Factors affecting radar range resolution EECS 725 Introduction to Radar Presented by Susobhan Das.
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Transcript of Factors affecting radar range resolution EECS 725 Introduction to Radar Presented by Susobhan Das.
Factors affecting radar range resolution
EECS 725 Introduction to Radar
Presented by
Susobhan Das
Outline……• Introduction
• Range Resolution
• Factors related to Range Resolution
• Theory of Range Resolution Development
• Dependency on relative RCS factor
• Dependency on Location Deviation
• Conclusion
• Reference
Introduction
Range Resolution
c : Speed of light in air /vacuum medium τ : Pulse width B : Bandwidth of the pulse = 1/τ
B
ccRd 22
Factors related to Range Resolution
Probability of resolving two targets
• Difference in RCS of the targets• SNR of the system• Separation between targets
Range resolution depends on
• Bandwidth of pulse• SNR of the system• RCS of the targets• Apparent target location ( deviation from the actual location)
2)( kRrk erf
2ln4
cB
2
1
)()(k
k rfrF
)(2
121 RRRm
)())()((2
121 mRFRFRF
σk RCS of the kth target (k=1,2)Rk Range location of the respective targetr range variable
Half Power bandwidth = c/2B
Gaussian profile of the pulse-compressed return signal from a single point target
Assuming random phase difference between two targets and distributed on [-π, +π]The envelop of the over all signal
Local minimum at
Deviation of peaks from the local minimum
Theory of Range Resolution Development
Continue…
)()()()(
11
12
12mm RFRFRR
RR
RFRF
kR
mR
: exact location of peaks
: exact location of minimum1.0
25.0
0)( drrdF 0)( 22 drrFd
0)()(22
1
k
kk rfRr
0)()2)(4(2
1
22 k
kk rfRr
12
For local minimum
Without loss of generality, assume Where α<1
)(2 LMdR
1
1
2
3
2
33)(LM
2ln
)(
4
LMd B
cR
Dependency on relative RCS factor
0)()2)(4()()()(2)( 2
1
222
1
k
kkk
kk RfRRRRRfRRRd
RdF
2
1
2
2
1
)(]1)(2[
)()(
kkk
kkk
RfRR
RfRRRR
kkk RR
dR
k
),(2 MDdR
11
2
1
1 2
11
2
1),( eWMD
k : deviation from the true location
: maximum allowable deviation relative to the target range
W-n nth branch Lambert W function
2ln
),(),(max
4
MDLMd B
cR
Dependency on Location Deviation
2ln
),(
4
MDd B
cR
Conclusion
• Common definition of Range Resolution modified with unequal strength of targets
• Existence of local minimum between two peaks and limiting deviation of peaks from true target location
Reference
1. Hasan S. Mir, and Blair D. Carlson, “On the Definition of Radar Range Resolution for Targets of Greatly Differing RCS” ieee transactions on instrumentation and measurement, vol. 61, no. 3, March 2012
2. P.-R. Wu, “A criterion for radar resolution enhancement with Burg algorithm,” IEEE Trans. Aerosp. Electron. Syst., vol. 31, no. 3, pp. 897–915,Jul. 1995.
3. H. S. Mir and J. D. Wilkinson, “Radar target resolution probability in a noise-limited environment,” IEEE Trans. Aerosp. Electron. Syst., vol. 44, no. 3, pp. 1234–1239, Jul. 2008.