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Estimation of detection threshold in multiple ship target situations with HF ground wave radar
Journal of Systems Engineering and Electronics Vol. 18, No. 4, 2007, pp.739–744
Estimation of detection threshold in multiple ship target situations with HF ground wave radar Li Hongbo, Shen Yiying & Liu Yongtan Research Institute of Electronics and Information, Harbin Inst. of Technology, Harbin 150001, P. R. China (Received November 9, 2006)
Abstract: A credible method of calculating the detection threshold is presented for the multiple target situations, which appear frequently in the lower Doppler velocity region during the surveillance of sea with HF ground wave radar. This method defines a whole-peak-outlier elimination (WPOE) criterion, which is based on in-peak-samples correlation of each target echo spectra, to trim off the target signals and abnormal disturbances with great amplitude from the complex spectra. Therefore, cleaned background noise samples are obtained to improve the accuracy and reliability of noise level estimation. When the background noise is nonhomogeneous, the detection samples are limited and often occupied heavily with outliers. In this case, the problem that the detection threshold is overvalued can be solved. In applications on experimental data, it is verified that this method can reduce the miss alarm rate of signal detection effectively in multiple target situations as well as make the adaptability of the detector better.
Keywords: HF ground wave radar, multiple target detection, outlier elimination, threshold estimation.
1. Introduction The signal detection with HF radar is commonly done in the spectral domain. The geometry of real target amplitude in two-dimensional range-velocity spectra is peak-like and it may be an essential discrimination for the detector to identify the target from external electromagnetic environment noise and seasurface echoes[1] . A kind of constant false alarm rate (CFAR) detection method based on the outlier elimination was proposed and studied in Refs.[1-3]. In its theoretical framework, not only the target signals but also the impulsive disturbances with great amplitude are called outliers, whose value lies abnormally far from others[4]. By eliminating the outliers entirely in a detection section, the cleaned background noise samples are obtained for the accurate estimation of the background noise level so as to calculate the detection threshold credibly. The general outlier elimination criterions, such as Grubbs criterion[5−6] , Chauvenet criterion[5] , Romanovsky criterion[6] , Dixon criterion[7]and 3σ criterion[5] , etc., merely adapt to the conditions that a relatively small percentage of outliers is contained
in the detection samples[6,8] . The method uses the model order criterion of Akaike, or Schwartz and Rissanen, has a bias term dependent upon the number of samples[9] . Projection statistics (PS) is a technique developed to detect N − dimensional snapshot outlier vectors[10] . The above methods are used to identify isolated outliers via the probability and statistics of data. They are not steady any more when the outlier occupy rate (γ- the ratio of the number of outliers to the number of total sample data) is higher and the statistics of sample data are biased severely. Thus, incomplete elimination, even invalid processing may be caused. However, the high γ situations often occur in ship detection with HF radar because of the following reasons. First, since environment noise and sea clutter involved in the background noise are considered as nonhomogeneous normal distributions[11] , the data segmenting technique is applied to make the noise samples approximately homogeneous in a detection section. So the number of samples in a section could not be overlarge[1]. Second, every target peak has a width of several samples because window weighting is used regularly to depress the side lobe in or-
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Li Hongbo, Shen Yiying & Liu Yongtan
der to suppress the energy leakage during spectrum transform[1,12]. And the peak width is also broadened when the target has the tangential movement relative to radar. Third, ships usually navigate slowly along the settled sea-route. When the channel is congested or narrow, for example, port, strait, island, and the water area nearby the coastline, the multiple target situations often appear. In a word, the background noise samples do not dominate quantitatively in the detection section. The detection threshold may be higher because outliers are present in the data used to estimate the noise level, which makes the miss alarm rate increased, and the weak targets shielded[9,13] .
the outlier (target signal or jamming) existing which should be eliminated and hypothesis H0 designated as the background noise sample which should be reserved. H1 : Y (n) = S(n) + X(n)
According to the property of target echo spectra, an improved outlier elimination criterion named wholepeak-outlier elimination (WPOE) criterion is defined in this paper to overcome such problems. It could reduce the estimation error of background noise level by trimming off whole correlative samples of target peak beforehand, and realize the reliable threshold detection.
1 i0 N . Supposing that it is an outlier, eliminate beforehand the whole peak Y (i), imin i, i0 imax which it belongs to. Y (i) should be identified with ⎧ ⎪ imin i < i0 ⎪ ⎪ |Y (i)| < |Y (i + 1)| ⎪ ⎪ ⎨ |Y (i)| < |Y (i − 1)| i0 < i imax (2) ⎪ ⎪ |Y (imin )| |Y (imin − 1)| ⎪ ⎪ ⎪ ⎩ |Y (imax )| |Y (imax + 1)|
2. Whole-peak-outlier elimination (WPOE) criterion The spectra of received signals in HF radar are complex data after being sampled, orthogonalized, and Fourier transformed. Assume that in a detection section the measured series is Y (n), n = 1, 2, · · · , N , which may be expressed as the sum of both target signals (including impulsive disturbance) designated as S(n), and background noise, designated as X(n). X(n) is Gaussian noise with zero mean. Xr (n) and Xi (n), which are the real and imaginary parts of X(n), are uncorrelated but in the same distribution. This statistical property is observed to be independent of radar operating frequency, scattering cell size and sea state[11,14] . Therefore, the probability density function (PDF) of complex Gaussian noise can be expressed as p(Xr , Xi ) =
2 1 − Xr2 +X i e 2σ2 2 2πσ
(1)
where σ is the standard deviation of noise. The outlier distinguished criterion is a binary hypothesis testing. That is, hypothesis H1 designated as
H0 :
Y (n) = X(n)
Concerning the property that samples in a target peak are correlated mutually, we construct a peak-wise (peaks are processed in turn) outlier elimination criterion called WPOE criterion. The detailed approach is as follows. a) Find the sample with maximum amplitude during the detection section, |Y (i0 )| = max |Y (n)|, 1nN
b) Calculate the standard deviation σ ¯ of remaining samples as the variance estimation of background noise which has the apriority of zero mean. c) Set the threshold to distinguish the outlier. Give the decision one by one for the samples in the peak pre-eliminated in step a) or has been eliminated before, according to discriminant (3), where ρ is the outlier discrimination factor independent of σ ¯ [2−3] . If the amplitude is higher than the threshold, consider it to be an outlier and eliminate it verily, and subtract 1 from the amount of samples, N = N − 1. If lower, reserve the sample. After all outliers are eliminated, the procedure should return to step a) with the remaining samples. If there are no outliers distinguished any more, the procedure is completed. H1
|Y (n)| ≷ ρ¯ σ
(3)
H0
In above procedure, the formula expressed as (2) could detach the target peaks overlapped partially and weaken the nulling effect that the weak target is shielded by the strong one. The samples of the pre-eliminated peak will be eliminated verily in step
Estimation of detection threshold in multiple ship target situations with HF ground wave radar c) only if its amplitude is higher than the threshold. Thus, the noise samples in the bottom of the target peak are reserved as well as the peak made of noise, and the discrimination operation is not to be processed unrestrained. What’s more, the remaining samples are not shifted after the outliers are eliminated so as to protect the original shape of the spectrum. The WPOE criterion, a kind of peak-wise discrimination, is better than the point-wise one proposed in Ref.[2]. The reason is that the outliers could be eliminated more entirely in terms of the holistic analysis of peak and σ ¯ describes the statistics of background noise more properly. In addition, since the outlier elimination is not equivalent to signal detection, we can choose ρ comparatively independently to calculate the threshold and ensure the outlier be distinguished credibly.
3. Capacity analysis of WPOE criterion In this section we make a quantitative analysis of WPOE criterion. The target returns demodulated are approximated to sine wave[1]. After window weighting and Fourier transform, they form a peak with a width in spectrum. For simplicity, we present such an example that Hanning window is selected and the targets’ Doppler frequency are exactly on the point of quantification. The maximum amplitude of the target peak is |S(m)| = S0 , and the amplitude of two neighbor sample points is |S(m + 1)| = |S(m − 1)| ≈ S0 /2. Assume that during N total samples there are M targets with same amplitude as above and not overlapped each other. The amount of outliers is 3M since per target occupies 3 spectral lines. M outliers’ amplitude are S0 and the other 2M are S0 / 2. The outlier occupy rate γ is equal to 3M /N . The rest of the samples are background noise, which is Gaussian with zero mean as Eq. (1). As the amplitude mean of complex noise is σ π/2, Signal-to-noise ratio, i.e. SNR, of the target S0 is η = σ π/2 As the module of X(n) obeys the Rayleigh distribution[15] , a variance estimation insensitive to
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the existence of outliers can be derived as below. N 2 1 |Y (n)| (4) σ ¯= π N n=1 The outlier elimination criterion proposed in Ref.[2] used Eq. (4) to calculate σ ¯.
N 3M 2 1 σ ¯ |X(n)| + |S(m)| = π N n=1 m=1
2M σ 1+η N (5) Using the WPOE criterion, a target peak including 3 outliers is taken off beforehand. Then another estimation of variance σ ¯ is obtained by N −3 1 2 σ ¯ = |Y (n)| π N − 3 n=1 ⎞⎤ ⎡ ⎛ 3(M−1) N −3 2⎣ 1 ⎝ |X(n)| + |S(m)|⎠⎦ = π N − 3 n=1 m=1
2(M − 1) σ 1+η N −3 (6) Since γ = 3M/N < 1 and N > 3, we can demonstrate easily that 2(M − 1) 2M < N −3 N
(7)
The estimation error caused by the background noise samples in Eq. (5) and Eq. (6) may be ignored, thus we have σ ¯ < σ ¯ (8) The WPOE method degrades γ so as to make σ ¯ smaller, the threshold of outlier discrimination lower and the outliers eliminated more efficiently. Since X(n) is zero mean, the amplitude of target line is approximated to |Y (m)| = |S(m) + X(m)| ≈ |S(m)|
(9)
With the given significant testing level α, ρ can be calculated by[3] √ ρ = −2 ln α (10) The discriminant is √ π |Y (m)| = S = ση > ρ¯ σ = σ ¯ −2 ln α 2
(11)
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Li Hongbo, Shen Yiying & Liu Yongtan
According to M = γN/3, simultaneous with Eq. (6) and Eq. (11), we have 1 − 2 − ln α/π/η 3 − 9/N 3 (12) γ< + 2 N 2 − ln α/π 1 − 2 − ln α/π/η Assume that β = and critical 2 − ln α/π discriminating point as γmax , which can be written as 3 3 3 (13) γmax = β + 1− β 2 N 2 For the sake of keeping the background noise homogeneous, the length of the detection section is smaller than 35 in general as well as βmax ∈ (0.3, 0.4)[1,3]. Hereby, although γmax is decreasing a little with the increscent N , it still not lower than 50%. Fig. 1 shows the relationship curves between γmax and η with the given α and N . It is obvious that γmax of WPOE discrimination is beyond 50%. This excellent performance, that can satisfy most occasions, is the base of the following threshold signal detection. If there are too much more outliers in the section, the dominant is not the background noise anymore so that the detection could not be processed normally.
in the high-resolution Doppler frequency spectra. At first data segmenting technique is used to make the noise samples approximately homogeneous in a detection section. Then the signal detection in multiple target situations is divided into two relatively independent sub-procedures: outlier elimination in noise level estimation and the signal threshold detection. The diagram of signal detector is shown in Fig. 2.
Fig. 2
The diagram of signal detector
Use WPOE criterion to eliminate target samples and peak-like disturbances from the detection section for a reliable and accurate estimation of background noise level. Thereafter, we can calculate the detection threshold associating with the detector parameters: probability of false alarm Pf and probability of detection Pd . In addition, the samples which may belong to target signal are also separated at the same time as the outliers are eliminated. It is in favor of improving the efficiency of signal processing since the target detection is simply carried out through these outliers.
5. Experiment results
Fig. 1
The γmax − η relationship curves
4. Signal detector The sweep bandwidth of HF Ground wave radar is not sufficient to earn high range resolution. The number of data is small and the noise is fluctuated in range dimension. So the signal detection is mostly done
The Doppler velocity amplitude spectra of ship detecting experiments are shown as Figs. 3 and 4. The range is 90 km and 55 km respectively. The Bragg peaks, i.e., the first-order sea echoes of radar, are exactly a pair of boundaries. The signal detection is divided into 6 data sections without detection of Bragg region. There are 4 targets with low Doppler velocity between two Bragg peaks. Especially, 3 targets are in the 3rd section which contains 21 samples. In Fig. 3, there are 4, 4, 3 outliers respectively in 3 target peaks.
Estimation of detection threshold in multiple ship target situations with HF ground wave radar γ=11/21≈52.4%. In Fig. 4, there are 3, 4, 3 outliers respectively in 3 target peaks. γ=10/21≈47.6%. The main detection parameters are: α=0.001, Pd = 0.9 and Pf = 0.0001.
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and the threshold calculated by the WPOE criterion is nearly equivalent between the inside and outside of Bragg peaks. It has been verified that the WPOE method is credible to estimate the detection threshold when the samples are few and outliers occupied heavily in multiple target sections. The problem that the strong targets have a nulling effect on the weak ones may be overcome so that the capability of weak target detection is improved. In application to the instance shown in Fig. 4, this new method could also effectively update the abnormal detection threshold and make it follow the change of noise level although the background noise fluctuates severely.
6. Conclusion
Fig. 3
Fig. 4
Measured Doppler spectrum (range 90 km)
Measured Doppler spectrum (range 55 km)
The thin line with plus marker in Figs.3 and 4 denotes the detection threshold calculated by the method previously proposed in Ref.[2]. It is obvious that in multiple target situations the detection threshold is overvalued caused by incomplete outlier elimination. There is 1 target missed in the 3rd section. Compared with above performance, the WPOE criterion could make the threshold fall 5.13 dB and 10.35 dB respectively. And 3 targets are all detected. In Fig. 3, the background noise fluctuates smoothly
We present a new outlier elimination method named WPOE criterion to achieve the signal detection threshold reliably in multiple ship target situations with HF radar. In view of the property that the samples in a target peak are correlated, WPOE criterion is adapted for the instance that the detection samples is limited and occupied heavily with outliers. The results of the experiment indicate that this method could reduce the miss alarm loss effectively even if γ is above 50%, make the capability of the detector better and ensure the proper detection of target signal. It should be noted that the signal with high SNR is not certain to be real target through the detection merely in the Doppler velocity dimension. Sometimes the amplitude of broadcasting and industry disturbance may also exceed the threshold. Therefore, further detection and discrimination should be done in the range dimension, where the method proposed in this paper can also be used.
References [1] Shen Yiying. A study of signal detection for high frequency ground wave over-the-horizon radar. Ph.D. thesis, Harbin Institute of Technology, 1999. [2] Shen Yiying, Yu Faxin, Liu Yongtan. Design of complex signal CFAR detector with excellent performance. Journal of Harbin Institute of Technology, 2000, 32(6): 33–36. [3] Shen Yiying, Liu Yongtan. Elimination of wild values in complex data for threshold estimation of signal detection. Modern Radar, 1999, 21(3): 39–43.
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[4] Nasi J, Sorsa A, Leiviska K. Sensor validation and outlier detection using fuzzy limits. Proceedings of the 44th IEEE Conference on Decision and Control, 2005: 7828–7833. [5] Gao Lin, Gao Zuolei. Applied algorithm collection with
1977,13(4): 338–343. [14] Ioup G E, Ioup J W. Higher order statistical analysis of ocean noise measurements for performance prediction.
Grant # N00014-95-0648, Technical Report for
22Feb1995–21Feb1996, 1996: 87–108.
FORTRAN. Beijing: Academy Press, 1994. [6] Wang Zhengming, Yi Dongyun. Modeling and parameter estimation of measuring data. Changsha: Press of Na-
[15] Zhao Shuqing, Zheng Wei. Random signal analysis. Harbin: Press of Harbin Institute of Technology, 1999.
tional University of Defense Technology, 1996. [7] Jia Peiran, Chen Kejun, He Li. Ballistics of long-distance rocket. Changsha: Press of National University of Defense Technology, 1993. [8] Amidan B G, Ferryman T A, Cooley S K. Data outlier detection using the Chebyshev theorem. IEEE Conference on Aerospace, 2005: 1–6.
Li Hongbo was born in 1980. She received M. S. degree in communication and information systems in 2002. She is now an instructor and a doctoral candidate in Harbin Institute of Technology. Her research interests include radar signal detection and data processing. E-mail: drbobo@sina. com
[9] Michal D P, Fuhrmann D R. Multiple target detection for an antenna array using outlier rejection methods. IEEE International Conference on Acoustics, Speech, and Signal Processing, 1993: 45–48. [10] Schoenig G N, Picciolo M L, Mili L. Improved detection of strong nonhomogeneities for STAP via projection statistics. IEEE International Radar Conference, 2005: 720–
Shen Yiying was born in 1960. He received Ph. D. degree in electronic engineering in 1999. He is now a professor in Harbin Institute of Technology. He is active in radar signal design and processing, system design and simulation, and weak signal detection.
725. [11] Barrick D E, Shider J B. The statistics of HF sea-echo doppler spectra. IEEE Trans. on Antennes and Prop,
Liu Yongtan was born in 1936. He graduated from Tsinghua University in 1958. He was elected as a
New York:
member of The Chinese Academy of Sciences and The Chinese Academy of Engineering in 1991 and 1994 re-
[13] Rickard A R, Dillard G M. Adaptive detection algorithms
spectively. He is a member of CIE Editorial Committee and senior member of IEEE. He has been working
1977, 25(1): 19–28. [12] Skolnik M I. Introduction to radar system. McGraw-Hill Book Company, Inc, 1980.
for multiple target situations.
IEEE Trans.
on AES,
on radar system engineering and signal processing.
Estimation of detection threshold in multiple ship target situations with HF ground wave radar Li Hongbo, Shen Yiying & Liu Yongtan Research Institute of Electronics and Information, Harbin Inst. of Technology, Harbin 150001, P. R. China (Received November 9, 2006)
Abstract: A credible method of calculating the detection threshold is presented for the multiple target situations, which appear frequently in the lower Doppler velocity region during the surveillance of sea with HF ground wave radar. This method defines a whole-peak-outlier elimination (WPOE) criterion, which is based on in-peak-samples correlation of each target echo spectra, to trim off the target signals and abnormal disturbances with great amplitude from the complex spectra. Therefore, cleaned background noise samples are obtained to improve the accuracy and reliability of noise level estimation. When the background noise is nonhomogeneous, the detection samples are limited and often occupied heavily with outliers. In this case, the problem that the detection threshold is overvalued can be solved. In applications on experimental data, it is verified that this method can reduce the miss alarm rate of signal detection effectively in multiple target situations as well as make the adaptability of the detector better.
Keywords: HF ground wave radar, multiple target detection, outlier elimination, threshold estimation.
1. Introduction The signal detection with HF radar is commonly done in the spectral domain. The geometry of real target amplitude in two-dimensional range-velocity spectra is peak-like and it may be an essential discrimination for the detector to identify the target from external electromagnetic environment noise and seasurface echoes[1] . A kind of constant false alarm rate (CFAR) detection method based on the outlier elimination was proposed and studied in Refs.[1-3]. In its theoretical framework, not only the target signals but also the impulsive disturbances with great amplitude are called outliers, whose value lies abnormally far from others[4]. By eliminating the outliers entirely in a detection section, the cleaned background noise samples are obtained for the accurate estimation of the background noise level so as to calculate the detection threshold credibly. The general outlier elimination criterions, such as Grubbs criterion[5−6] , Chauvenet criterion[5] , Romanovsky criterion[6] , Dixon criterion[7]and 3σ criterion[5] , etc., merely adapt to the conditions that a relatively small percentage of outliers is contained
in the detection samples[6,8] . The method uses the model order criterion of Akaike, or Schwartz and Rissanen, has a bias term dependent upon the number of samples[9] . Projection statistics (PS) is a technique developed to detect N − dimensional snapshot outlier vectors[10] . The above methods are used to identify isolated outliers via the probability and statistics of data. They are not steady any more when the outlier occupy rate (γ- the ratio of the number of outliers to the number of total sample data) is higher and the statistics of sample data are biased severely. Thus, incomplete elimination, even invalid processing may be caused. However, the high γ situations often occur in ship detection with HF radar because of the following reasons. First, since environment noise and sea clutter involved in the background noise are considered as nonhomogeneous normal distributions[11] , the data segmenting technique is applied to make the noise samples approximately homogeneous in a detection section. So the number of samples in a section could not be overlarge[1]. Second, every target peak has a width of several samples because window weighting is used regularly to depress the side lobe in or-
740
Li Hongbo, Shen Yiying & Liu Yongtan
der to suppress the energy leakage during spectrum transform[1,12]. And the peak width is also broadened when the target has the tangential movement relative to radar. Third, ships usually navigate slowly along the settled sea-route. When the channel is congested or narrow, for example, port, strait, island, and the water area nearby the coastline, the multiple target situations often appear. In a word, the background noise samples do not dominate quantitatively in the detection section. The detection threshold may be higher because outliers are present in the data used to estimate the noise level, which makes the miss alarm rate increased, and the weak targets shielded[9,13] .
the outlier (target signal or jamming) existing which should be eliminated and hypothesis H0 designated as the background noise sample which should be reserved. H1 : Y (n) = S(n) + X(n)
According to the property of target echo spectra, an improved outlier elimination criterion named wholepeak-outlier elimination (WPOE) criterion is defined in this paper to overcome such problems. It could reduce the estimation error of background noise level by trimming off whole correlative samples of target peak beforehand, and realize the reliable threshold detection.
1 i0 N . Supposing that it is an outlier, eliminate beforehand the whole peak Y (i), imin i, i0 imax which it belongs to. Y (i) should be identified with ⎧ ⎪ imin i < i0 ⎪ ⎪ |Y (i)| < |Y (i + 1)| ⎪ ⎪ ⎨ |Y (i)| < |Y (i − 1)| i0 < i imax (2) ⎪ ⎪ |Y (imin )| |Y (imin − 1)| ⎪ ⎪ ⎪ ⎩ |Y (imax )| |Y (imax + 1)|
2. Whole-peak-outlier elimination (WPOE) criterion The spectra of received signals in HF radar are complex data after being sampled, orthogonalized, and Fourier transformed. Assume that in a detection section the measured series is Y (n), n = 1, 2, · · · , N , which may be expressed as the sum of both target signals (including impulsive disturbance) designated as S(n), and background noise, designated as X(n). X(n) is Gaussian noise with zero mean. Xr (n) and Xi (n), which are the real and imaginary parts of X(n), are uncorrelated but in the same distribution. This statistical property is observed to be independent of radar operating frequency, scattering cell size and sea state[11,14] . Therefore, the probability density function (PDF) of complex Gaussian noise can be expressed as p(Xr , Xi ) =
2 1 − Xr2 +X i e 2σ2 2 2πσ
(1)
where σ is the standard deviation of noise. The outlier distinguished criterion is a binary hypothesis testing. That is, hypothesis H1 designated as
H0 :
Y (n) = X(n)
Concerning the property that samples in a target peak are correlated mutually, we construct a peak-wise (peaks are processed in turn) outlier elimination criterion called WPOE criterion. The detailed approach is as follows. a) Find the sample with maximum amplitude during the detection section, |Y (i0 )| = max |Y (n)|, 1nN
b) Calculate the standard deviation σ ¯ of remaining samples as the variance estimation of background noise which has the apriority of zero mean. c) Set the threshold to distinguish the outlier. Give the decision one by one for the samples in the peak pre-eliminated in step a) or has been eliminated before, according to discriminant (3), where ρ is the outlier discrimination factor independent of σ ¯ [2−3] . If the amplitude is higher than the threshold, consider it to be an outlier and eliminate it verily, and subtract 1 from the amount of samples, N = N − 1. If lower, reserve the sample. After all outliers are eliminated, the procedure should return to step a) with the remaining samples. If there are no outliers distinguished any more, the procedure is completed. H1
|Y (n)| ≷ ρ¯ σ
(3)
H0
In above procedure, the formula expressed as (2) could detach the target peaks overlapped partially and weaken the nulling effect that the weak target is shielded by the strong one. The samples of the pre-eliminated peak will be eliminated verily in step
Estimation of detection threshold in multiple ship target situations with HF ground wave radar c) only if its amplitude is higher than the threshold. Thus, the noise samples in the bottom of the target peak are reserved as well as the peak made of noise, and the discrimination operation is not to be processed unrestrained. What’s more, the remaining samples are not shifted after the outliers are eliminated so as to protect the original shape of the spectrum. The WPOE criterion, a kind of peak-wise discrimination, is better than the point-wise one proposed in Ref.[2]. The reason is that the outliers could be eliminated more entirely in terms of the holistic analysis of peak and σ ¯ describes the statistics of background noise more properly. In addition, since the outlier elimination is not equivalent to signal detection, we can choose ρ comparatively independently to calculate the threshold and ensure the outlier be distinguished credibly.
3. Capacity analysis of WPOE criterion In this section we make a quantitative analysis of WPOE criterion. The target returns demodulated are approximated to sine wave[1]. After window weighting and Fourier transform, they form a peak with a width in spectrum. For simplicity, we present such an example that Hanning window is selected and the targets’ Doppler frequency are exactly on the point of quantification. The maximum amplitude of the target peak is |S(m)| = S0 , and the amplitude of two neighbor sample points is |S(m + 1)| = |S(m − 1)| ≈ S0 /2. Assume that during N total samples there are M targets with same amplitude as above and not overlapped each other. The amount of outliers is 3M since per target occupies 3 spectral lines. M outliers’ amplitude are S0 and the other 2M are S0 / 2. The outlier occupy rate γ is equal to 3M /N . The rest of the samples are background noise, which is Gaussian with zero mean as Eq. (1). As the amplitude mean of complex noise is σ π/2, Signal-to-noise ratio, i.e. SNR, of the target S0 is η = σ π/2 As the module of X(n) obeys the Rayleigh distribution[15] , a variance estimation insensitive to
741
the existence of outliers can be derived as below. N 2 1 |Y (n)| (4) σ ¯= π N n=1 The outlier elimination criterion proposed in Ref.[2] used Eq. (4) to calculate σ ¯.
N 3M 2 1 σ ¯ |X(n)| + |S(m)| = π N n=1 m=1
2M σ 1+η N (5) Using the WPOE criterion, a target peak including 3 outliers is taken off beforehand. Then another estimation of variance σ ¯ is obtained by N −3 1 2 σ ¯ = |Y (n)| π N − 3 n=1 ⎞⎤ ⎡ ⎛ 3(M−1) N −3 2⎣ 1 ⎝ |X(n)| + |S(m)|⎠⎦ = π N − 3 n=1 m=1
2(M − 1) σ 1+η N −3 (6) Since γ = 3M/N < 1 and N > 3, we can demonstrate easily that 2(M − 1) 2M < N −3 N
(7)
The estimation error caused by the background noise samples in Eq. (5) and Eq. (6) may be ignored, thus we have σ ¯ < σ ¯ (8) The WPOE method degrades γ so as to make σ ¯ smaller, the threshold of outlier discrimination lower and the outliers eliminated more efficiently. Since X(n) is zero mean, the amplitude of target line is approximated to |Y (m)| = |S(m) + X(m)| ≈ |S(m)|
(9)
With the given significant testing level α, ρ can be calculated by[3] √ ρ = −2 ln α (10) The discriminant is √ π |Y (m)| = S = ση > ρ¯ σ = σ ¯ −2 ln α 2
(11)
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Li Hongbo, Shen Yiying & Liu Yongtan
According to M = γN/3, simultaneous with Eq. (6) and Eq. (11), we have 1 − 2 − ln α/π/η 3 − 9/N 3 (12) γ< + 2 N 2 − ln α/π 1 − 2 − ln α/π/η Assume that β = and critical 2 − ln α/π discriminating point as γmax , which can be written as 3 3 3 (13) γmax = β + 1− β 2 N 2 For the sake of keeping the background noise homogeneous, the length of the detection section is smaller than 35 in general as well as βmax ∈ (0.3, 0.4)[1,3]. Hereby, although γmax is decreasing a little with the increscent N , it still not lower than 50%. Fig. 1 shows the relationship curves between γmax and η with the given α and N . It is obvious that γmax of WPOE discrimination is beyond 50%. This excellent performance, that can satisfy most occasions, is the base of the following threshold signal detection. If there are too much more outliers in the section, the dominant is not the background noise anymore so that the detection could not be processed normally.
in the high-resolution Doppler frequency spectra. At first data segmenting technique is used to make the noise samples approximately homogeneous in a detection section. Then the signal detection in multiple target situations is divided into two relatively independent sub-procedures: outlier elimination in noise level estimation and the signal threshold detection. The diagram of signal detector is shown in Fig. 2.
Fig. 2
The diagram of signal detector
Use WPOE criterion to eliminate target samples and peak-like disturbances from the detection section for a reliable and accurate estimation of background noise level. Thereafter, we can calculate the detection threshold associating with the detector parameters: probability of false alarm Pf and probability of detection Pd . In addition, the samples which may belong to target signal are also separated at the same time as the outliers are eliminated. It is in favor of improving the efficiency of signal processing since the target detection is simply carried out through these outliers.
5. Experiment results
Fig. 1
The γmax − η relationship curves
4. Signal detector The sweep bandwidth of HF Ground wave radar is not sufficient to earn high range resolution. The number of data is small and the noise is fluctuated in range dimension. So the signal detection is mostly done
The Doppler velocity amplitude spectra of ship detecting experiments are shown as Figs. 3 and 4. The range is 90 km and 55 km respectively. The Bragg peaks, i.e., the first-order sea echoes of radar, are exactly a pair of boundaries. The signal detection is divided into 6 data sections without detection of Bragg region. There are 4 targets with low Doppler velocity between two Bragg peaks. Especially, 3 targets are in the 3rd section which contains 21 samples. In Fig. 3, there are 4, 4, 3 outliers respectively in 3 target peaks.
Estimation of detection threshold in multiple ship target situations with HF ground wave radar γ=11/21≈52.4%. In Fig. 4, there are 3, 4, 3 outliers respectively in 3 target peaks. γ=10/21≈47.6%. The main detection parameters are: α=0.001, Pd = 0.9 and Pf = 0.0001.
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and the threshold calculated by the WPOE criterion is nearly equivalent between the inside and outside of Bragg peaks. It has been verified that the WPOE method is credible to estimate the detection threshold when the samples are few and outliers occupied heavily in multiple target sections. The problem that the strong targets have a nulling effect on the weak ones may be overcome so that the capability of weak target detection is improved. In application to the instance shown in Fig. 4, this new method could also effectively update the abnormal detection threshold and make it follow the change of noise level although the background noise fluctuates severely.
6. Conclusion
Fig. 3
Fig. 4
Measured Doppler spectrum (range 90 km)
Measured Doppler spectrum (range 55 km)
The thin line with plus marker in Figs.3 and 4 denotes the detection threshold calculated by the method previously proposed in Ref.[2]. It is obvious that in multiple target situations the detection threshold is overvalued caused by incomplete outlier elimination. There is 1 target missed in the 3rd section. Compared with above performance, the WPOE criterion could make the threshold fall 5.13 dB and 10.35 dB respectively. And 3 targets are all detected. In Fig. 3, the background noise fluctuates smoothly
We present a new outlier elimination method named WPOE criterion to achieve the signal detection threshold reliably in multiple ship target situations with HF radar. In view of the property that the samples in a target peak are correlated, WPOE criterion is adapted for the instance that the detection samples is limited and occupied heavily with outliers. The results of the experiment indicate that this method could reduce the miss alarm loss effectively even if γ is above 50%, make the capability of the detector better and ensure the proper detection of target signal. It should be noted that the signal with high SNR is not certain to be real target through the detection merely in the Doppler velocity dimension. Sometimes the amplitude of broadcasting and industry disturbance may also exceed the threshold. Therefore, further detection and discrimination should be done in the range dimension, where the method proposed in this paper can also be used.
References [1] Shen Yiying. A study of signal detection for high frequency ground wave over-the-horizon radar. Ph.D. thesis, Harbin Institute of Technology, 1999. [2] Shen Yiying, Yu Faxin, Liu Yongtan. Design of complex signal CFAR detector with excellent performance. Journal of Harbin Institute of Technology, 2000, 32(6): 33–36. [3] Shen Yiying, Liu Yongtan. Elimination of wild values in complex data for threshold estimation of signal detection. Modern Radar, 1999, 21(3): 39–43.
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[4] Nasi J, Sorsa A, Leiviska K. Sensor validation and outlier detection using fuzzy limits. Proceedings of the 44th IEEE Conference on Decision and Control, 2005: 7828–7833. [5] Gao Lin, Gao Zuolei. Applied algorithm collection with
1977,13(4): 338–343. [14] Ioup G E, Ioup J W. Higher order statistical analysis of ocean noise measurements for performance prediction.
Grant # N00014-95-0648, Technical Report for
22Feb1995–21Feb1996, 1996: 87–108.
FORTRAN. Beijing: Academy Press, 1994. [6] Wang Zhengming, Yi Dongyun. Modeling and parameter estimation of measuring data. Changsha: Press of Na-
[15] Zhao Shuqing, Zheng Wei. Random signal analysis. Harbin: Press of Harbin Institute of Technology, 1999.
tional University of Defense Technology, 1996. [7] Jia Peiran, Chen Kejun, He Li. Ballistics of long-distance rocket. Changsha: Press of National University of Defense Technology, 1993. [8] Amidan B G, Ferryman T A, Cooley S K. Data outlier detection using the Chebyshev theorem. IEEE Conference on Aerospace, 2005: 1–6.
Li Hongbo was born in 1980. She received M. S. degree in communication and information systems in 2002. She is now an instructor and a doctoral candidate in Harbin Institute of Technology. Her research interests include radar signal detection and data processing. E-mail: drbobo@sina. com
[9] Michal D P, Fuhrmann D R. Multiple target detection for an antenna array using outlier rejection methods. IEEE International Conference on Acoustics, Speech, and Signal Processing, 1993: 45–48. [10] Schoenig G N, Picciolo M L, Mili L. Improved detection of strong nonhomogeneities for STAP via projection statistics. IEEE International Radar Conference, 2005: 720–
Shen Yiying was born in 1960. He received Ph. D. degree in electronic engineering in 1999. He is now a professor in Harbin Institute of Technology. He is active in radar signal design and processing, system design and simulation, and weak signal detection.
725. [11] Barrick D E, Shider J B. The statistics of HF sea-echo doppler spectra. IEEE Trans. on Antennes and Prop,
Liu Yongtan was born in 1936. He graduated from Tsinghua University in 1958. He was elected as a
New York:
member of The Chinese Academy of Sciences and The Chinese Academy of Engineering in 1991 and 1994 re-
[13] Rickard A R, Dillard G M. Adaptive detection algorithms
spectively. He is a member of CIE Editorial Committee and senior member of IEEE. He has been working
1977, 25(1): 19–28. [12] Skolnik M I. Introduction to radar system. McGraw-Hill Book Company, Inc, 1980.
for multiple target situations.
IEEE Trans.
on AES,
on radar system engineering and signal processing.