Adaptive Radar Detection in the Presence of Multiple Alternative Hypotheses Using Kullback-Leibler Information Criterion-Part I: Detector Designs

In this paper, we develop a new elegant systematic framework relying on the Kullback-Leibler Information Criterion to approach the design of one-stage adaptive detection architectures for multiple hypothesis testing problems in radar. Specifically, at the design stage, we assume that one out of seve...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2021, Vol.69, p.3730-3741
Main Authors: Addabbo, Pia, Han, Sudan, Biondi, Filippo, Giunta, Gaetano, Orlando, Danilo
Format: Article
Language:English
Subjects:
Adaptive radar detection
Constant false alarm rate
Criteria
generalized likelihood ratio test
Hypotheses
Hypothesis testing
Jamming
kullback-leibler information criterion
Likelihood ratio
model order selection
multiple alternative hypothesis testing
Null hypothesis
Parameters
Probability density functions
Radar
Radar detection
Radar scattering
Radar signal processing
Radar tracking
Regularization
Testing
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Summary:In this paper, we develop a new elegant systematic framework relying on the Kullback-Leibler Information Criterion to approach the design of one-stage adaptive detection architectures for multiple hypothesis testing problems in radar. Specifically, at the design stage, we assume that one out of several alternative hypotheses may be in force and that only one null hypothesis exists. Then, starting from the case where all the parameters are known and proceeding towards the adaptivity with respect to the entire parameter set, we come up with decision schemes for multiple alternative hypotheses consisting of the sum between the compressed log-likelihood ratio based upon the available data and a penalty term accounting for the number of unknown parameters. Such a term arises from suitable approximations of the Kullback-Leibler Divergence between the true and a candidate probability density function. Interestingly, under specific constraints, the proposed decision schemes can share the constant false alarm rate property by virtue of the Invariance Principle. Finally, we also show that the new architectures can be viewed as the result of a suitable regularization of the log-likelihood.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2021.3089440