Adaptive clutter rejection by DOA tracking using  unscented filters for atmospheric radars By Dr. C.Vijaykumar  and  Arpit...
<ul><li>Introduction to Problem  </li></ul><ul><li>Clutter Rejection method for Atmospheric Radars   </li></ul><ul><li>DOA...
 
Introduction to Problem <ul><li>Clutter Removal Stationary as well as Moving </li></ul><ul><li>Currently done by  </li></u...
DOA Estimation Procedure <ul><li>1. Compute the auto covariance matrix R from the data vector. </li></ul><ul><li>2. Comput...
DOA Update using Unscented Kalman Filter
State Space Model <ul><li>System dynamics are non-linear functions of the system states. </li></ul><ul><li>Moving Source i...
State Space Model cont ..  v (n)  and  w(n)  are independent zero mean Gaussian noise vector for State space model and Mea...
Unscented Transform <ul><li>Instead of linearizing the non linear function, sample  the density function of  the present s...
<ul><li>1.Find 2n+1 (9) sigma points (  i ) from the initial estimate of state vector (Where n is the size of the state v...
<ul><li>3.  Prediction of the state estimate at time (k+1) with the measurement up to time k is given by,   </li></ul><ul>...
<ul><li>6. Predicted Observation </li></ul><ul><li>7. Calculate Kalman Gain as  </li></ul><ul><li>W(k+1)=P XZ (k+1/k) P YY...
<ul><li>9. Update of the error covariance is  </li></ul><ul><li>P(k+1/k+1 ) = P (k+1 / k) -  P YY (k+1/k)  W(k+1) T   </li...
Clutter Rejection Method <ul><li>DCMP-CN algorithm </li></ul><ul><li>proposed by Sato, T.   </li></ul><ul><li>[3] </li></u...
Weight Vector Calculation Algorithm
<ul><li>Simulation  </li></ul><ul><li>1. Four fully coherent sources are simulated. One is stationary, and its multipath a...
Measurements ANGLE INDEGGREES ANGLE IN DEGGREES
 
CONCLUSIONS <ul><li>1. DOA estimation is done by differential MUSIC. This gives high resolution estimates than simple FFT ...
References <ul><li>R. Rajagopal & P.R. Rao: &quot;A Generalized Algorithm for DOA Estimation in Passive Sonar&quot;, IEE P...
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My presentation in MST -11 International Workshop

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  • My presentation in MST -11 International Workshop

    1. 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. 2. <ul><li>Introduction to Problem </li></ul><ul><li>Clutter Rejection method for Atmospheric Radars </li></ul><ul><li>DOA Estimation using Differential MUSIC </li></ul><ul><li>DOA Update using Unscented Kalman Filter </li></ul><ul><li>Clutter Rejection Algorithm </li></ul><ul><li>Simulation Results </li></ul><ul><li>Conclusions </li></ul>Organization of the Presentation
    3. 4. Introduction to Problem <ul><li>Clutter Removal Stationary as well as Moving </li></ul><ul><li>Currently done by </li></ul><ul><li>Offline or using adaptive filtering </li></ul><ul><li>Assuming either the noise or signal spectra </li></ul><ul><li>Applying filter based on above assumptions </li></ul><ul><li>Adaptive antenna technique makes no assumption on signal spectra. </li></ul><ul><li>We applied high resolution estimation techniques and subsequent kalman filtering technique to suppress the clutter </li></ul>
    4. 5. DOA Estimation Procedure <ul><li>1. Compute the auto covariance matrix R from the data vector. </li></ul><ul><li>2. Compute the difference matrix </li></ul><ul><li>where E is the MxM exchange matrix. </li></ul><ul><li>where S is signal covariance matrix, Q is the unknown noise spatial covariance matrix and A is the array direction matrix </li></ul><ul><li>3.Perform the eigen decomposition of the matrix D. </li></ul><ul><li>4. Estimate the DOA’s using the psuedo power spectrum using MUSIC . </li></ul><ul><li>5. Differential MUSIC : It gives the signal direction even when signal and noise are spatially correlated [1]. </li></ul>
    5. 6. DOA Update using Unscented Kalman Filter
    6. 7. State Space Model <ul><li>System dynamics are non-linear functions of the system states. </li></ul><ul><li>Moving Source is modeled based on velocity model </li></ul><ul><li>System states for this case becomes </li></ul><ul><li>X (n) = [ X r Y r U r V r ] T = [ X/r Y/r U/r V/r] T </li></ul><ul><li>where X r and Y r are rectangular co-ordinates of the target </li></ul><ul><li>Range r = sqrt (X 2 + Y 2 ), </li></ul><ul><ul><ul><ul><li>U = x-velocity, V= y-velocity, T = sampling time period </li></ul></ul></ul></ul>
    7. 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)
    8. 9. Unscented Transform <ul><li>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]. </li></ul><ul><li>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. </li></ul>
    9. 10. <ul><li>1.Find 2n+1 (9) sigma points (  i ) from the initial estimate of state vector (Where n is the size of the state vector) </li></ul><ul><li>2.Transform the sigma points through non-linear measurement model, </li></ul>DOA Tracking – Unscented Kalman Filtering x i (k +1 / k) = f [x (n), y (n), Vx (n), Vy (n)]
    10. 11. <ul><li>3. Prediction of the state estimate at time (k+1) with the measurement up to time k is given by, </li></ul><ul><li>4. The predicted covariance is given as </li></ul><ul><li>5. Transform each of the prediction points using measurement model </li></ul><ul><li>Where T is the inverse of matrix in state space model </li></ul>
    11. 12. <ul><li>6. Predicted Observation </li></ul><ul><li>7. Calculate Kalman Gain as </li></ul><ul><li>W(k+1)=P XZ (k+1/k) P YY (k+1/k) </li></ul><ul><li>P YY (k+1/k) is Innovation Covariance </li></ul><ul><li>8. State update after the measurement is given by </li></ul>
    12. 13. <ul><li>9. Update of the error covariance is </li></ul><ul><li>P(k+1/k+1 ) = P (k+1 / k) - P YY (k+1/k) W(k+1) T </li></ul><ul><li>10. Follow the same process for each time step. </li></ul><ul><li>11. If the magnitude of error covariance increases successively for each time step. We classify that source as stationary source. </li></ul><ul><li>12. Moving source - DOA update given by kalman filter at each time step </li></ul><ul><li> Stationary source - DOA is measure given by Differential MUSIC algorithm </li></ul>
    13. 14. Clutter Rejection Method <ul><li>DCMP-CN algorithm </li></ul><ul><li>proposed by Sato, T. </li></ul><ul><li>[3] </li></ul><ul><li>Additional Constraints </li></ul><ul><li>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 </li></ul>
    14. 15. Weight Vector Calculation Algorithm
    15. 16. <ul><li>Simulation </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul>
    16. 17. Measurements ANGLE INDEGGREES ANGLE IN DEGGREES
    17. 19. CONCLUSIONS <ul><li>1. DOA estimation is done by differential MUSIC. This gives high resolution estimates than simple FFT based algorithms </li></ul><ul><li>2.The proposed algorithm gives better state estimation of moving objects </li></ul><ul><li>3.Thus the proposed algorithm results in effective sidelobe canceling for atmospheric radars. </li></ul><ul><li>4. We would validate the proposed algorithm with NARL active phased array radar data, expected in March, 2007. </li></ul>
    18. 20. References <ul><li>R. Rajagopal & P.R. Rao: &quot;A Generalized Algorithm for DOA Estimation in Passive Sonar&quot;, IEE Proc. Part F, Vol. 150. No. 1 Feb 1993. pp. 12-20. </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul>
    19. 21. Thank You

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