Statistical Analysis of High Resolution Land Clutter

1
Statistical Analysis of High Resolution Land
Clutter

• G Davidson
• Kochi University of Technology
• H D Griffiths
• University College London
• S Ablett
• Dstl

2
Overview

• Large amount of Byson C-band (VV) frequency agile
  radar data operated in mixed clutter environment
  of Worcester.
• Analysis suggests that no single distribution
  fits well.
• Dominated by varying statistics including
  non-stationarity, clutter edges and
  discontinuities related to environment.
• Due to instrumental effects and sample
  uncertainty, performance predictions were
  erroneous.
• Show a 7dB detection gain (Pfa of 10-4) possible
  when the normalised log estimate U is used as a
  measure of uncertainty. Proposed CFAR has a
  variable threshold multiplier as an empirical
  function of U.
• Uses real data to include all instrumental
  effects.

3
Aim
Intensity
Terrain Height

• Analyse high resolution data and determine
  possible target detection gain from using
  non-Gaussian statistics.

4
Data Acquisition

• Frequency Agile 30m
• Pulse compression into range cells of 1 metre.
• 96 Azimuth Swaths,500 Range Gates,128
  Frequencies,Repeated 32 times,For 7
  attenuations
• Total 1?109 samples
• 100m azimuth resolution

• The natural local statistics to analyse were the
  100 compressed range cells within each range gate.

5
Distribution Analysis

• Normalised log estimate U reasonable for both K
  and Weibull

Shape parameter
(Blacknell, Oliver)
6
Dynamic Range Digitisation
Gaussian U -1 U -2 U -3 U -4 U -5 U
-6 Spiky

• Byson instrumentation has a strong effect upon U

7
Individual Gate Attenuation

• 0dB to 50dB attenuation required over entire scene

8
U Measured for Entire Scene

• Wide variation in U but Motorway and Railway
  visible

9
Range Cell Traces
Motorway (dB)
Open Area (linear)

• Two cases with identical measured U obviously
  have very different statistics and may not be
  Independent Identically Distributed

10
Step Effect upon U
10dB 15dB 20dB

• Steps in the data seriously alter the estimate of
  U, such that the clutter variance is
  over-estimated

11
Edge Corrupted or K?
Edges
Stable K
Edge Present Stable Gaussian Stable K
12
Scene Likelihood Analysis
Edge-like
log10 likelihood
K-like

• More edge-corrupted speckle than K, except
  motorway is visibly K-like.

13
Detection Algorithm

• Postulate Distribution

Environmental, Weibull, K, ??

• Estimate Shape

Low sample number, edge corruption

• N-sum Distribution

Mathematically intractable, stability over
time/range

• Pfa Calculation

Mathematical architecture choice

• Pd Calculation

Monte Carlo often used

• Dynamic Range, Digitisation, Pulse Compression

14
Empirical Method
Gaussian
Spiky

• Empirical distributions are already used
  (Weibull). A large dataset means the mathematics
  can be avoided by directly mapping the shape
  estimate to the required threshold.

15
Fixed Multiplier CFAR
Intensity
Range

• Threshold multiplier chosen for Pfa of 10-4 over
  scene

16
Variable Multiplier CFAR
U
Intensity
Range
U

• Threshold multiplier now a function of U for Pfa
  of 10-4

17
Real Data/Simulated Target

• 16 Pulse CFAR
• 4 Guard Cells
• Pfa 10-4
• Swerling 0 target

7dB

• At Pd 0.5 7dB target gain

18
Conclusions

• Land data can be so variable that the concept of
  a stable statistical distribution is not useful
  for small sample numbers.
• Normalised log estimator U can illustrate this
  variability, but it is susceptible to edges,
  digitisation and small samples.
• Likelihood analysis suggested that a large
  proportion is affected by edges, but CAGO didnt
  help.
• Fixed multiplier CFAR false alarms dominated by
  motorway and other spiky areas strongly
  correlated to environment.
• Instead of empirically fitting distributions such
  as Weibull to single pulse data, weve
  empirically fitted the required threshold for a
  variable multiplier CFAR architecture as f(U).
• When all instrumentation effects are included,
  still see a 7dB improvement in performance.
  Normalised log U is useful as a general measure
  of uncertainty.