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MAXIMUM LIKELIHOOD JOINT ASSOCIATION, TRACKING, AND FUSION IN STRONG CLUTTER Leonid Perlovsky Harvard University and the AF Research Lab Seminar Department of Electrical and Computer Engineering, University of Connecticut Storr, 6 Mar., 2009

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OUTLINE Related research Combinatorial complexity and logic Dynamic logic Joint likelihood, math. formulation Examples Publications, recognition

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RELATED RESEARCH > 50 publications by Perlovsky and co-authors on concurrent association, tracking, and fusion (+ > 200 other applications) –Perlovsky, L. I. (1991). Model Based Target Tracker with Fuzzy Logic. 25th Annual Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA. –Perlovsky, L.I., Schoendorf, W.H., Tye, D.M., Chang, W. (1995). Concurrent Classification and Tracking Using Maximum Likelihood Adaptive Neural System. Journal of Underwater Acoustics, 45(2), pp.399-414. Many publications by Bar-Shalom, Streit, Luginbuhl, Willett, Avitzour, and co-authors Similarity: algorithms related to EM Differences: –Formulation of likelihood –Maximization procedures –Performance: linear complexity, Cramer-Rao Bound Cramer-Rao Bound for joint association and tracking –Perlovsky, L.I. (1997). Cramer-Rao Bound for Tracking in Clutter and Tracking Multiple Objects. Pattern Recognition Letters, 18(3), pp.283-288.

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COMBINATORIAL COMPLEXITY 50 years of difficulties Detect signal in noise and clutter at the farthest possible distance SP, detection, exploitation, fusion, tracking, etc. in noise/clutter –Requires association (pixels objects) before detection If 1 object, no noise: (1) detect pixels, (2) detect objects, (3) recognize targets –Joint detection-discrimination-classification… Combinatorial Complexity (CC) –Need to evaluate large numbers of combinations (pixels objects), operations: ~M N –A general problem (since the 1950s) SP, detection, recognition, tracking, fusion, exploitation, situational awareness,… Pattern recognition, neural networks, rule systems… Combinations of 100 elements are 100 100 –Larger than the number of particles in known Universe Greater than all the elementary events in the Universe during its entire life CC affects many SP algorithms –Our sensors under-utilize signals –Work much worse than Cramer-Rao Bound information-theoretic limit

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CC vs. LOGIC CC is related to formal logic –Gödel proved that logic is “illogical,” “inconsistent” (1930s) –CC is Gödel's “incompleteness” in a finite system Fuzzy logic –How to select degree of fuzziness? –The mind fits fuzziness for every process => CC Logic pervades all algorithms and neural networks –Rule systems, fuzzy systems ( degree of fuzziness ), pattern recognition, neural networks ( training uses logic ) Probabilistic association (Bar-Shalom) –Overcame logic in association –Where all logical steps overcome?

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DYNAMIC LOGIC overcame logic limitations CC is related to logic –CC is Gödel's “incompleteness” in a finite system –Logic pervaded all algorithms and neural networks in the past rule systems, fuzzy systems (degree of fuzziness), pattern recognition, neural networks (training uses logical statements) Dynamic Logic is a process-logic –“from vague to crisp” (statements, targets, decisions…) Overcomes CC –Fast algorithms

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OUTLINE Related research Combinatorial complexity and logic Dynamic logic Joint likelihood, math. formulation Examples Publications, recognition

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JOINT LIKELIHOOD for tracks and clutter Total likelihood –L = l ({x}) = l (x(n)) no assumption of “independence” Conditional likelihoods –l (x(n)) = r(m) l (x(n) | M m (S m,n)) –l (x(n) | M m (S m,n)) is a conditional likelihood for x(n) given m {x(n)} are not independent, M(n) may depend on n’ CC: L contains M N items: all associations of pixels and models (LOGIC)

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EXAMPLES OF MODELS Linear track model –M m (S m,n) = X m + V m *t; S m = (X m, V m, r m, C m -1 ) Gaussian conditional likelihoods –l (x(n) | M m (S m,n)) = (2 ) -d/2 (detC) -1/2 exp{ -0.5 [ x(n) - M m (S m,n) ] T C m -1 [ x(n) - M m (S m,n) ] } –No “Gaussian” assumption errors are Gaussian mixture of any pdfs can be used Uniform clutter model –r m, l (x(n) | M m (S m,n)) = 1/ volume(x)

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DYNAMIC LOGIC (DL) non-combinatorial solution Start with a set of signals and unknown models –any parameter values S m –associate models with signals (vague) –(1)f(m|n) = r(m) l (n|m) / r(m') l (n|m') Improve parameter estimation –(2)S m = S m + f(m|n) [ ln l (n|m)/ M m ]*[ M m / S m ] Continue iterations (1)-(2). Theorem: DL is a converging system - likelihood increases on each iteration

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OUTLINE Related research Combinatorial complexity and logic Dynamic logic Joint likelihood, math. formulation Examples Publications, recognition

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TRACKING AND DETECTION BELOW CLUTTER y DL starts with uncertain knowledge and converges rapidly on exact solution Performance achieves joint CRB for association and estimation

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01 km TRACKING AND DETECTION BELOW CLUTTER Cross-Range Range 1 km 0 (a) True Tracks detections Range 1 km 0 cd (b) efg h Multiple Hypothesis Testing “logical” complexity ~ 10 1800 ; DL complexity ~ 10 6 ; S/C ~ 18 dB improvement

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NUMBER OF TARGETS Active models and one dormant model -Only r(m) is estimated for the dormant model -The dormant model is activated if r(m) > threshold -An active model is deactivated if r(m) < threshold -In this example threshold = 0.001 of the total signal -threshold = 0.001 x (n)

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LOCAL MAXIMA Practically it is not a problem Reasons -Vague initial states smooth local maxima -Activation and deactivation eliminates local convergences -In system applications, new data are coming all the time local maxima come and go, real tracks persist

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JOINT FUSION, ASSOCIATION, TRACKING, AND NAVIGATION 3 platforms-sensors Targets cannot be detected or tracked with one sensor All data are processed simultaneously GPS is inadequate for triangulation - Relative platform positions have to be estimated jointly with target tracks Multiple Hypothesis Testing “logical” complexity ~ 10 17000

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Sensor 1 (of 3): Model Evolves to Locate Target Tracks in Image Data UNCLASSIFIED truthdataInitial uncertain model Models converged to the truthImproved model after few iterationsFew more iterations

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Sensor 2 (of 3): Model Evolves to Locate Target Tracks in Image Data UNCLASSIFIED

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Sensor 3 (of 3): Model Evolves to Locate Target Tracks in Image Data UNCLASSIFIED

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NAVIGATION, FUSION, TRACKING, AND DETECTION this is the basis for the previous 3 figures, all fused in x,y,z, coordinates

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OUTLINE Related research Combinatorial complexity and logic Dynamic logic Joint likelihood, math. formulation Examples Publications, recognition

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PUBLICATIONS 300 publications OXFORD UNIVERSITY PRESS (2001; 3 rd printing) Neurodynamics of High Cognitive Functions with Prof. Kozma, Springer, 2007 Sapient Systems with Prof. Mayorga, Springer, 2007

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RECOGNITION 2007 Gabor Award -The top engineering award from International Neural Network Society (INNS) Elected to the Board of Governors of INNS 2007 John L. McLucas Award -The top scientific award from the US Air Force

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CONCLUSION Dynamic Logic – an approach to improve algorithms and developing new ones –Being developed since late 1980s –Proven breakthrough in several areas More can be done 16-Sep-05 24

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2 – In previous chapters: – We could design an optimal classifier if we knew the prior probabilities P(wi) and the class- conditional probabilities P(x|wi)

2 – In previous chapters: – We could design an optimal classifier if we knew the prior probabilities P(wi) and the class- conditional probabilities P(x|wi)

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