Signal Detection Basics - CFAR
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1 Signal Detection Basics - CFAR Types of noise clutter and signals targets Signal separation by comparison threshold detection Signal Statistics - Parameter estimation Threshold determination based on the required P fa CFAR detectors design Detection Performance Vassilis Anastassopoulos, Physics Department
2 Noise clutter and Signal Target 2/35
3 Detection by comparison with a threshold p Clutter pdf p Signal pdf p P d P d Deferent Detectors P fa SCR Mean m of Threshold T=am Receiver Operating Characteristics 3/35
4 Signal in background Noise Targets in Sea Clutter Targets in Search Radar Target Declaration Signal Separation Threshold detection The Statistics p c of the clutter and the Target p t Fundamentals of Radar Signal Theory Mark Richards McGraw-Hill 25 Chapters 6 & 7 An Estimator z of the statistics of the signal mean z=m An Assumption of the behavior statistics of the Target Determination of Threshold T=az for specific P fa Performance assessment PDSCR 4/35 Clutter Statistics Rayleigh Weibull K-pdf Target Statistics Swerling models CFAR Detectors CA case OW case OS case
5 Radar Detection as Hypothesis Testing Hypothesis H : The measurement is a result of interference only null Hypothesis Hypothesis H : The measurement is a combined result of interference and echoes from Targets The signals are described statistically by means of their pdfs and thus we have to employ Statistical Decision Theory. Actually we need the pdf of the Noise p c and the pdf of the Target p t : Clutter Target w Clutter + Target w+ Probability of Detection P d : Probability to correctly declare a target Probability of False Alarm P fa : Probability to declare a target when it is not present Probability of Miss P m : Probability to miss a target while it is present P m =-P d p Clutter pdf p Signal pdf p P d p Clutter pdf p c Signal+Clutter pdf p w+c P fa Mean m of Threshold T=am Mean m of Threshold T=am 5/35
6 Signals and Statistics Signal+noise Spectrum and histogram 6/35
7 Images and Statistics /
8 Decision based on the Likelihood Ratio p Clutter pdf p c Signal+Clutter pdf p w+c T P p H d fa Mean m of Threshold T=am T P p H d d Pattern Recognition The Neyman-Pearson decision rule: Choose the threshold T so that P d is maimized, subject to P fa a It is an optimization problem the solution of which leads to the decision rule p p H H H H Estimation of the mean 8/35 Case of p H Gaussian P fa T T T p erf p H H P d fa d erf T P fa
9 9/35 Clutter and Target Statistics a a c c c a f ep,c,a > a c F ep Weibull pdf For a=2 Rayleigh pdf 2 / ep 2 / 2 2 / 2 / s s s n s p n n χ 2 distribution n s,,, ep b s s s s b p b b Generalized Gamma 2 4 / c m c dy y p y p p m m m The K-distribution is a compound statistical model i.e. The speckle is Rayleigh distributed with mean y, which is Gamma distributed b=2. K m is the modified bessel function of the third kind and order m, while c is the scale parameter.
10 High Resolution Clutter /35
11 GC-pdf modeling /35
12 p Clutter pdf p c Estimation of the mean Signal+Clutter pdf p w+c T P p H d fa Mean estimation using the averager: m =[+2+ +n]/n is it an optimal estimator? n= Mean m of Threshold T=am 4 2 Uniform distribution with mean /
13 p Clutter pdf p c Estimation of the mean Signal+Clutter pdf p w+c T P p H d fa Mean estimation using the averager: m =[+2+ +n]/n Mean m of Threshold T=am n=5 Optimal estimator: For the same number of variables the smallest variance in the estimation of the required parameter /35
14 Estimation of the mean and P fa evaluation [ az] p H T az P P d fa p Clutter pdf p c Signal+Clutter pdf p w+c Since the threshold T=am =az is not fied, but its is actually a random variable which follows a new pdf?, We have to determine steps. A way to find an optimal estimator. 2. To find the pdf of the estimate 3. To modify the epression for P fa and P d. P fa Mean m of P[ Threshold T=am az] T az p P[ H d a] p z d 4/35
15 5/35 Case of Weibull - statistics a a c c c a f ep a c F ep 2 ] [ a r c E r r Fits well to sea statistics. Mathematically it is well described. With statistical fit tests or using moment matching techniques we can certify or not the validity of the distribution. However, estimation of the parameters at each point of the signal space we need an optimal estimator.
16 Parameter estimation with statistical fit-tests Histogram with blue eperimental pdf for a squared Sea region on a VV-SAR image with scale parameter c=492, and και shape parameter a=2,6. Parameter estimation for this region many points was carried out by the MATLAB command Wblfit and confidence interval 99%. 6/35
17 Maimum Likelihood Estimation 7/35
18 Maimum Likelihood Estimation 8/35
19 Maimum Likelihood Estimation 9/35
20 Maimum Likelihood Estimation 2/35
21 2/35
22 22/35
23 23/35
24 24/35
25 25/35 ML-Parameter Estimation Weibull pdf /3 2 / 2 / ep 2 c c c f
26 ML-Parameter Estimation Weibull pdf 2/3 26/35
27 ML-Parameter Estimation Weibull pdf 3/3 27/35
28 28/35 The pdf of the estimator statistic /3 2 / 2 / ep 2 c c c f Weibull pdf
29 The pdf of the estimator statistic 2/3 29/35
30 The pdf of the estimator statistic 3/3 3/35
31 OW-CFAR Performance 3/35
32 32/35 Basic steps for CFAR detection Knowledge of the statistics of the clutter. Optimal statistic for mean estimation. Pdf of this statistic. Evaluation of P fa. Threshold evaluation. P d evaluation for various SCRs Performance assessment - ROC ] [ ] [ d p a P d H p az P P z az T fa N c fa N T P 2 / ] [ ] [ d p a P d H p az P P z az T d Assessment using Simulation
33 CFAR performance 33/35
34 Conclusions /2 For robust detectors we employ Order Statistic Estimators. Performance Assessment contains performance on clutter edges, and target masking. Clutter maps constitute a-priori knowledge for the clutter statistics of a regions. Accelerate detection. 34/35
35 Conclusions 2/2 We eamined CFAR detection of point targets in specific clutter statistics and described performance assessment. Many other detection topics remain: - Distributed targets - Coherent detection - Detection using multi-channel signals What is detection and its quality; How this can be used in decision fusion; 35/35
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