1

  • )

) γ sin( ρ ( ) ..., , | , γ, ρ, (

N i i N

i x x x

{ }

) ..., , | ξ , γ, ρ, ( min arg ξ , , γ , ρ

1

  • ξ

, γ, ρ, N

x x ϕ Λ = ϕ

ϕ ∗ ∗ ∗ ∗

Frequency interval between local minima: N / 2π ≈ γ ∆

rad rad

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Optimization algorithm

10 Harmonic signal parameters estimation

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Optimization algorithm efficiency

11 Harmonic signal parameters estimation

Frequency, [rad] %

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Estimations censoring

12 Harmonic signal parameters estimation

We propose and investigate a method of reducing the measuring system sensitivity to the appearance of gross errors by an a posteriori censoring of results of frequency measurements.

     ∆ > ∆ ∆ ≤ ∆ = ∆ s estimation unreliable f f С s estimation reliable f f f с , , , , ) (

cr * fl cr * *

, We consider that a more reliable result is the

  • ne at which the signal power

S

P significantly

exceeds the noise power

2

σ . In this case the

following decision rule for erroneous estimate is useful.

( )

d P

S

< σ∗

2 * /

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Guaranteed estimation of frequency

13 Harmonic signal parameters estimation

Goal: to get guaranteed estimations of parameters as corresponding limited sets ] , [ ], , [ ], , [ ϕ ϕ ϕ ω ω ω ∈ ∈ ∈ A A A . Maximum amplitude of an interferences is limited and a priori known. Solution of N-2 compatible inequalities system gives us bounds of frequency estimations

ε 4 y c y 2 y

2 n 1 n n

≤ + +

− −

,

1 N ,..., 2 n − =

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Guaranteed estimation of amplitude and phase

14 Harmonic signal parameters estimation

Let us to define quadrangle made by crossing of strips and Also we will define as minimal rectangle for each . ) (Ω

n

P

) (Ω Π n ) (

1 Ω

Π −

n

} cos ~ sin ~ : ~ { ) (

2 1

ε ≤ − Ω + Ω = Ω Π

n n

y n A n A A  ϕ = cos

1

A A ϕ = sin

2

A A

T

A A A ] ~ , ~ [ ~

2 1

= 

i i i i

P A P

4 ,..., 1 4 ,..., 1

max min

= =

≤ ≤

i i i i

ϕ ≤ ϕ ≤ ϕ

= = 4 ,..., 1 4 ,..., 1

max min

1 1 , − = +

∈ ∈

N n n n

P P A

1 , + n n

P

) (Ω

n

P

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Simulation results

15 Harmonic signal parameters estimation

, ) ~ sin(

n n

n A y ξ + ϕ + ω = , 5 = A , 5 , ~ = ω , 1 , = ξn , 5 , = ϕ 32 = N

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The main publications list

16 Harmonic signal parameters estimation

  • 1. Prokopenko I.G. Radar signal parameters estimation in MTI tasks / I. G. Prokopenko, I. P.

Omelchuk, Y. D. Chyrka // SPS – 2011 : int. sci. conf., 8-10 June 2011. : mat. of conf. – J., 2011.

  • 2. Житецкий Л.С. Гарантированное оценивание параметров зашумленного гармонического сиг-

нала по короткой выборке / Л.С. Житецкий, Ю.Д. Чирка // Автоматика – 2011 : міжнар. наук. конф., квіт. 2011 р.. : матеріали конф. – Л., 2011.

  • 3. Prokopenko I.G. Robust frequency estimation / I. G. Prokopenko, I. P. Omelchuk, Y. D.

Chyrka // IRS – 2012 : int. sci. conf., 23-25 May 2012. : mat. of conf. – W., 2012. – 319-321 pp.

  • 4. Chyrka, Y. D. Radar signal parameters estimation in MTD tasks [ Igor Prokopenko, Igor

Omelchuk, Yuriy Chyrka] // International Journal of Electronics and Telecomunications. –

  • 2012. – № 2. – 159-164 pp.
  • 5. Прокопенко І. Г. Оцінка параметрів гармонічного сигналу на обмеженому інтервалі спостере-

ження / І. Г. Прокопенко, І. П. Омельчук, Ю. Д. Чирка та ін. // Електроніка та системи управ- ління. – 2010. – № 1 (23). – С. 31–38.

  • 6. Прокопенко І. Г. Цензурування оцінок частоти гармонічного сигналу / І. Г. Прокопенко, І. П.

Омельчук, Ю. Д. Чирка // Електроніка та системи управління. – 2010. – № 4 (26). – С. 12–15.

  • 7. Омельчук, І. П., Чирка Ю.Д. Features of the instantaneous frequency estimation algorithm with pre-

filtering // Наукоємні технології. – 2013. – № 2. – С. 210-214.

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Proposed Fast Frequency Lock Loop

17 Synchronization systems

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Simulation results – Adaptive filtering

18 Synchronization systems

Transient processes of the fast FLL with sinusoidal reference signal.

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Simulation results – Comparison

19 Synchronization systems

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20 Synchronization systems

Publications list

  • 1. Prokopenko I. Enhanced technique of frequency aquisition [Igor Prokopenko, Igor

Omelchuk, Yuriy Chyrka, Vitalii Vovk] // Signal Processing Symposium (SPS-2013): International Conference Proceedings, Jachranka, Poland, June 5-7, 2013 / Chair K.

  • Kulpa. – Jachranka, 2013.
  • 2. Prokopenko I. Fast Frequency-Lock Loop [Igor Prokopenko, Igor Omelchuk, Yuriy

Chyrka, Vitalii Vovk] // International Radar Symposium (IRS-2013): International Conference Proceedings, Dresden, Germany, June 19-21, 2013 / Chair H. Rohling. – Dresden, 2013.

  • 3. Prokopenko I. Fast frequency tracking [Igor Prokopenko, Igor Omelchuk, Yuriy Chyrka,

Vitalii Vovk] // TKEA. – 2013. 1-8 pp.

  • 4. Чирка, Ю.Д. Швидкі системи підлаштування частоти [Ю. Д. Чирка, І.Г. Прокопенко,

І. П. Омельчук] // ХІ МНТК «Авіа-2013», Київ, 21-23 травня 2013 р. : Мат-ли. – Київ: НАУ-Друк, 2013. – Київ: НАУ, 2013.

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Slow moving targets detection algorithm

21 Signal detection

Goal: to improve effectiveness of detection of signal with low Doppler frequency. Idea: according to empiric Bayesian approach, unknown parameters in the optimal detection algorithm are replaced by their grounded estimations:

( ) ( ) ( ) ( )

c y N i yi y i x N i xi x i

C s y s x > σ ⋅ ξ − + σ ⋅ ξ −

∗ = ∗ ∗ ∗ = ∗ ∗

∑ ∑

2 1 2 1

Thus, an interference is considered as constant i ∀ ξ = ξ ξ = ξ , ,

y yi x xi

, that allows to simplify signal processing procedures, dividing them into independent by quadrature. The harmonic signal estimations are calculated on the basis of its parameters estimations

( )

∗ ∗ ∗

γ ϕ ρ = , ,

1 * i

s s

. The estimation of noise variances is determined as

( )

( )

( )

∑

∗ ∗ − ∗

ξ − − − = σ

N

s x N

1 2 i i i 1 2

1

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Simulation results

22 Signal detection

Research parameters: Sample size N = 16

dB P P 15 /

s

=

η

dB P P 10 / =

η ξ

1- Adaptive, r=1 2- Adaptive, r=0,95 3- Single canceller, r=1 4- Single canceller, r=0,95

2 1 3 4

D

γ , rad

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Track detection

23 Signal detection

Goal: improve effectiveness of track detection and track’s parameters estimation algorithms for grayscale two-dimentional images. Stage 1: signal samples selection Stage 2: trajectory parameters estimation by ordinary least squares

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Track detection

24 Signal detection

Stage 3: signal detection Comparison of effectiveness:

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25 Signal detection

Publications list

  • 1. Prokopenko I. Detection of Markov signals in the mixture with Markov interferences [Igor Pro-

kopenko, Igor Omelchuk, Filix Yanovskyi, Yuriy Chyrka] // Signal Processing Symposium (SPS- 2009): International Conference Proсeedings, Jachranka, Poland, May 26-28, 2009 / Chair K. Kulpa. – Jachranka, 2009. 2. Prokopenko I. Two-stage Rapid Target s Detection Algorithm [Igor Prokopenko, Igor Omelchuk, Yuriy Chyrka, Vitalii Vovk] // Signal Processing Symposiun (SPS-2013): International Conference Proсeedings, Jachranka, Poland, June 5-7, 2013 / Chair K. Kulpa. – Jachranka, 2013.

  • 3. Prokopenko I. Tracking and Detection of Rapid Moving Targets [Igor Prokopenko, Igor

Omelchuk, Yuriy Chyrka, Vitalii Vovk] // International Radar Symposiun (IRS-2013): International Conference Proсeedings, Dresden, Germany, June 19-21, 2013 / Chair H. Rohling. – Dresden, 2013.

  • 4. Прокопенко І. Г. Квазікогерентна міжперіодна обробка імпульсних радіолокаційних сигналів /

І. Г. Прокопенко, І. П. Омельчук, Ю. Д. Чирка // Наукоємні технології. – 2009. – № 1. – C. 91– 97.

  • 5. Антонюк В. М. Моделювання алгоритмів виявлення рухомих об’єктів / В. М. Антонюк, Ю. Д.

Чирка // Політ-2008 : міжнар. наук. конф., 10–11 квіт. 2008 р. : тези доп. – К. : НАУ, 2008. – С. 177.

  • 6. Прокопенко І.Г., Чирка Ю.Д. Дослідження адаптивних алгоритмів виявлення гармонічного

сигналу: Тези доповіді // Матеріали МНТК «Політ-2011», 9-11 квітня 2011 р., Київ. – Київ: НАУ, 2011.

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Goal

26 Clusterization

Goal: to improve clusterization algorithm for separation of two or multiple combined samples when one of them is relatively small. Some examples:

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Signal model and the algorithm

27 Clusterization

We assume that we observe the single-dimension compound process as determined limited sample of independent counts N

( )

i мi i вi i i

s s x η + ς + ς − = 1

,

N i ... , 2 , 1 =

. In this case we can use adequate statistical model of a signal-interference situation which has bimodal probability density function of counts amplitude

( ) ( ) ( ) ( )

N i x f P x f P x f

м м i м МВБ в в i в МВБ i

, 1 , , | , | 1 , | = Θ + Θ − = Θ θ θ θ

We propose the new empirically obtained algorithm that is more precise in comparison to known algorithms when probability of a smaller sample

МВБ

P

does not exceed 0.1

( )

( ) ( )

( )

( ) ( ) ( )

( ) 

         σ − =

n n n

M r M r n n r n r x

  • pt

y y y m V

, , , ,

max arg

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Simulation results

28 Clusterization

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29 Clusterization

Publication list

  • 1. Прокопенко, І.Г. Підвищення стійкості розшарування малих вибірок [І.Г.Прокопенко, д.т.н.,

проф., Ю.Д.Чирка., асп., І.П.Омельчук, к.т.н., НАУ, Київ] : Тези доповіді // Всеукр. НМК «Проблеми розвитку глобальної системи зв’язку, навігації, спостереження та організації повітряного руху CNS/ATM», Київ, 29 листопада 2012: Тези доповідей. – Київ: НАУ-Друк,

  • 2012. – С.89.
  • 2. Патент № 2 345 678, Україна, МПК G06F7/06. Пристрій для виділення сигналу передостанньо-

го рангу. Автори І.П.Омельчук, І.Г.Прокопенко. Заявка подана 15.10.2008. Отримано позитив- не рішення 20.01.2009.

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Goal

30 EEG Processing

Goal: to improve diagnostics of brain deseases by tracking of brain rhythms and detection signal phenomena by electroencefalography signal processing. Some examples of EEG:

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EEG Processing

31 EEG Processing

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Signal splitting

32 EEG Processing

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Spike detection

33 EEG Processing

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Spike detection

34 EEG Processing

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35 EEG Processing

Publication list

  • 1. Омельчук, И.П., Чирка, Ю.Д., Каплун, Ю.О. Частотно-временной анализ электроэнцефало-

грамм / Всеукр. НМК «Проблеми розвитку глобальної системи зв’язку, навігації, спостережен- ня та організації повітряного руху CNS/ATM», Київ, 21-22 листопада 2011: Тези доповідей. – Київ: НАУ-Друк, 2011. – С.80.

  • 2. Чирка, Ю.Д., Якушевський, В.В. Стійке оцінювання статистичних характеристик спайків елек-

троенцефалограм [Наукові керівники – Омельчук І.П., к.т.н., Прокопенко І.Г., д.т.н., проф.] : Тези доповіді / Всеукр. НПК молодих учених і студентів «Проблеми навігації та управління рухом», Київ, 29 листопада 2012: Тези доповідей. – Київ: НАУ-Друк, 2012. – С.73.

  • 3. Патент № 84833, Україна, МПК G066F7/06. Спосіб виявлення спайків енцефалограми. Автори

І.П.Омельчук, І.Г.Прокопенко, Ю.Д.Чирка. Заявка подана 23-11-2012. Дата публікації 11-11-

  • 2013. Бюлетень №21)
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Goal and simulation algorithm

36 RADAR model

Goal: to make simple radar simulation complex for laboratory works which includes generation of many targets, non-stationary noise and chaotic impulse interference; calculation of false alarm and detection probabilities, some range and azimuth processing, visual indication of information.

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Simulation examples

37 RADAR model

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Simulation examples

38 RADAR model

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Goal

39 Simulation modeling

Goal: to make a program for simulation modeling of a manufacturing line that allows to set multiple different simultaneous manufacturing paths, change time distribution parameters.

FO1 FO2 FO3 τі,1 τі,2 τі,3 Resources Product Time diagram of modeling of single-component system

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Examples of schemes

40 Simulation modeling

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Current researches and plans for future work

41 Simulation modeling

Current researches: increasing robustness of estimation procedures to presence

  • f an impulse interference and optimization of signal separation and

demodulation. Plans for future work: complex radar signal processing and detection, adaptation and optimization radar structure and parameters.

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42