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Ambiguity in Radar and Sonar

Ambiguity in Radar and Sonar. Paper by M. Joao D. Rendas and Jose M. F. Moura Information theory project presented by VLAD MIHAI CHIRIAC. Introduction.

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Ambiguity in Radar and Sonar

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  1. Ambiguity in Radar and Sonar Paper by M. Joao D. Rendas and Jose M. F. Moura Information theory project presented by VLAD MIHAI CHIRIAC

  2. Introduction • Radar is a system that uses electromagnetic waves to identify the range, altitude, direction, or speed of both moving and fixed objects such as aircraft, ships, motor vehicles, weather formations, and terrain. • The ambiguity is a two-dimensional function of delay and Doppler frequency showing the distortion of an uncompensated match filter due to the Doppler shift of the return from a moving target

  3. Introduction (cont.) Ambiguity function for Barker code

  4. Introduction (cont.) • Ambiguity function from the point of view of information theory and is based on Kullback directed divergence • Models: - radar/sonar with unknown power levels - passive in which the signals are random - mismatched

  5. Kullback direct divergence • The Kullback direct divergence is a measure of similarity between probability densities. • The KDD between two multivariate Gauss pdf’s p and q, which have the same  and distinct covariance matrices Rand R0

  6. Types of probability distribution functions • Exponential densities (Gauss, gamma, Wishart and Poisson). • These distribution depends on unspecified parameter called natural parameter • The subfamily of exponential pdfs that results by parametrizing the natural parameter is called the curved exponential family.

  7. Estimation of the interest parameters • Estimate the natural parameter from the measured samples by computing the unstructured maximum-likelihood (ML) • Estimate the desired parameters by minimizing the KDD distance between the true pdf and the curved exponential family.

  8. The two step principle

  9. Generalized log-likelihood ratio

  10. Model • Source signal: • Received signal: • Channel model: • Noise + interference:

  11. Ambiguity: No nuisance parameters • The ambiguity function when we estimate , conditioned on the occurrence of 0 is: where Iub(0) is an upper bound of I(0:)

  12. Ambiguity: Unwanted parameters • Two subfamilies: VS • The generalized likelihood ratio: where

  13. Ambiguity: Unwanted parameters (cont.)

  14. Ambiguity: Unwanted parameters (cont.) • Consider the problem of estimation of the parameter  from observations described by the model G, where  is an unknown nonrandom vector of parameters. • Definition – Ambiguity: The ambiguity function in the estimation of  conditioned on the occurrence of 0 = (0, 0) is:

  15. Ambiguity: Modeling inaccuracies • For this situation the model is: where  is a vector which contains parameters, approximately known associated with propagation

  16. Ambiguity: Modeling inaccuracies (cont.) • The generalized likelihood ratio: • Consider the parameter estimation problem described by the curved exponential family G000 using the probabilistic model G001 at the receiver. • The ambiguity function in the estimation of , given that 0 is the true value of the parameter is:

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