Real time IMMPDAF algorithm has been implemented and tested in LabVIEW. Single aircraft flight profiles have been simulated  and the plot data from multiple radars observing the single aircraft are generated with noise as well as clutter. The performance of the algorithm is evaluated using standard procedures. Since it is implemented and tested in LabVIEW, this algorithm can be easily realized in hardware for real time tracking applications

Girija, G

Naidu, VPS

English

NAL-IR

Implementation of IMMPDAF Algorithm in LabVIEW for Multi Sensor Single Target Tracking

National Aerospace Laboratories Institutional Repository

(Implementation of IMMPDAF Algorithm        inLabVIEW for Multi Sensor Single TargetTrackingVPS Naidu and Girija G.Abstract—Real time IMMPDAF algorithm has been implemented and tested in LabVIEW. Single aircraft flight  profiles  havebeen simulated  and the plot data from multiple radars observing the single aircraft are generated with noise as well as  clutter.  Theperformance of the algorithm  is  evaluated  using  standard  procedures.  Since  it  is  implemented  and  tested  in  LabVIEW,  thisalgorithm can be easily realized in hardware for real time tracking applications.Keywords—IMMPDAF, Target tracking, IMM and LabVIEW. INTRODUCTIONTARGET tracking problem is more difficult task if the target is maneuvering. Insensitivity of the  Kalman  filter  to  trackthe target whose behavior pattern keeps on changing with time has long been  acknowledged  and  wide  selections  ofmethods have been developed to identify maneuvers and change the filter consequently [1].  An  innovative  approachcalled the Interacting Multiple Model Kalman Filter (IMMKF)  has  been  developed  that  seems  to  present  superiorperformance to other approaches for  maneuvering  target  tracking  [2-5].  The  IMMKF  uses  several  target  motionmodels (i.e. constant velocity, constant acceleration, co-ordinate turn model etc.) and has been successfully applied  totrack large maneuvering targets.In this paper, plot data from three sensors/radars whose  detection  probabilities  are  less  than  unity  which  inturnresults in clutter are used to track a single aircraft executing a figure of eight in x-y plane. Data  association  is  criticalwhen the detection probability is less than unity in  the  presence  of  clutter  or  false  alarm.  One  simple  solution  isnearest  neighbor  filter  [6].  This  fails  when  the  false  alarm  rate  increases   or   one   encounter   low   observablemaneuvering target. To solve this problem, all measurements within a gate are used instead of only one  measurementresulting  in  probabilistic  data  association  filter  (PDAF)  technique.   In  this  paper   an   IMMPDAF   which   is   acombination of IMMKF with PDAF is used to track the target.  IMMPDAF algorithm  is  implemented  in  LabVIEWand tested for tracking a single aircraft using plot data coming from multiple sensors. Once the IMMPDAF  algorithmis validated in LabVIEW, it can be easily realized in hardware for real time tracking applications.IMMPDAF ALGORITHMIn this section the algorithmic detail of IMMPDAF which is a combination of IMMKF and PDAF is given.Probabilistic Data Association [6,7]The PDAF algorithm calculates the association probabilities for each valid measurement at the current time to thetarget of interest. This probabilistic information is used in a tracking filter (PDAF) that accounts for the  measurementorigin uncertainty. If there are m measurements falling within the gate at time and it is assumed that there is  only  onetarget of interest and track has been initialized, the association events ={is the target originated measurement},{none of the measurement is target originated},are mutually exclusive and exhaustive for . The probability that the valid measurement is target originated is,                        (1)The probability that none of the measurements is target originated, defined as                             ,                           (2)where ,is the innovation for the validated measurement, is the innovation covariance, is the spatial  density  of  the  clutter,  isthe detection probability  andis  the  detection  probability  of  the  target-originated  measurement  falling   inside  thevalidation regionThe combined innovation is                            (3)This combined innovation is added to the predicted measurement to get valid measurement.IMM AlgorithmIMM uses several possible models for target’s motion and a probabilistic switching between  these  models.  It  isimplemented with multiple parallel filters, where each of the filters corresponds to one of the assumed models. Duringeach sampling period, all the filters in the IMM are in operation. The overall state  estimate  is  a  combination  of  theestimates from the individual filters. The LabVIEW implementation of IMM algorithm is shown in Fig-1.Mixing and InteractionFor the event , the mixed estimate and the covariance are computed as                         (4)         (5)The mixing probabilities are given by                     (6)where the predicted mode probability is computed byThe mode switching process is specified by the following transition probabilities, where denotes the probability of  anevent, which means is the probability that model at instant is switching over to model at instant.Kalman FilterKalman filter is used with appropriate target motion  models  to  update  the  mixed  state  estimates  with  currentmeasurement. Separate filters are used for each mode. In  each  filter,  the  predictive  part  consists  of  the  followingequations:Predicted state:    (7)Predicted measurement:  (8)Predicted state covariance:     (9)Innovation covariance:        (10)The measurement update part consists of the following equations:Filter gain:                               (11)Innovation:                          (12)Updated state estimate:                 (13)Updated state covariance:             (14)Mode Probability UpdateThe likelihood function for matched filter is Gaussian density function of innovation  with zero mean and covariance.It is computed as       (15) where denotes the dimension of the innovation vector .The mode probability is updated using likelihood’s and the predicted mode probabilities  for .                                (16)where the normalization factorState Estimate CombinerFinally the estimated states  and covariance  from each filter  are  combined  using  the  updated  mode  probability  toproduce overall state estimate  and the associated covariance.         (17)                                                                                             (18)PLOT DATA SIMULATIONSingle fighter aircraft trajectory is simulated and the plot data of respective tracking  radars  are  generated  to  testthe  tracking  algorithm.  Initially  the  aircraft  trajectory  is  simulated  w.r.t  reference  point  (latitude:;  longitude:  ;altitude:) in local ENV (East-North-Vertical) frame at constant height (100m) using:• constant velocity model during straight and level flight• coordinated turn model during the turning phase of the flight [6]Then based on the sensors specifications (i.e. location and its attributes), sensor models are built to transform thesimulated aircraft trajectories into plot data.Aircraft Trajectory SimulationThe  aircraft  trajectory  is  simulated  (with  2  seconds  sampling  interval)  in  local  ENV  frame  using  discretekinematic model,                                                             (19)where : vector of target states, : state transition matrix, : model index, : discrete time index and : total number of datapointsThe state vector  consists of position and velocity of the target (aircraft) in X and Y coordinates of ENV  frame  as   atkth scan. where, : position of target in coordinate (m), : velocity of  target   in   coordinate  (m/s),  :  position  of  targetincoordinate (m), : velocity of target in coordinate (m/s) and  turning rate of the target (rad/sec)The state transition matrix for the non-maneuvering phase is:And for the turning phase [6]In present simulation, the angular rate  is taken as 0.2618 rad/sec (i.e.150 deg/sec).  For  left  turn  (LT),  is  consideredpositive and for right turn (RT)  is considered negative. T is the  sampling  interval  and  is  taken  as  2  seconds.  Theinitial state vector and way points (turns) of aircraft are given in Table 1.Sensor ModelThree sensors (radar-1, radar-2 and radar-3) are modelled to get the plot data using  the  information  provided  inthe Table 2. The radar characteristics are representative of some radars used in  tracking  for  air  defense  application.Sensor-1 outputs i.e. azimuth, elevation and range are shown in Fig-2.Data ConversionSince association requires the measurements from different sensors to be in common reference frame, the aircrafttrajectory in ECEF frame is transformed to ENV frame w.r.t. sensor location as:(20)The subscript  indicates the sensor reference.RESULTS AND DISCUSSIONImplementation of IMMPDAF algorithm in LabVIEW is shown in Fig-3. The measurements from the three sensorsat each scan are concatenated and used in measurement updation stage. The converted  measurements  that  enter  intothe tracking algorithm are shown in Fig-4. The true and estimated target trajectories are shown in Fig-5. It is observedthat the estimated trajectory is very close to the true trajectory even in dense clutter that shows  the  robustness  of  theIMMPDAF. The performance of the tracking algorithm is evaluated using  standard  procedure.  It  is  found  that  thetracking algorithm is robust and the results are not presented here due to space constraints.CONCLUSIONReal time IMMPDAF algorithm has been implemented and tested in LabVIEW. Single aircraft flight profiles  havebeen simulated and the plot data from multiple radars observing the single aircraft are generated with noise as well  asclutter.   Since it is implemented and tested in LabVIEW, this algorithm can be  easily  realized  in  hardware  for  realtime tracking applicationsREFERENCES1] X. Rong Li and Vesselin P. Jilkov, “Survey of Maneuvering Target Tracking. Part  I:  Dynamic  Models”,  IEEE  Trans.  on  Aero.  and  Elec.Sys., Vol.39(4), pp.1333-1364, Oct. 2003.2] Bar-Shalom.Y and Xiao Rong Li, Multitarget - Multisensor Tracking:  Principles and Techniques, 1995 (ISBN 0-9648312-0-1).3] Blom, H.A.P, and Bar-Shalom.Y, “The Interacting Multiple Model Algorithm for Systems  with  Markovian  Switching  Coefficients”,  IEEETrans. Aut. Con., vol AC-33, pp780-783, Aug 1988.4] E. Mazor, A. Averbuch, Y.Bae-Shalom and J.Dayan, “Interacting Multiple  Model  Methods  in  Target  Tracking:  A  Survey”,  IEEE  Trans.Aero. Elec. Sys., vol.34, pp103-23, 1998.5] Iliyana Simeonova and Tzvetan Semerdjiev, “Specific Features of IMM Tracking Filter Design”,  Information  &  Security,  An  InternationalJournal, vol.9, pp154-165, 2002.6] Samuel Blackman and Robert Popoli, Design and Analysis of Modern Tracking Systems,  Artech House, London, 1999.7] Bar-Shalom Y. and E. Tse, “Tracking in a Cluttered Environment  with  Probabilistic  Data  Association”,  Automatica,  Vol.  II,  pp.451-460,1975.VPS Naidu was born in Andhra Pradesh. He obtained M.E. in Medical    electronics from  Anna  University  Chennai  in  1997.  He  is  working  atNational Aerospace Laboratories, Bangalore as scientist since December   2001. His areas of interest are: image registration, tracking and fusion.Dr. (Mrs.) Girija G,  received  her  Ph.D.  from  Bangalore  University  in  1996.  She  is  presently  working  as  Scientist  at  National  AerospaceLaboratories (NAL), Bangalore. Her areas of research are: modeling, parameter estimation of aerospace vehicles and multi sensor data  fusion.  Sheis a recipient of NAL Foundation Day Award for Research in the year 1995. She  has  published  about  50  research  papers.  She  is  a  member  ofAeronautical Society of India.VPS Naidu is with the Multi Sensor Data Fusion Lab, Flight Mechanics and Control Division, National  AerospaceLaboratories,   Bangalore-17,   India   (phone:    91-080-25086536;    fax:    91-080-25298293;    e-mail:    vpsnaidu@css.nal.res.in).Girija G., is with the Multi Sensor Data Fusion Lab, Flight Mechanics and  Control  Division,  National  AerospaceLaboratories, Bangalore-17, India, (e-mail: girijag@css.nal.res.in).-------------------------------------------TABLE IISENSOR SPECIPICATIONS|                |SPECIFICATIONS     |SENSOR-1    |SENSOR-2     |SENSOR-3     ||SENSOR LOCATION |LATITUDE           |------      |--------     |-----------  ||IN WGS-84 FRAME |                   |            |             |             ||                |LONGITUDE          |-------     |--------     |-----------  ||                |ALTITUDE           |0 M         |0 M          |0 M          ||ACCURACIES      |AZIMUTH            |0.0880      |0.0880       |0.330        ||                |ELEVATION          |0.0880      |0.0880       |0.330        ||                |RANGE              |120 M       |120 M        |250 M        ||FIELD OF VIEW   |Azimuth            |            |             |             ||                |Elevation          |            |             |             ||                |Range              |Km          |Km           |Km           ||Detection       |                   |0.9         |0.8          |0.5          ||probability     |                   |            |             |             ||False alarm rate|                   |10-10       |10-10        |10-11        |,, are standard deviations of azimuth, elevation and range respectively,  is detection probability,  is false alarm,  ,   ,areazimuth, elevation and range FOV max. and min. respectivelyFig. 1 IMM algorithm in LabVIEWTABLE ITARGET INITIAL STATE VECTOR AND WAYPOINTS|INITIAL STATE VECTOR               |WAY POINTS  (X,Y) IN KM                       ||                                   |                                              |IS A STATE VECTOR,  IS LEFT TURN AND RIGHT TURNFig. 2 Sensor outputs in azimuth, elevation and rangeFig. 5 Estimated target trajectory using IMMPDAF tracking algorithmFig. 4 Converted measurements that enter in to the tracking algorithmFig. 3 IMMPDAF algorithm implemented in LabVIEWFig. 5 Estimated target trajectory using IMMPDAF tracking algorithm

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Implementation of IMMPDAF Algorithm in LabVIEW for Multi Sensor Single Target Tracking

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