My presentation in MST -11 International Workshop

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  • 1. Adaptive clutter rejection by DOA tracking using unscented filters for atmospheric radars By Dr. C.Vijaykumar and Arpit Gupta Dhirubhai Ambani Institute of Information and Communication Technology Gandhinagar, Gujarat
  • 2.
    • Introduction to Problem
    • Clutter Rejection method for Atmospheric Radars
    • DOA Estimation using Differential MUSIC
    • DOA Update using Unscented Kalman Filter
    • Clutter Rejection Algorithm
    • Simulation Results
    • Conclusions
    Organization of the Presentation
  • 3.  
  • 4. Introduction to Problem
    • Clutter Removal Stationary as well as Moving
    • Currently done by
    • Offline or using adaptive filtering
    • Assuming either the noise or signal spectra
    • Applying filter based on above assumptions
    • Adaptive antenna technique makes no assumption on signal spectra.
    • We applied high resolution estimation techniques and subsequent kalman filtering technique to suppress the clutter
  • 5. DOA Estimation Procedure
    • 1. Compute the auto covariance matrix R from the data vector.
    • 2. Compute the difference matrix
    • where E is the MxM exchange matrix.
    • where S is signal covariance matrix, Q is the unknown noise spatial covariance matrix and A is the array direction matrix
    • 3.Perform the eigen decomposition of the matrix D.
    • 4. Estimate the DOA’s using the psuedo power spectrum using MUSIC .
    • 5. Differential MUSIC : It gives the signal direction even when signal and noise are spatially correlated [1].
  • 6. DOA Update using Unscented Kalman Filter
  • 7. State Space Model
    • System dynamics are non-linear functions of the system states.
    • Moving Source is modeled based on velocity model
    • System states for this case becomes
    • X (n) = [ X r Y r U r V r ] T = [ X/r Y/r U/r V/r] T
    • where X r and Y r are rectangular co-ordinates of the target
    • Range r = sqrt (X 2 + Y 2 ),
          • U = x-velocity, V= y-velocity, T = sampling time period
  • 8. State Space Model cont .. v (n) and w(n) are independent zero mean Gaussian noise vector for State space model and Measurement model with vector size 4*1 and 1*1 respectively Corresponding Measurement model is given by Θ (n) = arctan[ y(n) / x(n) ] + w(n)
  • 9. Unscented Transform
    • Instead of linearizing the non linear function, sample the density function of the present state and propagate the samples and build the next state [2].
    • Sigma Points: Points are chosen to match mean and covariance of the random variable. (2n+1) sigma points are needed to represent the vector of n-length.
  • 10.
    • 1.Find 2n+1 (9) sigma points (  i ) from the initial estimate of state vector (Where n is the size of the state vector)
    • 2.Transform the sigma points through non-linear measurement model,
    DOA Tracking – Unscented Kalman Filtering x i (k +1 / k) = f [x (n), y (n), Vx (n), Vy (n)]
  • 11.
    • 3. Prediction of the state estimate at time (k+1) with the measurement up to time k is given by,
    • 4. The predicted covariance is given as
    • 5. Transform each of the prediction points using measurement model
    • Where T is the inverse of matrix in state space model
  • 12.
    • 6. Predicted Observation
    • 7. Calculate Kalman Gain as
    • W(k+1)=P XZ (k+1/k) P YY (k+1/k)
    • P YY (k+1/k) is Innovation Covariance
    • 8. State update after the measurement is given by
  • 13.
    • 9. Update of the error covariance is
    • P(k+1/k+1 ) = P (k+1 / k) - P YY (k+1/k) W(k+1) T
    • 10. Follow the same process for each time step.
    • 11. If the magnitude of error covariance increases successively for each time step. We classify that source as stationary source.
    • 12. Moving source - DOA update given by kalman filter at each time step
    • Stationary source - DOA is measure given by Differential MUSIC algorithm
  • 14. Clutter Rejection Method
    • DCMP-CN algorithm
    • proposed by Sato, T.
    • [3]
    • Additional Constraints
    • N s is the direction of s th clutter being reported at each time step by unscented filter for moving clutter or DOA estimate given by MUSIC algorithm for stationary clutter
  • 15. Weight Vector Calculation Algorithm
  • 16.
    • Simulation
    • 1. Four fully coherent sources are simulated. One is stationary, and its multipath and two are moving objects. The signals were corrupted by spatially colored noise with an unknown covariance matrix.
    • 2. These sources radiate electromagnetic energy and are received by a LES radar array of size n=625 with inter-element spacing of λ/2, where λ is the wavelength of the received signal.
    • 3. Initial DOA's are θ 1 (n i ) = 40, θ 2 (n i ) = 70 and θ 3 (n i ) = 25 and θ 4 (n i ) = 35. θ 2 denotes the multipath of first source. Θ 3 and θ 4 denotes the DOA of moving objects.
  • 17. Measurements ANGLE INDEGGREES ANGLE IN DEGGREES
  • 18.  
  • 19. CONCLUSIONS
    • 1. DOA estimation is done by differential MUSIC. This gives high resolution estimates than simple FFT based algorithms
    • 2.The proposed algorithm gives better state estimation of moving objects
    • 3.Thus the proposed algorithm results in effective sidelobe canceling for atmospheric radars.
    • 4. We would validate the proposed algorithm with NARL active phased array radar data, expected in March, 2007.
  • 20. References
    • R. Rajagopal & P.R. Rao: "A Generalized Algorithm for DOA Estimation in Passive Sonar", IEE Proc. Part F, Vol. 150. No. 1 Feb 1993. pp. 12-20.
    • Simon J. Julier and J.K. Uhlman: “ Unscented filtering and nonlinear estimation ”, Proc. of the IEEE. Volume 92, Issue 3, Mar 2004 Page(s):401 – 422.
    • Kamio , K. , Nishimura, K. , and Sato, T. : “ Adaptive sidelobe control for clutter rejection of atmospheric radars ”, Proc. of 10th International Workshop on Technical and Scientific Aspects of MST Radar (MST10). Page(s) 4005-4012. SRef-ID: 1432-0576/ag/2004-22-4005 ANNALES - Volume 22, Number 11, 2004.
  • 21. Thank You