ABSTRACT
Thresholds ............................................................ 734
13.3.2. Extreme Value Theory ........................................................ 735
13.3.3. The Radar Problem.............................................................. 736
13.3.4. Methods for Estimating Thresholds .................................... 737
13.3.4.1. Estimates Based on Raw Data............................. 737
13.3.4.2. Estimates Motivated by the Extreme
Value Theory........................................................ 738
13.3.5. The Generalized Pareto Distribution................................... 739
13.3.5.1. Methods for Estimating the Parameters
of the GPD ........................................................... 742
13.3.5.2. Estimation of Thresholds ..................................... 748
13.3.6. Numerical Results................................................................ 749
Distributions ......................................................... 749
13.3.6.2. Empirical Properties of the Estimators for
Known Distributions ............................................ 749
13.3.6.3. Effect of the Choice of l on the Threshold
Estimates .............................................................. 756
13.3.7. Examples.............................................................................. 758
13.3.7.1. Known Distribution Case..................................... 758
13.3.7.2. An Unknown Distribution Case........................... 759
13.4. Performance of the LOD for Multivariate Student-T
and K-Distributed Disturbances........................................................ 764
13.4.1. The Multivariate Student-T Distribution............................. 764
13.4.1.1. The Locally Optimum Detector........................... 766
13.4.1.2. Computer Simulation of Performance................. 768
13.4.1.3. Results of the Computer Simulation ................... 771
13.4.2. The Multivariate K-Distribution.......................................... 776
13.4.2.1. The Locally Optimum Detector........................... 778
13.4.2.2. Computer Simulation of Performance................. 780
13.4.2.3. Conclusions .......................................................... 783
13.4.3. Determining LOD Threshold with Real Data..................... 785
13.5. Performance of the Amplitude Dependent LOD ............................. 788
13.5.1. The Amplitude Dependent LOD for the Multivariate
K-Distributed Disturbance ................................................... 789
13.5.1.1. Results of Computer Simulation.......................... 790
13.5.2. The Amplitude Dependent LOD for the Student-T
Distributed Disturbance ....................................................... 794
13.5.2.1. Conclusions .......................................................... 796
13.6. Conclusions ....................................................................................... 797
13.6.1. Summary.............................................................................. 797
13.6.2. Suggestion for Future Research .......................................... 798
In radar applications it is found that the received target signal is contaminated
with clutter and thermal noise. The received signal due to undesired reflections
from land, sea, atmosphere etc. is called clutter. The thermal noise generated by
the receiver hardware is typically modeled as a Gaussian random process. This
kind of noise is always present. Depending upon the situation, the clutter may or
may not be modeled as a Gaussian random process. Also, the power associated
with the background clutter may be orders of magnitude larger than the receiver
thermal noise or the desired signal power.
