Modified cell averaging CFAR detector based on Grubbs criterion in multiple-target scenario

Transcription

1 Modfed averagng CFAR detector based on Grubbs crteron n multple-target scenaro We Zhou, Student Member, IEEE, Junhao Xe, Senor Member, IEEE, Kun X, Yuhan Du Key Laboratory of Marne Envronmental Montorng and Informaton Processng, Mnstry of Industry and Informaton Technology Harbn Insttute of Technology Harbn, Chna E-mal: {zhouw, xj, kunx, duyuhan}@ht.edu.cn Abstract Constant false alarm rate (CFAR) s the desred property for automatc target detecton n unknown and nonstatonary background. In ths paper, a modfed averagng CFAR detector based on Grubbs crteron (CAG-CFAR) s proposed for multple-target scenaro, whch s encountered when two or more targets are dsplayed closely n the range doman. The CFAR property of the proposed method wth respect to the dstrbuton parameter n exponental-dstrbuted background s verfed va Monte Carlo smulatons. The CAG-CFAR detector does not requre a pror knowledge of the number of nterferng targets, achevng a robust detecton performance wth a low computatonal burden. Comparsons of the detecton performance of the CAG-CFAR detector wth several relevant compettors verfy the effectveness and superorty of the proposed method n multple-target stuaton wth an unknown number of the nterferng targets. Keywords target detecton; Grubbs crteron; CFAR; multple targets I. ITRODUCTIO As an adaptve threshold technque, constant false alarm rate (CFAR) detector s wdely used for radar automatc detecton n an unknown clutter envronment. Gven the lack of a pror knowledge of the practcal clutter background, target detecton wth a fxed threshold suffers an excessve ncrease n the false alarm rate and an ntolerable decrease n the detecton performance. As a cure, CFAR detector sets a threshold dynamcally by estmatng the mean power of the local background, and multplyng t by a multplcaton factor whch depends on the desred false alarm rate and the statstcal characterstcs of the background. Consequently, the potental targets can be detected correctly n dfferent clutter backgrounds wth a constant false alarm rate, whch s mportant n modern radar system applcaton and recevng popularty n recent years [] []. Cell-averagng CFAR (CA-CFAR) [2], [3] s the earlest type of CFAR detector, of whch the detecton performance has been demonstrated to approach the deal eyman-pearson detector wth an ncrease of the reference n homogenous exponental envronment. However, CA-CFAR suffers sgnfcant performance degradaton n multple-target scenaro owng to the maskng effect, and the false alarm wll ncrease at the clutter edge [4]. The greatest of selecton CFAR (GO- CFAR) provdes exent performance n mantanng CFAR property n the case of clutter edge [5]. However, the severe maskng effect lmts the detecton performance n multpletarget scenaro, and the CFAR loss wll ncrease n a homogenous background. The ordered statstc CFAR (OS- CFAR) [6] s advantageous for target detecton n multpletarget scenaro. Ths method selects the k th sample of the ampltude rank-ordered reference s to represent the mean power of the local clutter, exhbtng a more robust detecton performance compared to CA-CFAR and GO-CFAR n multple-target stuaton. However, t stll suffers an excessve false alarm rate n the clutter edges [7]. Furthermore, the censored-class CFAR detectors, such as censored mean-level detector (CMLD) [8] and trmmed mean CFAR (TM-CFAR) detector [4], are proposed for target detecton n multpletarget scenaro wth an acceptable CFAR loss n homogenous background. The outlers and potental targets n the reference wndow of the CFAR processor wll be elmnated for an accurate estmaton of the background level. However, the number of nterferng targets s requred to be pror known, whch s generally mpossble n practcal scenaro. To elmnate the dependence on the number of nterferng targets, the generalsed CMLD and automatc CMLD are respectvely ntroduced n [9] and [20], whle the correspondng computatonal burden s heavy owng to the teraton n outler rejecton and estmaton of background level. In ths paper, a modfed CA-CFAR detector based on Grubbs crteron (CAG-CFAR) s proposed n exponental background, whch s commonly utlsed to descrbe the clutter power dstrbuton n coherent low range-resoluton radar. The Grubbs crteron s appled to prevent the nfluence on the background level estmaton ntroduced by the outlers and potental targets n the reference wndow of CFAR processor. The proposed detector s demonstrated to mantan CFAR property wth respect to the dstrbuton parameter n exponental-dstrbuted background. Smulaton results show that the CAG-CFAR detector does not requre a pror knowledge of the number of nterferng targets, achevng a robust detecton performance wth a low computatonal burden. The effectveness and superorty of the proposed method n multple-target scenaro wth an unknown number of the The work was supported by Specal Research Foundaton for Harbn Scence and Technology Innovaton Talents (RC204XK009022) and atonal atural Scence Foundaton of Chna key project (632005).

2 nterferng targets are verfed by performance comparsons wth relevant CFAR detectors. The remanng parts of ths paper are organzed as follows. The tradtonal CFAR detectors n exponental background are ntroduced brefly n Secton II. The Grubbs crteron and the detecton scheme of CAG-CFAR are provded n Secton III. In Secton IV, the motvatons and advantages of the proposed method are verfed usng smulatons. A general concluson s presented n Secton V. II. TRADITIOAL CFAR DETECTORS In ths secton, the schemes of CA-CFAR, GO-CFAR, OS- CFAR, TM-CFAR, and CMLD are ntroduced. The man purpose of all CFAR processor s to declare the target present or absent by settng an adaptve threshold, whch s determned dynamcally by the estmated background level and the desred false alarm rate. The target detecton s usually performed through the sldng wndow technque, of whch the block dagram s provded n Fg.. The n-phase and quadrature sgnals after pulse compresson are frst square-law detected, and the successve outputs are stored n a tapped delay lne, whch conssts of the reference wndow, guard s and under test (CUT). The samples n the reference wndow P are usually assumed to be statstcally ndependent and dentcally dstrbuted (IID) random varables n homogenous clutter envronment. The local background level s estmated usng the samples n the leadng and laggng halves of the reference wndow. The samples n the guard s are dscarded to elmnate the mpact of the potental target n the CUT on background level estmaton. The adaptve threshold s obtaned by multplyng the estmated local power level wth a multplcaton factor, whch s related to the desred false alarm rate. The multplcaton factor s also known as scalng factor or normalzed factor [5], [6]. If the magntude of CUT exceeds the adaptve threshold, the target s declared to be present. Assumng that the samples n the reference wndow are random varables X, X 2,, X, denotes the length of the reference wndow. The statstcal power samples n reference wndow P satsfy exponental dstrbuton. The probablty densty functon (PDF) of exponental dstrbuton could be expressed as exp x 2 f x () where x denotes the power of the clutter sample, denotes the dstrbuton parameter. The detecton schemes of the referenced CFAR methods are provded as follows. A. CA-CFAR In the CA-CFAR detector, the background level s estmated by the mean power of the samples n the reference wndow, as Z X (2) CA B. GO-CFAR The GO-CFAR method selects the maxmum of the two statstcal values n the leadng and laggng wndow as the background level estmate, whch can be gven by 2 Z 2 max X, X GO 2 (3) C. OS-CFAR The OS-CFAR method uses the estmate of the background level by selectng a sample after a value rank-ordered process. Assumng that the rank-ordered sequence s () (2) ( ) X X X (4) where X () denotes the mnmum and X ( ) denotes the maxmum value n the reference wndow. By selectng a certan order k, the representatonal average background level s ( k ) Z X, k, 2,, (5) OS The nose level representatve rank k s determned by the pre-assgned false alarm rate and the length of the reference wndow. D. CMLD In CMLD, the n largest ranks of the rank-ordered sequence gven n (4) are dscarded from the estmaton of background level, whch can be gven as Z n CMLD n X n (6) Obvously, CMLD works well when the number of nterferng targets s no greater than n. reference wndow P square-law detector X X 2 CUT X 2 X T Multplcaton factor Background level estmator Estmated background level Z target Z Comparator {: 0: no target Fg.. Block dagram of sldng wndow technque.

3 E. TM-CFAR The TM-CFAR detector s often regarded as a generalsaton of the OS-CFAR. In ths detector, the references samples are sorted frstly, as provded n (4). The background level s estmated as a lnear combnaton of the rank-ordered samples, replacng the sample selected by a certan order k. In addton, a total of T samples from the lowest ranks and T 2 samples from the largest ranks are dscarded from the estmaton of background level. Ths process s advantageous for outler rejecton. It s worth mentonng that, however, the number of nterferng targets s also requred to be pror known, showng a smlarty to CMLD. The background level of TM-CFAR s Z T2 X T T 2 (7) TM T, T2 T In addton, t s obvous that the CA-CFAR, OS-CFAR, and CMLD methods are specal cases of the TM-CFAR method. III. THE CAG-CFAR PROCESSOR In ths secton, the prncple of CAG-CFAR detector s provded. Ths method conssts of two procedures: outler rejecton wth Grubbs crteron and detecton threshold estmaton. A. Outler rejecton wth Grubbs crteron The exstence of outlers, sea spkes, nterferng targets n the reference wndow of CFAR detector may lead to an unavodable bas n the estmaton of background level, whch wll greatly affect the detecton performance. Thus, outler rejecton s essental for detecton threshold estmaton n radar system. Typcal crterons for outler rejecton n raw data conssts of Lomnaofsk norm (Student's t test), Grubbs crteron, Dxon crteron, and 3 crteron [2]. In ths paper, the Grubbs crteron s utlsed for outler rejecton, wheren two reasons are consdered: ) Grubbs crteron s feasble when the sample sze s small and 2) the crtcal value s only related to the sample sze and sgnfcant level. Gven the clutter background s unknown n practcal scenaro and the sze of reference s s usually lmted, Grubbs crteron s more approprate n radar applcaton when compared to the others. Assume the elements n a set of measurements sequence S, S2,, S satsfy normal dstrbuton. We form a statstc as S max S (8) where S S denotes the mean value of the raw data. For convenence, we assume that S S from (8). Thus, the sample S j should be dscarded n the orgnal measurement set for data processng f the followng nequalty s satsfed, as j g, 2 ˆ (9) where ˆ S S 2 denotes the estmated standard dervaton of the raw data, g, 2 s the crtcal value whch s determned by the sample sze and sgnfcant level. Crtcal values wth several typcal parameters are lsted n TABLE I. The outler rejecton wth Grubbs crteron wll be repeated on the rest of samples untl no outler s declared. B. Detecton scheme of CAG-CFAR In CAG-CFAR, the background level s estmated by the sample processed by Grubbs crteron n the reference wndow. ote that the Grubbs crteron s establshed based on the assumpton the samples satsfy normal dstrbuton. In exponental-dstrbuted background, the n-phase (I) and quadrature (Q) samples of the complex radar returns are known to satsfy normal dstrbuton wth zero mean and constant 2 varance, thus, the requrement for the applcaton of Grubbs crteron s satsfed. It s reasonable to beleve that f the I or Q sample of a complex radar return appears to be an outler, the resultant ampltude or power after envelope- or square-law detecton wll also behave as an outler. Ths s the man motvaton of the desgn of CAG-CFAR detector. The background level wll be estmated accurately by applyng Grubbs crteron to the outler rejecton n the I and Q samples whch locate n the reference wndow before square-law detecton, respectvely. The smplfed block dagram of CAG-CFAR s llustrated n Fg. 2. Comparng to Fg., ths detector contans an addtonal reference wndows C, and the rest parts of the CAG- CFAR are dentcal to those n Fg.. The reference wndow C n Fg. 2 contans the complex radar returns wth the same order of Fg. before square-law detecton, wheren the I and Q sgnals of each sample are avalable and stored n the subreference wndow marked by CI, and CQ. Ths ndcates that X 2 2,, 2,, I Q. The detaled scheme for background level estmaton of CAG-CFAR detector s as follows: ) Outler ndex recordng: By applyng Grubbs crteron to the I and Q sgnals of reference samples n reference wndow C, respectvely, the ndexes of the potental outlers n correspondng sub-reference wndows CI and CQ are recorded. 2) Outler rejecton: The man purpose s to dscover and elmnate the outler n the reference wndow P for a relatvely accurate estmaton of background level. Gven the ndexes of the potental outlers n I and Q sgnals of reference samples TABLE I. sample sze CRITICAL VALUES OF GRUBBS CRITERIO sgnfcance level

4 square-law detector reference wndow C complex radar return CI n-phase quadrature CQ I I 2 CUT I 2 Q Q 2 CUT Q 2 I Q Grubbs crteron Grubbs crteron Background level estmator Fg. 2. Smplfed block dagram of CAG-CFAR processor (omtted parts are dentcal to Fg. ). are avalable after step ), the samples whch have the same ndexes n reference wndow P are dscarded from the background level estmaton. 3) Background level estmaton: Assume that a total of M samples n reference P should be dscarded, the background level s estmated as the mean value of the rest of M samples. In addton, some comments are provded based on step 2). The sample n reference wndow P should be dscarded f the correspondng I or Q sgnal n reference wndow C s declared to be a potental outler by Grubbs crteron. The outler declaratons n both I and Q sgnals are not requred. Ths ndcates that the ndexes of outlers n reference wndow P s gven by where p CI and CQ CI CQ p p p (0) p denotes the ndexes of outlers n CI and CQ of reference C, and p, 2,, pcq, 2,, CI,. For example, f the 3, 6, and 9-th samples n CI and the 4 and 6-th samples n CQ of reference wndow C are declared to be outlers, the 3, 4, 6, and 9-th samples n reference wndow P should be dscarded from the background level estmaton. IV. PERFORMACE ASSESSMET In ths secton, the detecton performance of the referenced CFAR detectors n multple-target scenaro s nvestgated. We assume that the prmary target, namely the target of nterest, s located n the CUT whle multple nterferng targets appear n the reference wndow smultaneously. The Marcum (nonfluctuatng) target s generated to evaluate the detecton performance of the relevant CFAR detectors n exponentaldstrbuted clutter wthout the addtonal nterference ntroduced by the target fluctuaton. Two representatve scenaros two or more nterferng targets wth the nterference-to-clutter rato (ICR) of 20 db, two or more nterferng target wth same power of the prmary target are consdered. A. Proof of CFAR property In ths subsecton, the CFAR property of CAG-CFAR detector n exponental-dstrbuted background s nvestgated. Owng to the outler rejecton by Grubbs crteron, the analytcal expresson of the PDF of the estmated background level and the correspondng false alarm rate of CAG-CFAR detector are also dffcult to be obtaned. Consequently, the P fa s preferred to be estmated by Monte-Carlo method. The false alarm rates of CAG-CFAR versus multplcaton factors for dfferent dstrbuton parameters are llustrated n Fg. 3. The length of reference wndow s 32 and the guard sze s 3. Three optons of, such as, 0, and 00, are consdered. The sgnfcant level for Grubbs crteron s A total of 9 0 Monte Carlo trals are performed for any combnaton of the dstrbuton parameter and multplcaton factor. Results n Fg. 3 show that the proposed method mantans CFAR property wth respect to snce the curves of P fa wth dfferent dstrbuton parameters concde. A locally enlarged subfgure s provded for better vsual effect. The mnor dfferences between the results wth dfferent parameters are due to the lmted precson of the Monte Carlo smulaton and can be neglected. B. Detecton performance n multple-target scenaro In ths subsecton, the detecton performances of CAG- Fg. 3. False alarm rates of CAG-CFAR for dfferent n exponentaldstrbuted background.

5 (a) (b) Fg. 4. Detecton probabltes wth (a) two nterferng targets and (b) three nterferng targets for ICR = 20 db. (a) (b) Fg. 5. Detecton probabltes wth (a) two nterferng targets and (b) three nterferng targets for ICR = SCR. CFAR, GO-CFAR, OS-CFAR, CMLD, CA-CFAR and TM- CFAR are nvestgated though smulatons. The length of reference wndow s 32 and the guard sze s 3 for each 4 detector. The desred false alarm rate s 0. Wthout loss of generalty, the nose level representatve rank k of OS-CFAR s 24, whch s well suted for practcal applcatons [6]. The number of censored samples for CMLD s and T T2 2 for TM-CFAR; these confguratons reveal that the maxmum acceptable numbers of nterferng targets for CMLD and TM- CFAR are and 2, respectvely. The false alarm rates of the referred compettors have been detaled n the references cted n Secton I. In Fg. 4(a), two Marcum nterferng targets wth the ICR of 20 db are smulated. In ths condton, CAG-CFAR acheves a smlar performance wth TM-CFAR, whch s demonstrated to outperform the other compettors. OS-CFAR also works well whle the CFAR loss s relatvely larger. The performance of CMLD s serously affected snce the correspondng maxmum acceptable number of nterferng targets s only. The detecton probabltes of the CA and GO detectors decrease sgnfcantly owng to the serous maskng effect. If the number of nterferng targets s larger than T 2, however, the detecton performance of TM-CFAR wll also decrease sgnfcantly, as shown n Fg. 4(b) wheren the number of nterferng target s 3. In ths condton, the CAG- CFAR acheves the superor performance when compared to the other compettors owng to ts ndependence to the number of nterferng targets. The outlers, whch ncludes the returns of nterferng targets, wll be dscarded adaptvely by Grubbs crteron wth CAG-CFAR. Gven that the nterferng target number s unknown n practcal scenaro, the dsadvantages of TM-CFAR, OS-CFAR, and CMLD wth pre-assgned confguratons wll be exhbted obvously. In Fg. 5, the ICRs of the nterferng targets are equal to the sgnal-to-clutter rato (SCR) of the prmary target. The numbers of nterferng targets n Fg. 5(a) and (b) are 2 and 3, respectvely. Ths condton wll ntroduce the most serous maskng effect because the powers of the nterferng targets are dffcult to be averaged unless the length of reference wndow s suffcently large, whch s usually dffcult to be satsfed n practcal scenaro. Results n Fg. 5 exhbt smlartes to Fg. 4, whle the CA-CFAR, GO-CFAR detectors are saturated n varyng degrees. When the nterferng target number reaches 3, the CAG-CFAR s demonstrated to be optmal n these methods. The robustness and effectves of CMLD and TM- CFAR wth napproprate pre-assgned confguratons wll degraded sgnfcantly, as shown n Fg. 5(b). ote that the OS- CFAR works robustly n these scenaros because the correspondng background level s estmated by the k -th sample n the reference wndow. In ths condton, the robustness and the ablty of ant-nterferng targets of OS- CFAR are enhanced whle the CFAR loss wll accordngly ncrease. C. Results analyss and dscusson TABLE II provdes the SCR mprovement of the proposed method compared to the OS-CFAR detector, whch s demonstrated to work robustly n multple-target scenaro. The results of GO-CFAR, CMLD, CA-CFAR, and TM-CFAR are also provded for better comparson. Wthout loss of generalty, we set the requred SCR to satsfy the detecton probablty of 0.85 as the reference. Four condtons marked by Stuaton (Stu.), 2, 3, and 4 represent the scenaros of Fg. 4(a), Fg. 4(b), Fg. 5(a), and Fg. 5(b), respectvely. The results n Table II valdate the superorty of the proposed method, especally under the multple-target scenaro. In addton, the computatonal costs of the referenced detectors are nvestgated quanttatvely, as shown n TALBE III. Wthout loss of generalty, the processor cycle count, whch TABLE II. SCR mprovement (db) TABLE III. SCR IMPROVEMET OF REFERRED CFAR METHODS WITH RESPECT TO OS-CFAR Stuaton Stu. Stu. 2 Stu. 3 Stu. 4 CAG GO nf a -nf CMLD CA nf TM a. nf denotes the nfnte, namely the correspondng target s mss-detected. COMPUTATIOAL COMPLEXITIES OF REFERRED CFAR DETECTORS Processor cycle count b CA GO OS CMLD TM CAG b. The processor cycle count s calculated based on the TgerSHARC archtecture of Analog Devces, Inc.

6 s drectly related to the computatonal burden of a certan algorthm, s calculated based on the TgerSHARC dgtal sgnal processor (DSP) produced by Analog Devces, Inc. The processor cycle count s able to provde an objectve evaluaton of the computatonal complexty owng to ts ndependence of the speed of DSP chp. Results show that the result of CAG- CFAR s smlar to those of CA-CFAR and GO-CFAR. Ths result reveals that the CAG-CFAR acheves hgh effcency when compared to others owng to the relatvely small processor cycle count. Concludng, the CAG-CFAR outperforms the rest of the compettors by takng the detecton performance nto consderaton. V. COCLUSIO In ths study, the authors propose a modfed averagng CFAR detector for multple-target scenaro based on Grubbs crteron. The outlers n the reference wndow are dscarded automatcally by Grubbs crteron, thus, the background level s able to be estmated accurately. The CAG-CFAR detector s demonstrated to mantan CFAR property wth respect to the dstrbuton parameter n exponental-dstrbuted background va Monte Carlo smulatons. The proposed method does not requre a pror knowledge of the number of nterferng targets, achevng a robust detecton performance wth a low computatonal burden. Quanttatve performance evaluatons verfy the effectveness and superorty of the proposed method when compared to several relevant compettors n multpletarget scenaro wth an unknown number of nterferng targets. Gven the complextes of unknown nterferng targets, such as number and magntude, the CAG-CFAR detector s predcted to be feasble and advantageous n practcal scenaro, such as sea clutter where the sea spkes occur. Future study s requred to nvestgate the performance of CAG-CFAR detector n stuatons of clutter edges. 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