2. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #1/77 Estimation of Signal Models for
Aerospace and Industrial Applications Anirban Krishna Bhattacharyya
Department of Electrical Engineering Indian Institute of Technology
Kharagpur http://www.iitkgp.ac.in
3. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #2/77 Motivation and Overview
Figure 1: Motivation
4. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #2/77 Motivation and Overview 1.
Particle Swarm Optimization, proposed algorithms 2. Parametric
Spectral Estimation of non-stationary rational stochastic processes
3. Noise modeling to enhance estimation (application to aerospace
target tracking) 4. Model Predictive Guidance 5. Fault detection
and monitoring for Hot Steel Rolling process 6. Conclusion Figure
1: Motivation
5. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #3/77 Particle Swarm Optimization
(PSO) Evolutionary optimization - Kennedy and Eberhart [11]. Basic
PSO: Velocity assignment for each of the M particles is given by
vi(t + 1) = Wvi(t) + C1rand()(xpb,i(t) xi(t)) + C2rand()(xgb(t)
xi(t)) where, t is iteration step , xi(t) = [x1 i (t), ...., xN i
(t)]T is position vector in RN . Particles best: xpb,i(t) = arg max
t [f (xi(t))] . Global best: xgb(t) = arg max i max t [f (xi(t))]
.
6. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #4/77 Particle Swarm Optimization
(PSO) Large number of function evaluations required to converge, so
several variants have been proposed. Table 1: Literature map
Innovation Literature Boundary Conditions [1, 27, 12, 24, 22]
Variation of Weights [27, 23, 13, 3, 25] Preservation of Diversity
[13, 3] Hierarchy [13, 3, 5, 15, 21] Probability of convergence to
the global optimum increased, but number of function evaluations
still quite large.
7. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #5/77 Particle Swarm Optimization
(PSO) Kennedy and Mendes = fully informed swarms perform better
[20, 14, 16]. I Number of iterations used is very high or the
search space is very small. I In case of premature termination
cannot be ascertained that the solution achieved is a local optima.
Table 2: Comparison of Algorithms Algorithm/ Function Search
Problem Paper Evaluations Space Dimension SEPSO [13] 200000 (10,
10) 30 ARPSO [13] 400000 (5.12, 5.12) 20 DoLPSO [13] 200000 (100,
100) 50 (H or M) PSO-TVAC [3] 200000 (10, 10) 30 CPSO [5] 200000
(5.12, 5.12) 30 FDR-PSO [15] 10000 (2.048, 2.048) 20
8. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #6/77 Redistributed Local Search
PSO (RLSPSO) Redistribution of the Swarm: If xgb(t 1) = xgb(t).
xi(t) = xpb,i(t) + ( rand() (xgb(t) xpb,i(t))); x axis yaxis 10 5 0
5 10 10 5 0 5 10 xpb,l(t) xpb,j(t) xpb,k(t) xgb(t) Local
exploration around xgb(t): Explore the region around xgb(t). xi(t)
= xi(t) + ( rand() (xgb(t) xi(t)))
9. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #7/77 Hybrid Gradient Descent PSO
(HGDPSO) Hybrid between Levenberg-Marquardt (LM-NLS) and RLSPSO.
Switches between the two based on the following conditions:
Condition 1 if tness improves when doing LM-NLS then Continue
LM-NLS else if LM-NLS terminates then Switch to PSO else if tness
then Stop end if Condition 2 if tness at (xgb(t)) improves then
Switch to LM-NLS else if tness not improving then Continue PSO else
if tness then Stop end if Figure 2: Hybrid optimization scheme
Guarantees that in case of premature termination local optima is
reached.
10. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #8/77 Numerical Experiments Table
3: Test functions used in numerical experiments Sphere: fSph(x) = N
i=1 x2 i Rosenbrock: fRos(x) = N1 i=1 (100(xi+1 x2 i ) 2 + (xi 1)2)
Rastrigin: fRas(x) = N i=1 x2 i 10 cos(2xi) + 10 Griewank: fGri(x)
= 1 4000 N i=1 x2 i N i=1 cos xi i + 1 Table 4: Parameters w c1 c2
Initial 0.9 2.5 0.5 Final 0.4 0.5 2.5 Table 5: Test Environment
Function Dimension Initialization Search Space Goal Sphere 30 100
100 0.01 Rastrigin 30 100 100 100 Rosenbrock 30 100 100 100
Griewank 30 600 600 0.1
11. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #9/77 Results: RLSPSO Table 6: Number of
iterations to convergence to set optimal value (1000 ensembles)
Function Mean Median Mode Success Ratio Sphere 447 430 424 1.0
Rastrigin 518 515 405 1.0 Rosenbrock 933 743 1600 0.848 Griewank
424 395 391 0.99 Table 7: Optimal values in 200000 function
evaluations (1000 ensembles) Function Mean Standard deviation Min
Sphere 3.297 e-11 5.141 e-11 1.116 e-14 Rastrigin 1.4895 1.2208
1.345 e-13 Rosenbrock 30.989 38.075 6.578 Griewank 1.709 e-02 2.106
e-02 5.274 e-13
12. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #10/77 Results: RLSPSO 500 400 300 200 100 0 0
50 100 150 200 250 300 Gbest Frequency Histogram of f(xgb (t)) for
1000 ensembles of the Rosenbrock function (a) Rosenbrocks function.
7 6 5 4 3 2 1 0 0 50 100 150 200 250 Gbest Frequency Histogram of
f(xgb (t)) for 1000 ensembles of the Rastigrin function (b)
Rastrigins function. Figure 3: Histograms of tness
13. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #11/77 Results: HGDPSO 40 30 20 10 0 0 100 200
300 400 500 600 Gbest Frequency (a) Rastrigins function. 25 20 15
10 5 0 5 10 15 20 25 Gbest Frequency (b) Rosenbrocks function.
Figure 4: Histograms of tness
14. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #12/77 Results: HGDPSO CF 6 proposed by Liang,
Suganthan and Deb [10]. 500 400 300 200 100 0 0 50 100 150 Gbest
Frequency Figure 5: Histogram of tness Table 8: Number of function
evaluations Function Minimum Maximum Mean Rastrigin 78420 196510
175510 Rosenbrock 167470 191240 181949 CF 6 64844 68816 67185
15. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #13/77 Parametric Spectral
Estimation Rao [18] = Evolutionary spectrum matching time varying
autoregressive model (AR) Grenier [9, 8, 7] = Orthogonal basis
function based Time varying autoregressive moving average (ARMA)
model Kaderli and Kayhan [2] = Estimators tting the parametric
spectrum expression to an estimated time-frequency distribution
Matz and Hlawatsch [6] = ARMA models and parameter estimators for
the underspread processes Jachan et. al. [17] and Matz and
Hlawatsch [6] = spectral analysis furnishes satisfactory results
only for underspread processes. I No method to determine the order
of the AR and MA parts. I Applicable only to slow
non-stationary/underspread processes. Singular value based order
estimation Cadzow [4] Zhang and Zhang [26] for AR and for ARMA
models resp.
16. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #14/77 Non-stationary Order
Estimation Non-stationary rational stochastic process: p i=0 an i
x(n i) = q j=0 bn j w(n j) Autocorrelation matrix is Rx = rx(0, 0)
rx(0, 1) rx(0, N) rx(1, 1) rx(1, 0) rx(1, N 1) . . . . . . . . .
rx(N, N) rx(N, N + 1) rx(N, 0) Articial auto-correlation matrix for
time instant n Rn x = rx(n, 0) rx(n, 1) rx(n, n) rx(n, 1) rx(n, 0)
rx(n, n + 1) . . . . . . . . . rx(n, n) rx(n, n + 1) rx(n, 0)
17. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #15/77 Non-stationary Order
Estimation 1 2 3 4 5 6 0.9999 0.9999 0.9999 0.9999 1 1 1 k (k) (a)
Order of AR part of model is 2. 2 4 6 8 0.85 0.9 0.95 1 k (k) (b)
Order of AR part of model is 5. Figure 6: Model changes order
suddenly from ARMA(2,2) to ARMA(5,5).
18. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #16/77 Time-varying ARMA Parameter
Estimation rx(n, 0) + an 1 rx(n, 1) + + an 3 rx(n, 3) = f1 s (An)
rx(n, 1) + an 1 rx(n, 0) + + an 3 rx(n, 2) = f2 s (An) rx(n, 2) +
an 1 rx(n, 1) + + an 3 rx(n, 1) = bn 0 bn 2 rx(n, 3) + an 1 rx(n,
2) + + an 3 rx(n, 0) = 0 . . . rx(n, l) + an 1 rx(n, l + 1) + + an
3 rx(n, l + 3) = 0 where f1 s (An) = (bn 0 )2 + (bn 1 )2 + (bn 2 )2
an 1 bn 0 bn 1 an 1 bn 1 bn 2 + (an 1 )2bn 0 bn 2 an 2 bn 0 bn 2 f2
s (An) = bn 0 bn 1 + bn 1 bn 2 an 1 bn 0 bn 2 An = [an 1 an 2 an 3
bn 0 bn 1 bn 2 ]T and l is the maximum delay up to which the
equations are considered.
19. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #17/77 Results:Spectrum Estimation
Example used by Kaderli and Kayhan [2] an 1 = 0 an 2 = 0.55 1.2 n N
2 N1 2 bn 0 = 1 bn 1 = 0.7 1.2 n N 2 N1 2 bn 2 = 0.36 The signals
length is N = 238.
20. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #18/77 Results:Spectrum Estimation Time (n)
Frequency(rad./sample) Actual Frequency Characteristics 50 100 150
200 0 1 2 3 Time (n) Frequency(rad./sample) Modeled Frequency
Characteristics 50 100 150 200 0 1 2 3 0.6 0.8 1 1.2 1.4 1.6 1.8
0.6 0.8 1 1.2 1.4 1.6 1.8 Figure 7: True and estimated spectrum
erramp = n |S(n, ej)| n | S(n, ej)| n |S(n, ej)| erramp = 3.1785
105
21. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #19/77 Results:Spectrum Estimation Comparison
of algorithms: Figure 8: Estimated parameters 50 100 150 200 0.04
0.02 0 0.02 0.04 Time (n) CoefficientValue a 1 true estimate 50 100
150 200 0.3 0.4 0.5 Time (n) CoefficientValue a 2 true estimate 50
100 150 200 0.996 0.998 1 1.002 1.004 Time (n) CoefficientValue b 0
true estimate 50 100 150 200 0.5 0.4 0.3 Time (n) CoefficientValue
b 1 true estimate 50 100 150 200 0.34 0.35 0.36 0.37 0.38 Time (n)
CoefficientValue b2 true estimate Figure 9: Estimated
parameters
22. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #20/77 Results:Spectrum Estimation Time (n)
Frequency(rad./sample) Actual Frequency Characteristics 20 40 60 80
100 0 1 2 3 Time (n) Frequency(rad./sample) Modeled Frequency
Characteristics 20 40 60 80 100 0 1 2 3 0.2 0.4 0.6 0.8 1 0.2 0.4
0.6 0.8 1 Figure 10: True and estimated spectrum 20 40 60 80 100
0.2 0 0.2 Time (n) CoefficientValue a 1 true estimate 20 40 60 80
100 0 0.1 0.2 Time (n) CoefficientValue a 2 true estimate 20 40 60
80 100 0.2 0.3 0.4 0.5 Time (n) CoefficientValue b 0 true estimate
20 40 60 80 100 0.4 0.2 0 0.2 Time (n) CoefficientValue b 1 true
estimate 20 40 60 80 100 0.4 0.2 0 0.2 0.4 Time (n)
CoefficientValue b2 true estimate Figure 11: Estimated parameters
erramp = 1.4913 103
23. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #21/77 Aerospace Target Tracking
Figure 12: Typical interception geometry.
24. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #22/77 Seeker Noise Modeling - Why? 15 16 17
18 19 20 21 0.5 0 0.5 1 1.5 SLR(deg./sec.) Time (sec.) kinematic
measurement Figure 13: Typical SLR variation Challenges: I Closing
velocity 3km/sec I Terminal phase 5 6sec I Sampling rate is 40Hz I
Required miss-distance 10m Estimator (Extended Kalman lter) used to
im- prove signal quality
25. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #23/77 Seeker Noise Figure 14: Seeker block
diagram Noise depends on relative displacement between the target
and the interceptor (RT M ).
26. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #24/77 Seeker Noise Modeling Figure 15: Black
box noise model
27. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #25/77 Noise Statistics Mean,
standard deviation and correlation obtained by taking expectation
over ensembles. Mean (RT M ) = E [ (RT M )] Standard deviation (RT
M ) = 1 N 1 N i=1 [i (RT M ) (RT M )]2 Correlation R = 1 N 1 N i=1
(i. i ) N is the number of ensembles.
28. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #26/77 Noise Statistics 0 2 4 6 8 10 12 7 6 5
4 3 2 1 0 1 Range to Go (Km.) NoiseMean(rad./sec.) Z Channel (a)
Mean of noise in the Z Channel. 0 2 4 6 8 10 12 5 0 5 10 15 20 25
Range to Go (Km.) NoiseMean(rad./sec.) Y Channel (b) Mean of noise
in the Y Channel. Figure 16: Variation of noise mean with RT M
.
29. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #27/77 Noise Statistics 0 2 4 6 8 10 12 0 0.05
0.1 0.15 0.2 0.25 Range to Go (Km.) NoiseStd(rad./sec.) Z Channel
(a) Std of noise in the Z Channel. 0 2 4 6 8 10 12 0 0.05 0.1 0.15
0.2 0.25 0.3 0.35 0.4 0.45 0.5 Range to Go (Km.)
NoiseStd(rad./sec.) Y Channel (b) Std of noise in the Y Channel.
Figure 17: Variation of noise standard deviation with RT M .
30. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #28/77 Noise Statistics 20 40 60 80 100 120
20406080100120 0 5 10 15 20 x 10 4 Delay Z Channel Delay
Correlation(rad.2 /sec.2 ) (a) Auto-correlation of noise in the Z
Channel. 20 40 60 80 100 120 20 40 60 80 100 120 0 5 10 15 20 x 10
4 Delay Y Channel Delay Correlation(rad.2 /sec.2 ) (b)
Auto-correlation of noise in the Y Channel. Figure 18:
Auto-correlation of noise in both channels.
31. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #29/77 Noise modeling: Approaches
1. White Noise with standard deviation (RTM ). 2. Colored Noise
(Auto-Regressive (AR) spectrum) with standard deviation (RTM ). 3.
Colored Noise ( RTM dependent Auto-Regressive Moving Average (ARMA)
spectrum ).
32. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #30/77 White Noise with std. (RTM )
Figure 19: Noise modeled as white noise with standard deviation (RT
M ) Varying noise standard deviation quantied as function of RT M
by curve-tting. In real-time varying measurement variance (Rl) at
each step l of the sequencing index used in Kalman lter by
interpolation from curve based on the RT M measurement obtained.
Kalman gain used in estimator Kl = Pl|l1HT l (HlPl|l1HT l +
Rl)1
33. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #31/77 Colored Noise with std. (RTM
) Figure 20: Noise modeled as colored noise with standard deviation
(RT M ) Noise sequence normalized with corresponding standard
deviation producing the normalized colored noise sequence i(RT M ).
i(RT M ) = i(RT M ) (RT M ) i = 1(1)N Auto-correlation of i(RT M )
computed. Order of the AR model estimated using i(RT M ) for the
model i(RT M ) = a1i(RT M 1) a2i(RT M 2) + b0 is white noise with
unity variance.
34. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #32/77 Colored Noise with std. (RTM ) 20 40 60
80 100 120 20 40 60 80 100 120 0.2 0 0.2 0.4 0.6 0.8 DelayDelay
SLR2 (rad.2 /sec.2 ) (a) Gamma axis 20 40 60 80 100
12020406080100120 0.4 0.2 0 0.2 0.4 0.6 0.8 DelayDelay SLR2 (rad.2
/sec.2 ) (b) Phi axis Figure 21: Auto-correlation of normalized
noise
35. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #33/77 Colored Noise with std. (RTM ) 1 2 3 4
5 0.7 0.75 0.8 0.85 0.9 0.95 1 k (k) (a) Gamma axis 1 2 3 4 5 0.65
0.7 0.75 0.8 0.85 0.9 0.95 1 k (k) (b) Phi axis Figure 22: AR model
order of normalized noise
36. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #34/77 Colored Noise with std. (RTM
) Yule-Walker equations: rx(0) + a1rx(1) + + a4rx(3) = (b0)2 rx(1)
+ a1rx(0) + + a4rx(2) = 0 . .. rx(l) + a1rx(l + 1) + + a4rx(l + 3)
= 0 Solved using the Data Least Square technique [19]. Augmentation
of states [x(k) Y (k) Y (k 1) Y (k 2) Y (k 3) Y (k 4) Z (k) Z (k 1)
Z (k 2) Z (k 3) Z (k 4)]T where the Y s and Zs depict noise states
in the Y and Z channels respectively and x(k) is the kinematic
state
37. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #35/77 Colored Noise ( ARMA(RTM ))
Figure 23: Seeker noise modeled as colored noise. 1 2 3 4 5 6 0.9
0.95 1 p Value 1 2 3 4 5 6 7 8 0.8 0.9 1 q Value Figure 24: Order
estimation of ARMA model for Z axis seeker noise
38. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #36/77 Results:Noise Modeling 20 40
60 80 100 120 20 40 60 80 100 120 1 0 1 2 x 10 5 Delay Delay SLR2
(rad.2 /sec.2 ) (a) Phi axis 20 40 60 80 100 120 20 40 60 80 100
120 1 0 1 2 3 x 10 5 DelayDelay SLR2 (rad.2 /sec.2 ) (b) Gamma axis
Figure 25: SLR measurement error covariance
39. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #37/77 Results:Noise Modeling (a)
Phi axis (b) Gamma axis Figure 26: SLR estimation error covariance
with stationary white noise model
40. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #38/77 Results:Noise Modeling White Noise with
standard deviation (RT M ): 50 100 150 50 100 150 1 2 3 4 5 x 10 7
Delay Delay SLR2 (rad.2 /sec.2 ) (a) Phi axis 50 100 150 50 100 150
0 2 4 6 8 x 10 7 Delay Delay SLR2 (rad.2 /sec.2 ) (b) Gamma axis
Figure 27: Estimation error covariance
41. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #39/77 Results:Noise Modeling Colored Noise
with standard deviation (RT M ): AY = [0.0584 0.0405 0.0358 +
0.0007] and AZ = [0.0146 0.0405 0.0221 0.017] 50 100 150 50 100 150
2 4 6 8 10 x 10 7 Delay Delay SLR2 (rad.2 /sec.2 ) (a) Phi axis. 50
100 150 50 100 150 0 2 4 6 8 x 10 7 Delay Delay SLR2 (rad.2 /sec.2
) (b) Gamma axis. Figure 28: Estimation error covariance
42. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #40/77 Results:Noise Modeling Colored Noise (
RT M dependent ARMA spectrum ): RTM Frequency(rad./sample) 20 40 60
80 100 0 0.5 1 1.5 2 2.5 3 0.01 0.02 0.03 0.04 (a) Phi axis. RTM
Frequency(rad./sample) 20 40 60 80 100 0 0.5 1 1.5 2 2.5 3 0.005
0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 (b) Gamma axis. Figure
29: Spectrogram of noise
43. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #41/77 Results:Noise Modeling 50 100 150 50
100 150 0 2 4 6 x 10 7 Delay Delay SLR2 (rad.2 /sec.2 ) (a) Phi
axis. 50 100 150 50 100 150 0 5 10 15 x 10 7 Delay Delay SLR2
(rad.2 /sec.2 ) (b) Gamma axis. Figure 30: Estimation error
covariance
44. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #42/77 Model Predictive Guidance
(MPG) Figure 31: Guidance Loop
45. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #43/77 Model Predictive Guidance
(MPG) TPNCa Target y Ta TV MV x r y PPNCa LOS Missile Figure 32:
Lateral acceleration (Latax)
46. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #44/77 Model Predictive Guidance (MPG) Figure
33: General Model Predictive Problem Plant [28] . Y(t) = AY(t) +
Bu(t) where Y = . y .. y . aT . aM T , . aT is the tar- get
acceleration, . aM is the achieved acceleration. Optimization
problem, min |y(tf )| such that tf t0 |u(t)| dt is minimum ulim
u(t) ulim, t0 t tf | . u | . ul , t0 t tf The constraints are
|ulim| = 120m/sec2, ul = 3m/sec3, t0 = 0 and tf = 50.
47. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #45/77 Model Predictive Guidance (MPG) Figure
34: Model Predictive Guidance
48. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #46/77 Results:MPG 52 42 32 22 12 2 0 10 20 30
40 50 60 Time to go (sec) ComputedCommandedAcceleration(m/sec2 )
Figure 35: Input proles computed by optimizer
49. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #47/77 Results:MPG 42 32 22 12 2 15 20 25 30
35 40 45 Time to go (sec) CommandedAcceleration(m/sec2 ) (a)
Commanded Acceleration. 42 32 22 12 2 20 40 60 80 100 120 140 Time
to go (sec) LateralMiss(m) (b) Lateral Miss. Figure 36: Predictive
Guidance.
50. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #48/77 Results:MPG 0 10 20 30 40 50 60 10 0 10
20 30 40 50 Time samples Commandedacceleration(m./s.2 ) T model
known T model unknown (a) Commanded Acceleration. 0 10 20 30 40 50
60 0 20 40 60 80 100 120 140 160 Time samples Lateralmiss(m.) T
model known T model unknown (b) Lateral Miss. Figure 37: Comparison
between correct and wrong models
51. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #49/77 Fault detection and
monitoring The typical operational modes of rolling drive are as
following: I No Load (idling) I Single forward Rolling (Single
Load) I One forward and one reverse Rolling (Double Load) Figure
38: State transitions
52. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #50/77 Fault detection and monitoring 10 20 30
40 50 60 1000 500 0 500 1000 time (s) Ia(Amp) (a) Armature current
10 20 30 40 50 60 0 100 200 300 400 500 600 700 800 time (s) Va(V)
(b) Armature voltage Figure 39: Typical signals under idling
condition.
53. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #51/77 Fault detection and
monitoring 10 20 30 40 50 60 0 1 2 3 4 5 time (s) (rad/s) Figure
40: Rotational velocity
54. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #52/77 Fault detection and monitoring 10 20 30
40 50 60 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 time (s)
Ia(Amp) (a) Armature current 10 20 30 40 50 60 1050 1100 1150 1200
1250 time (s) Va(V) (b) Armature voltage Figure 41: Typical signals
under loaded conditions
55. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #53/77 Fault detection and
monitoring 10 20 30 40 50 60 7 7.5 8 8.5 time (s) (rad/s) Figure
42: Rotational velocity
56. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #54/77 Fault detection and
monitoring 600 400 200 0 200 400 8 6 4 2 0 2 4 6 8 Va constant
decreasing increasing Figure 43: Pattern of and Va.
57. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #55/77 Fault detection and
monitoring p(x) = K k=1 N(x|k, k)P(k) where, P(k) is mixture
weight, subject to constraints 0 P(k) 1 and K k=1 P(k) = 1, and
N(x|k, k) is height of the kth component p.d.f. at vector x, given
by a Gaussian distribution of mean k and standard deviation k. GMMs
are developed for Va t and t . Va t gives a measure of the health
of power supply circuit, t gives a measure of the torque. min|k,k,P
(k) ||p(x) K k=1 N(x|k, k)P(k)|| such that 1 P(k) 0 K k=1 P(k) =
1
58. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #56/77 Fault detection and monitoring 100 200
300 400 500 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10 3 Motor Current
(A.) Probability pdf GMM (a) Probability of Ia (idling). 1500 2000
2500 3000 3500 4000 4500 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10 3 Motor
Current (A.)Probability pdf GMM (b) Probability of Ia (single
load). Figure 44: Probability distribution functions of Ia.
59. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #57/77 Fault detection and monitoring 10 20 30
40 50 60 0 2000 4000 6000 8000 time (s) Ia(Amp) 10 20 30 40 50 0
0.5 1 1.5 2 time (s) LoadFlag Figure 45: Load change detection
algorithm using CUSUM
60. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #58/77 Fault detection and monitoring 10 20 30
40 50 60 0 2000 4000 6000 8000 time (s) Ia(Amp) 10 20 30 40 50 60 0
2 4 6 8 time (s) (rad/s) 10 20 30 40 50 0 0.5 1 time (s) FaultFlag
(a) Algorithm used on normal motor. 10 20 30 40 50 0 2000 4000 6000
time (s) Ia(Amp) 10 20 30 40 50 0 2 4 6 8 time (s) (rad/s) 10 20 30
40 50 0 0.5 1 time (s) FaultFlag (b) Algorithm used on wobble
bearing vibration fault. Figure 46: Fault detection algorithm using
KL-divergence.
61. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #59/77 Conclusion Major
contributions: I A hybrid optimization algorithm, which combines
the speed of gradient descent techniques with the robustness of the
PSO. I A model order estimation algorithm for fast non-stationary
stochastic processes with rational power spectra. I A parametric
spectral estimation algorithm for non-stationary rational
stochastic processes. I An algorithm for estimation of a
statistical noise model of measurement noise and associated
estimator design for seeker-based aerospace target tracking for
homing missiles. I A Model Predictive Guidance algorithm for
interception of maneuvering aerospace targets which explicitly
considers practical technological constraints of the guidance and
control loops. I A fault and load detection algorithm for a steel
rolling mill using classier based on a Gaussian Mixture Model using
motor current, voltage and speed measurement.
62. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #60/77 References 1. A. Carlisle and G.
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Estimation of Signal Models for Aerospace and Industrial
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64. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
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65. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #63/77 References 22. Shenheng Xu and Yahya
Rahmat-Samii. Boundary Conditions in Particle Swarm Optimization
Revisited. Antennas and Propagation, IEEE Trans., 55(3):760 765,
Mar. 2007 23. P. N. Suganthan. Particle Swarm Optimiser with
Neighbourhood Operator. In Evolutionary Computation, 1999. CEC 99.
Proceedings of the 1999 Congress on, volume 3, pages 1958 1962,
1999 24. T. Huang and A. Mohan. A hybrid boundary condition for
robust particle swarm optimization. IEEE Antennas Wireless
Propagation Lett., 5:112 117, 2005 25. Tan Ying, Yang Ya-ping, and
Zeng Jian-chao. An Enhanced Hybrid Quadratic Particle Swarm
Optimization. In Proceedings of the Sixth International Conference
on Intelligent Systems Design and Applications, volume 2, pages 980
985, Oct. 2006 26. X. Zhang and Y. Zhang. Singular Value
Decomposition-Based MA Order Determination of Non-Gaussian ARMA
Models. Signal Processing, IEEE Trans., 41(8):2657 2664, Aug. 1993
27. Y Shi and R. Eberhart. A modied particle swarm optimizer. In
Evolutionary Computation Proceedings, 1998. IEEE World Congress on
Computational Intelligence., The 1998 IEEE International Conference
on, pages 69 73, May 1998 28. P. Zarchan. Tactical and Strategic
Missile Guidance. American Institute of Aeronautics and
Astronautics Inc., Virginia, 5 edition, 2007
66. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #64/77 Publications 1. "Particle swarm based
robust predictive control: application to guidance"In SIAM
Conference on Control and Its Applications (CT09) , Denver,
Colorado, USA, July 2009 2. "Modeling of RF seeker dynamics and
noise characteristics for estimator design in homing guidance
applications" In Industrial and Information Systems, 2008. ICIIS
2008. IEEE Region 10 and the Third international Conference on ,
IEEE, pages 1 - 7, 8-10 Dec. 2008 3. "Noise modeling of RF Seeker
for homing guidance applications" In Proceedings of International
Conference on Avionics Systems, Hyderabad, India, pages 255- 261,
Feb. 2008.
67. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #65/77 Thank You!!!!!
68. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #66/77 RLSPSO Algorithm: Initialize
Population repeat for some iterations do update w by w = (wmax
wmin) (itermax iter) /itermax + wmin update c1 by c1 = (c1min
c1max) (itermax iter) /itermax + c1max update c2 by c2 = (c2max
c2min) (itermax iter) /itermax + c2min update xpb,i(t) update
xgb(t) update vi(t + 1) by vi(t + 1) = Wvi(t) + C1rand()(xpb,i(t)
xi(t)) + C2rand()(xgb(t) xi(t)) x velocity of errant particles
using boundary conditions if xgb(t) has not improved then
Redistribute particles if errant particles produced then Place them
at the boundary end if end if end for for some iterations do xi(t)
= xi(t) + ( rand() (xgb(t) xi(t))) update xpb,i(t) update xgb(t)
end for until termination criteria is met or itermax is
reached
69. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #67/77 HGDPSO Algorithm: Start
optimization using LM-NLS from one of the search boundaries When
LM-NLS stops improving assign nal value of variables to xgb(t)
Initialize Population and assign xpb,i(t) Update xgb(t) repeat if
xgb(t) does not improve then Continue PSO with redistribution else
if xgb(t) has improved then Take xgb(t) as starting point for
LM-NLS Continue LM-NLS When LM-NLS stops improving assign nal value
of variables to xgb(t) Tell algorithm that xgb(t) has not improved
end if until termination criteria is met or itermax is reached
70. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #68/77 Results: RLSPSO 1 0.8 0.6 0.4 0.2 0 x
10 9 0 50 100 150 200 250 300 350 400 450 500 Gbest Frequency
Histogram of f(xgb (t)) for 1000 ensembles of the Sphere function
(a) Sphere function. 0.2 0.15 0.1 0.05 0 0 50 100 150 200 250 300
350 400 GbestFrequency Histogram of f(xgb (t)) for1000 ensembles of
the Griewank function (b) Griewanks function. Figure 47: Histograms
of tness
71. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #69/77 Stationary Order Estimation
p i=0 aix(n i) = q j=0 bjw(n j) where a0 = 1 and w(n) is a white
noise sequence. Extended order ARMA (pe, qe) model considered. pe
much larger than p. MA order assumed as qe so chosen that qe pe q
p. Extended order t (pe + 1) autocorrelation matrix Re constructed
rx(qe + 1) rx(qe) rx(qe pe + 1) rx(qe + 2) rx(qe + 1) rx(qe pe + 2)
. . . . . . . . . rx(qe + t) rx(qe + t 1) rx(qe pe + t) t is at
least equal to p. The rank of Re will then give the AR order
p.
72. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #70/77 AR Order Estimation AR order
estimation: Singular values ii of Re computed and ordered such that
11 22 tt 0 Effective rank of Re determined using (k) = 2 11 + 2 22
+ + 2 kk 2 11 + 2 22 + + 2 tt 1 2 1 Effective rank thus obtained is
the AR order p.
73. G Title G Motivation and Overview G Particle Swarm
Optimization (PSO) G Redistributed Local Search PSO (RLSPSO) G
Hybrid Gradient Descent PSO (HGDPSO) G Numerical Experiments G
Results: RLSPSO G Results: HGDPSO G Parametric Spectrum G
Non-stationary Order Estimation G Time-varying ARMA Parameter
Estimation G Results:Spectrum Estimation G Aerospace Target
Tracking G Noise Statistics G Noise modeling: Approaches G
Results:Noise Modeling G Model Predictive Guidance (MPG) G Model
Predictive Guidance (MPG) G Fault detection and monitoring G
Conclusion G References G References G References G References G
Publications A. K. Bhattacharyya, Synopsis Seminar on
29/October/2009 Estimation of Signal Models for Aerospace and
Industrial Applications - slide #71/77 MA Order Estimation MA order
estimation: Extended order matrix Fe = f(0) f(1) f(qe) f(1) f(qe) .
. . 0 f(qe) where f() = p i=0 airx( i) Effective rank of Fe
identied using singular value decomposition and index and rank(Fe)
= q + 1
74. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #72/77 Noise P.d.f 0.25 0.2 0.15 0.1 0.05 0
0.05 0.1 0.15 0 50 100 150 200 250 300 350 Noise (rad./sec.)
Frequency Noise in Z Channel (a) Estimated p.d.f. of noise in the Z
Channel. 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 0 50 100 150 200
250 300 350 400 Noise (rad./sec.) Frequency Noise in Y Channel (b)
Estimated p.d.f. of noise in the Y Channel. Figure 48: Estimated
p.d.f. of noise in both channels.
75. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #73/77 2 Test Results 10 5 0 5 0 0.2 0.4 0.6
0.8 Seeker Noise (rad./sec.) CumulativeFrequency data true gaussian
distribution (a) C.d.f of normalized noise in SLR of Gamma Axis 10
5 0 5 0 0.2 0.4 0.6 0.8 Seeker Noise (rad./sec.)
CumulativeFrequency data true gaussian distribution (b) C.d.f of
normalized noise in SLR of Phi Axis Figure 49: C.d.f of normalized
noise in SLR for a particular RT M . 2 test done and observed that
at 5% condence noise may be assumed to come from Gaussian
Distribution.
76. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #74/77 Eqns. Method 2 State Equations: x(k +
1) Y (k + 1) Y (k) Y (k 1) Y (k 2) Z (k + 1) Z (k) Z (k 1) Z (k 2)
= F (k) x(k) Y (k) Y (k 1) Y (k 2) Y (k 3) Z (k) Z (k 1) Z (k 2) Z
(k 3) + G W d (k) Y (k) 0 0 0 Z (k) 0 0 0 + U(k) F(k) = F d(k) O154
O154 O115 AY O14 O315 I33 O35 O115 O14 AZ O315 O34 I33 O31 , G =
[E115 bY 0 O13 bZ 0 O13], AY = [aY 1 aY 2 aY 3 aY 4 ], AZ = [aZ 1
aZ 2 aZ 3 aZ 4 ], U(k) = Ud(k) O81
77. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #75/77 Eqns. Method 2 Process noise
covariance: Q(k) = Qd(k) O158 O115 RY O17 O323 O119 RZ O13 O323
Measurement Equation: rm(k) Y m(k) Z m(k) Y m(k) Z m(k) =
x(k)vx(k)+y(k)vy (k)+z (k)vz(k) 2 x(k)+2 y (k)+2 z (k) tan1 n l
tan1 m n2+l2 Y t (k) + Y (k)Y (k) Z t (k) + Z (k)Z (k) + r(k) Y (k)
Z (k) 0 0 Here, the unit LOS vector in ndash frame is given by l m
n = C fd f C f b Cb i Ci l 1 0 0 = cosY cosZ sinZ cosZ sinY
78. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #76/77 Eqns. Method 3 State Equations: X(k +
1) Y (k + 1) Y (k) Y (k 1) Y (k 2) Z (k + 1) Z (k) Z (k 1) Z (k 2)
= F(k) X(k) Y (k) Y (k 1) Y (k 2) Y (k 3) Z (k) Z (k 1) Z (k 2) Z
(k 3) + G W d (k) Y (k + 1) Y (k) Y (k 1) Y (k 2) Z (k + 1) Z (k) Z
(k 1) Z (k 2) + U(k) F(k) = F d(k) O154 O154 O115 AY O14 O315 I33
O35 O115 O14 AZ O315 O34 I33 O31 , G = [E115 BY O11 BZ O11], AY = a
(k+1)Y 1 a (k+1)Y 2 a (k+1)Y 3 a (k+1)Y 4 , AZ = a (k+1)Z 1 a
(k+1)Z 2 a (k+1)Z 3 a (k+1)Z 4 , BY = b (k+1)Y 0 b (k+1)Y 1 b
(k+1)Y 2 b (k+1)Y 3 , BZ = b (k+1)Z 0 b (k+1)Z 1 b (k+1)Z 2 b
(k+1)Z 3
79. A. K. Bhattacharyya, Synopsis Seminar on 29/October/2009
Estimation of Signal Models for Aerospace and Industrial
Applications - slide #77/77 Eqns. Method 3 Process noise
covariance: Q(k) = Qd(k) O158 O115 RY O17 O323 O119 RZ O13 O323 The
measurement equation: Z(k) Y m(k) Z m(k) = M(k) Y t (k) + Y (k) Z t
(k) + Z (k) + N(k) 0 0
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