Collision Target Detection Using a Single Antenna for Automotive RADAR

Transcription

1 Collision Target Detection Using a Single Antenna or Automotive RADAR Souleymane Abakar Issakha, Francois Vincent, Laurent Ferro-Famil, Frantz Bodereau To cite this version: Souleymane Abakar Issakha, Francois Vincent, Laurent Ferro-Famil, Frantz Bodereau Collision Target Detection Using a Single Antenna or Automotive RADAR International Radar Symosium (IRS) 7, Jun 7, Prague, Czech Reublic Proceedings the International Radar Symosium (IRS) 7 <hal-55573> HAL Id: hal htts://halarchives-ouvertesr/hal Submitted on 4 Jul 7 HAL is a multi-discilinary oen access archive or the deosit and dissemination o scientiic research documents, whether they are ublished or not The documents may come rom teaching and research institutions in France or abroad, or rom ublic or rivate research centers L archive ouverte luridiscilinaire HAL, est destinée au déôt et à la diusion de documents scientiiques de niveau recherche, ubliés ou non, émanant des établissements d enseignement et de recherche rançais ou étrangers, des laboratoires ublics ou rivés

2 Collision Target Detection Using a Single Antenna or Automotive RADAR S ABAKAR ISSAKHA *, F VINCENT **, L FERRO-MIL ***, F BODEREAU * * ZF-TRW AUTOCRUISE SAS, Brest, FRANCE {SouleymaneAbakarissakha; FrantzBodereau}@zcom ** University o Toulouse, France FrancoisVincent@isaer *** University o Rennes, France LaurentFerro-Famil@univ-rennesr Abstract: The goal o most modern automotive saety driver assistance unctions is to avoid ossible collisions Pedestrian rotection, redictive emergency braking or turn and crossing assist unctions are usually based on two stes First, the radar rovides detailed inormation on the environment, and then a detection rocedure is driven Because o the comlicated environment near the vehicle, this second ste is a diicult task to achieve in order to give reliable inormation to the driver In this aer, we roose to use the environment estimation and the detection ste into a simle and direct collision target detector Indeed, this rocedure allows detecting ossible collision targets, based on their tyical Doler signature, while rejecting all ixed and non-dangerous targets (clutter) Moreover, this detector only exloits a single antenna, and the necessary target seed vector inormation is obtained by a second order hase exansion using a long integration time, making the use o an antenna array unnecessary Introduction Among the dierent kinds o sensors develoed to imrove vehicle saety and autonomy, radar aears to be a solution o choice because o its all-weather oerating caability [] In addition, radar systems are easy to integrate on a car as they can be installed behind the bumers [] With new Euro-NCAP rocedures now requiring automated braking and edestrian saety unctionality, modern Advance Driver Assistance Systems (ADAS) need to give recise and reliable environment inormation The common scheme to achieve such a collision detection system is erormed in two stes First, the radar rovides a high resolution range, seed and Direction o Arrival (DoA) ma and then a detection ste is erormed to alert the driver o any ossible collision This last decision ste is not an easy task because o the comlicated environment surrounding the vehicle In this aer, we roose to adat a collision detection rocedure develoed or airborne radar in [3] to the seciic case o automotive sensing and we roose an otimal rocessing architecture This detector exloits a long integration time to imrove the seed vector estimation Hence, as it is done in Synthetic Aerture Radar (SAR), and using a second order exansion o the received signal hase, one can both estimate the radial and orthogonal, ie tangent, velocity vector comonents [3] It is then ossible to discriminate dangerous targets rom the others Indeed, all collision targets have a null orthogonal velocity comonent, with resect to the radar as oosite to non-dangerous targets whose orthogonal velocity is linked to their radial seed and angular osition A matched detector can be develoed in order to detect only collision targets while rejecting the main art o the clutter, ie the one having a non-null orthogonal velocity comonent This rocedure allows using all the rocessing stes into a single one but above all, only The 8th International Radar Symosium IRS 7, June 8-3, 7, Prague, Czech Reublic DGON

3 requires a single antenna as oosite to most advanced systems requiring an antenna array to estimate the DoA This direct collision target detection rocedure can then allow develoing low-cost ADAS systems This aer is organized as ollows Section introduces the data model used to deine the collision and intererence subsaces Then, in section 3, the detector is develoed and simulation results are resented in section 4 Section 5 describes theoretical erormances and inally, a ossible rocessing architecture is given in section 6 Data Model An automotive radar system moving at constant velocity vc is considered, as shown on Fig A ossible collision target at range d with constant velocity v t is heading toward the car u to an imact oint Other static targets are also resent at the same range d Figure : Static targets and collision target at range d For a target located at a suiciently large distance rom the radar, the target-radar distance may be aroximated using a second order Taylor series exansion as [3]: d ( t ) d + vr t + ar t + d v () where d is the initial osition o the target, v r and a r are resectively the relative radial velocity and acceleration, and v is the orthogonal velocity o the target In this aer, we only consider constant radial velocities, ie a r = Among all ossible values o v r and v, collision targets and non-dangerous ones belong to dierent subsaces Indeed, on may discriminate the ollowing categories o targets Static targets (clutter), whose two comonents o the relative seed vector may be written as a unction o the car velocity v c and o the target angular osition θ as vr = v c cosθ and v = vcsinθ Collision targets, characterized by v =, with an angular osition that remains constant as the radar moves One may remark that static targets located at θ =, ie right in ront o the car are indeed correctly considered as collision targets Moving, but non-dangerous targets, with,v v t

4 The radar considered here eriodically emits and receives signal, with a Pulse Reeat Interval (PRI) T r, whose ocusing in distance leads to a maing o the scene relectivity with a given range resolution δd Assuming a suiciently large range resolution value or a riori comensation o range cell migrations, the range ocused resonse o a moving target contained within a range resolution cell may be written, using the hase model exressed in () and or an arbitrary ulse occurrence m as: j( a + amtr + am Tr s (m) = αe ), with m M () 4πd where α is the target comlex resonse ater range ocusing, a =, with λ the carrier λ 4π wavelength, a v r π = = D is the sloe o the linear hase rotation due to v r and may be λ πv related to Doler requency D, a = is the quadratic term coeicient due to v λd Hence or long enough integration time(m )Tr, the term a can be exloited to estimate the target orthogonal velocityv Given this model, two dierent subsaces may be constructed based on the seed characteristics stated beore - The Collision Target Subsace: As seen beore, a collision target is characterized by a null orthogonal seed comonent, ie, a = As a consequence, ater range rocessing, the signal samled over M PRIs, within a given resolution cell, and originating rom a otential collision target can be written as ollows: x = h(a )α C M (3) ja Tr ja (M )Tr T where a and α are unknown, and h (a ) = [,e,,e ] is the target Doler hase evolution, that is a ure tone (without second order hase rotation) - The Static Target Subsace: As stated reviously, static targets have radial and orthogonal velocity comonents that deend on the radar velocity and on their angular osition Hence, the clutter resents in a range cell located at a distance d rom the radar may be reresented by a sum o comonents having random comlex resonses and ollowing a given hase model: c = Sβ (4) where β C P reresents the corresonding comlex and unknown resonses o the S s s P C M P with j( a ( v ) M T a ( v ) M T [ ] T c, θ ( ) r + c, θ ( ) r ) s =,, e the corresonding signature characterized by 4πv c cosθ π a ( vc, θ ) = and ( ) ( vc sinθ ) ² a vc, θ = λ λd The angular osition at which is observed a scatterer belongs to a domain whose limits are ixed by the scattering attern o the radar antenna, ie θ θ scattering that comose the clutter, and = [ ] b 3

5 3 Matched Detector A classical way to state the collision target detection roblem is based on the ollowing binary hyothesis test [4]: H : y = b H : y = hα + b (5) whose Maximum Likelihood leads to the so called matched detector, when the noise term b is assumed to ollow a Gaussian distribution and to be white in time, with a known ower: 4 H < T = y P y η (6) MD H hh where P h = is the rojection matrix onto the signal subsace and H the conjugate H h h transose oerator As h is a ure tone, it is straightorward to show that this detector simly consists in the square modulus o the Fourier transorm o the data Nevertheless, the restriction o the nuisance terms to a Gaussian white noise leading to the revious matched detector may be considered as a very strong hyothesis To be more recise, we can decomose the intererence term into a clutter art, whose resonse model is mentioned above, and a Gaussian white background noise n Moreover, as seen beore, the Doler signature o the clutter is signiicantly dierent rom that o a collision target, and this dierence may be used to urther discriminate these tyes o contribution, leading to a modiied binary hyothesis test [5]: H : y = Sβ+ n (7) H : y = hα + Sβ+ n However, even i the Doler signatures o the clutter and target subsaces are dierent, they overla in the ront region o the radar, as the orthogonal seed o the clutter tends to zero In other words, in ront o the radar, the clutter becomes a collision target too To revent a ossible ambiguity, we limit the clutter subsace to the side-regions rom the radar Hence, the column o S are constructed rom angular ositions θ belonging to [ θ θ ] and b [ θ θb ], where θ corresonds to a blanking angle This minimum angle needed to distinguish a static target rom a collision one can be estimated rom the second order hase exension term as it is the dierence between the hase signatures o collision and static targets: vc sin θ Δ ϕ = π t (8) λd The minimum blanking angle value θ is chosen so that the quadratic hase term in (8) equals π For such a value, it is exected that the two signatures may be searable (by a correlation rocessing, or instance) The minimum angle needed to dissociate the two subsaces is then deined as: λd θ = sin (9) D D = v M T is the synthetic antenna size where c ( ) r h >

6 It can be noticed that this minimum angle is inversely roortional to the square o the synthetic antenna size, and also deends on range Fig shows the evolution o this minimum angle as a unction o the target range or dierent synthetic antenna sizes and or a radar oerating at 77 GHz Obviously, the longer the antenna size, the better the subsace searation with a rice to be aid or this imrovement reresented by a longer detection duration and ossibly incomatible with the saety and braking requirements Nevertheless, rom Fig, we can see that D = m oers a good comromise, as it corresonds to a dislacement o hal a standard car length (or a signal duration o 44ms or v c = 5km / h ) which seems to be comatible with warning alerts, while limiting the minimum angle or searation to or ranges u to 5 m Figure : Minimum Angle to searate a collision target rom the clutter Now, based on the modiied binary hyothesis test rom (7), and assuming that n is a white gaussian noise with known variance, we can calculate the corresonding Generalized Likelihood Ratio Test (GLRT) [4][5]: H < T = y P y γ () where MMD h > y = P y and h = P h are the rojections o the data and target signature onto the S S P S H H subsace orthogonal to the clutter subsace I S( S S) S = Once again, the roosed rocessing consists in a modiied Fourier transorm as both the data and the target signature have to be rojected onto the subsace orthogonal to the clutter beore to be correlated 4 Simulation Results The goal o this art is to exhibit the sueriority o the roosed detection scheme comared to the classical Doler based one, on a simle examle We consider a waveorm with a carrier requency o = 77GHz, a bandwidth o B 75 = MHz and a PRI o T r = 5μs In this scenario, we consider that the radar is moving at v c = 5km / h, and a collision target aroaching erendicularly at v t = 5km / h rom an initial osition characterized by 5

7 d = m and θ = 3, as indicated on Fig The clutter is also at d = m with a clutter to noise ratio o CNR = 5dB The Signal to Clutter lus Noise Ratio is SCNR = db We consider an integration time o 44 ms corresonding to a synthetic antenna size o D = m As stated beore, the classical and roosed detection schemes corresond to Fourier or modiied Fourier transorms Fig 3 reresents the corresonding test values or each Doler requency hyothesis We can see that the classical Doler rocessing cannot detect the collision target as its Doler resonse is drown into the clutter one On the other hand, the roosed detection scheme allows to clearly detect the target (a) FFT beore detector (b) FFT ater detector Figure 3: Doler requency beore and ater target detector 5 Theoretical Perormances This art aims at comaring the theoretical erormances o the roosed detector comared to the classical Doler-based one To this end, we calculate the Probability o Detection ( P D ) o each detector or a given Probability o False Alarm ( P ), varying the Signal to Clutter lus Noise Ratio (SCNR) The two detectors having the same orm, it is straightorward to show that they are chisquared distributed under each hyothesis [5] [7] [8] [9] []: 6 T where ( ) MD ( y) χ : χ ( δ ) () under H under H and T ( y) MMD χ : χ ( δ ) () under H under H χ is the central chi-square distribution, χ ( δ ) and ( δ ) are the noncentral chisquare distributions, is the number o degree o reedom, δ μ μ T = and δ = h P h S σ σ are noncentrality arameters, wih μ and μ are resectivly the mean o signals due to (5) and T (7), σ and σ are resectivly the variannce due to (5) and (7), h PS h is the rocessing loss due to the oblique rojection Hence or a given P (or examle P = 6 ) we can comute the corresonding thresholds using ollowing relations: P P T > η P = P T > γ () = [ ] and [ ] MD H MMD H χ ()

8 Then the Probabilities o Detection P D can be comuted Fig 4 shows that the P D o the roosed detector is largely better than the classical detector or all SCNR values Figure 4: Probability o detection versus SCNR beore and ater detector 6 Processing Architecture Based on the revious analysis, we can now roose a ossible rocessing architecture or the collision target detector on Fig 5 As stated beore, to maintain a synthetic antenna length o D = m, we have to adat the integration time to the vehicle seed v c Moreover, or simlicity considerations, we have chosen a limited bandwidth o B = 75MHz comatible with the Doler rocessing without range migration comensation For D = m, T r = 5μs, v c = 5km / h and d = m, we can set some arameters such as: the integration time D D Tint = =44ms, the corresonding number o rams M = = 5 v v T and the blanking c c r angle θ = 5 66 Figure 5: Simliied architecture or the roosed Automotive Collision Detector 7 Conclusion In this aer, we have adated a collision target detector develoed or airborne radar to the automotive domain and we roosed a rocessing architecture comatible with its seciic requirements This rocessing rovides a direct detection scheme or ossible collision targets while automatically rejecting the clutter The main advantage o such a detector is that it only exloits a single antenna and could be considered as a solution o choice or low-cost ADAS systems This rocessing requires a longer integration time comared with classical automotive radar but is suitable with modern rocessing units 7

9 8 Reerences [] H Rholing, S Heuel, H Ritter, Pedestrian Detection Procedure integrated into an 4 GHz Automotive Radar, IEEE Radar, Washington DC, May [] F Kruse,F Folster, M Ahrholdt, H Rohling, M Meinecke Target Classiication Based on Near- Distance Radar Sensors, IEEE Intelligent Vehicles Symosium University o Parma, Italy, 7-77 June, 4 [3] P Goy, F Vincent and J-Y Tourneret, Clutter rejection or MTI radar using a single antenna and a long integration time, 4 th IEEE Worksho on Comutational Advances in Multi-sensor Adative Processing, , [4] R T Behrens and L L Schar, Signal rocessing alications o oblique rojection oerators, IEEE Trans Signal Process, vol 4, no 6, 43 44, June 994 [5] L L Schar and B Friedlander, Matched subsace detectors, IEEE Trans Signal Process, vol 4, no 8, 46 57, Aug 994 [6] Christian Walck, Hand-book on STATISTICAL DISTRIBUTIONS or exerimentalists, internal reort, University o Stockholm, December 996 [7] Arthur H M Ross, Algorithm or Calculating the Noncentral Chi-Square Distribution, IEEE TRANSACTIONS ON INFORMATION THEORY, VOL 45, NO 4, , MAY 999 [8] Fredrik Gustasson, Adative iltering and change detection John Wiley & Sons, [9] Thomas D Wickens, Elementary Signal Detection Theory, University o Caliornia, Los Angeles, Oxord University Press, [] Steven M KAY, Fundamentals o Statistical signal rocessing, Volume II: Detection theory, University o Rhode Island, Prentice Hall PTR, 993 8