1
Jeffrey Krolik, Michael Papazoglou, and Richard Anderson
Duke UniversityDepartment of Electrical and Computer Engineering
Durham, NC 27708
Over-the-Horizon Skywave RadarTarget Localization
With support from the Office of Naval Research, the Naval Research Lab,and the Counter-Drug Program of the Office of the Secretary of Defense
1999 Lincoln Laboratory ASAP Workshop
2
Remote Sensing in Multipath Propagation Channels
WHAT WE DO : Develop statistical signal and array processing techniques forelectromagnetic and acoustic remote sensing which exploit complex multipathpropagation to achieve enhanced performance.
BACKGROUND:
• Radar and sonar signal processing methods have historically relied on plane-wavepropagation models because of their analytic and computational simplicity.
• Methods for mitigating multipath propagation have been developed but typically exhibitperformance which is upper bounded by their behavior when multipath is absent.
• The idea of exploiting, rather than undoing, the effects of multipath propagation toachieve improved localization performance by use of a computational propagationmodel is the essence of matched-field processing (MFP)
• Our current projects involve multipath signal processing for passive and active sonar,over-the-horizon skywave radar, and tropospheric refractivity estimation usingmicrowave clutter from the sea surface.
3
Matched-field Altitude Estimation for OTH Radar
OBJECTIVE: To estimate aircraft target altitude to within 3000 feet using a limitednumber of dwells by matched-field processing of unresolved multipath returns incomplex delay-Doppler space.
BACKGROUND:
• Previous attempts at altitude estimation with OTH radar have required either excessivesignal bandwidth or revisits to resolve micro-multipaths in slant range or Doppler.
• Matched-field processing consists of correlated the observed data with predictions of theunresolved multipath signal as a function of hypothesized target position.
• Our approach to altitude estimation is aimed at precisely modeling the changes in themicro-multipath signal from revisit to revisit in complex delay-Doppler space.
ALTITUDE ESTIMATION CURRENT STATUS:
• Initiated by ONR in 1996 and transitioned to OSD Counter-Drug Program in 1997.
• Currently implemented on a real-time demonstration system attached to the Navy’sRelocatable OTH Radar (ROTHR).
4
Ground
Transmit Rays
Receive Rays
Baseline Rays
Dwell 1
Slan
t (km
)
2400
2500
2600
Dwell 2Sl
ant (
km)
2400
2500
2600
Dwell 3
Slan
t (km
)
2400
2500
2600
Dwell 4
Doppler (Hz)
Slan
t (km
)
−20 −10 0 10 202400
2500
2600
Dwell 5
Dwell 6
Dwell 7
Dwell 8
Doppler (Hz)−20 −10 0 10 20
Level (dB)30 40 50 60 70
Micro-multipath Returns in Delay-Doppler Space
• Within and across revisits,delay and Doppler differencesbetween micro-multipathsresult in complex target peakshape changes and fadingwhich is altitude dependent.
• Within and across revisits,delay and Doppler differencesbetween micro-multipathsresult in complex target peakshape changes and fadingwhich is altitude dependent.
• Overlapping micro-multipaths consist of acoherent sum of direct and surface-reflected returns which are unresolved inlog-amplitude delay-Doppler space.
• Overlapping micro-multipaths consist of acoherent sum of direct and surface-reflected returns which are unresolved inlog-amplitude delay-Doppler space.
5
Multi-dwell Matched-field Altitude Estimation
• Multi-dwell maximum likelihood altitude estimates exploit shape changes in complexdelay-Doppler return without requiring knowledge of target backscatter characteristics.
• Slow fluctuations due to target aspect changes and Faraday rotation are handled using afirst-order Markov model for unknown aircraft reflection coefficients.
• Ionospheric model and estimated target ground track can be obtained from current radar.
• Multi-dwell maximum likelihood altitude estimates exploit shape changes in complexdelay-Doppler return without requiring knowledge of target backscatter characteristics.
• Slow fluctuations due to target aspect changes and Faraday rotation are handled using afirst-order Markov model for unknown aircraft reflection coefficients.
• Ionospheric model and estimated target ground track can be obtained from current radar.
Ionospheric ParameterEstimation
SounderData
Micro-MultipathPropagation Model
Delay-Doppler SurfaceReplica Generation
Delay-DopplerSurface Observations
Two-DwellAltitude Log-Likelihood
Function
AccumulateMulti-dwell
Log-likelihood
Ground Track andHypothesized Altitude
Delay
X(k)
X(k-1)
6
A Markov Model for Complex Delay-Doppler Data
• Let vector xk denote the delay-Doppler neighborhood around a target at altitude, z, and
slant range, τ k, and Doppler ωk , during the kth revisit:
x H d nkj
k k k k ke zk= +θ τ ω( , , )
where the matrix Hk k k z( , , )τ ω contains the predicted post-compression micro-multipathwaveforms, dk, is the unknown reflection coefficient vector, θk is the unknown phase path,and nk is uncorrelated complex Gaussian noise.
• To handle Faraday rotation and slow aspect-dependent changes in the target backscatter, theunknown complex reflection coefficient vector, dk, is modeled as a first-order zero-meancomplex Gaussian Markov process.
• Thus xk is a time-evolving complex random process with unknown nonrandom parameters,z k k, ,τ ω , k=0,…,K, and θk, k = 1,…,K.
7
Maximum Likelihood Matched-field Altitude Estimation
• Using a Markov model for the time-dependent target reflection coefficients, the maximumlikelihood estimate of altitude is given by:
argmax log ( | , , ) log ( | , , , , )p z p zo o o k k k k kk
Kx x xτ ω τ ω θ+
%&'
()*
−=∑ 1
1
where p( )x is the multivariate complex Gaussian density function.
• ML estimates of τ k and ω k can be approximated by using the radar’s slant tracker output.
• ML estimates of θk may be solved analytically for this model so that only numericalevaluation of the time-evolving likelihood function accumulation over altitude is required.
8
Time (minutes)
Alti
tud
e (
kft)
0 10 20 30
5
10
15
20
25
30
35
40
No
rma
lize
d L
og
Lik
elih
oo
d
−50
−40
−30
−20
−10
0
MFAE Results for High and Low Flying Targets
• Time-evolving log-likelihood functions of aircraft altitude obtained using ROTHR data.• Time-evolving log-likelihood functions of aircraft altitude obtained using ROTHR data.
Time (minutes)
Alti
tude
(kf
t)
0 1 2 3 4 5
5
10
15
20
25
30
35
Nor
mal
ized
Log
Lik
elih
ood
−50
−40
−30
−20
−10
0
• Commercial flight at range of1200 km. FAA ground-truth is 35kft. Estimated altitude is 35.2 kft.
• Commercial flight at range of1200 km. FAA ground-truth is 35kft. Estimated altitude is 35.2 kft.
• Small aircraft at range of 2300km. GPS ground-truth is 5.2 kft.Estimated altitude is 4.9 kft.
• Small aircraft at range of 2300km. GPS ground-truth is 5.2 kft.Estimated altitude is 4.9 kft.
9
0 10 20 30 400
0.2
0.4
0.6
0.8
1
Altitude (kft)
Prob
abilit
y
0.5 kft5 kft10 kft20 kft30 kft
0 10 20 30 400
0.2
0.4
0.6
0.8
1
Altitude (kft)
Prob
abilit
y
0.5 kft5 kft10 kft20 kft30 kft
• Simulation results indicate that MFAEcan be performed using a radarbandwidth as low as 8 kHz with apossible SNR trade-off.
• Simulation results indicate that MFAEcan be performed using a radarbandwidth as low as 8 kHz with apossible SNR trade-off.
• Simulation results indicate that errorsare typically within 3000 ft. for low,medium, and high altitude aircraft.
• Simulation results indicate that errorsare typically within 3000 ft. for low,medium, and high altitude aircraft.
MFAE Altitude Error Probability Distributions
10
−4 −2 0 2 40
5
10
15
20
25
30
35
40
Altitude Rate (m/s)
Fin
al A
ltitu
de (
kft)
Log
Like
lihoo
d
−50
−40
−30
−20
−10
0
−4 −2 0 2 40
5
10
15
20
25
30
35
40
Altitude Rate (m/s)
Fin
al A
ltitu
de (
kft)
Log
Like
lihoo
d
−50
−40
−30
−20
−10
0
Estimation of Aircraft Altitude in Ascent or Descent
Simulated log-likelihood surface foran aircraft ascending from 5000 feetat 3.3 ft/s after 5 min.
Simulated log-likelihood surface foran aircraft ascending from 5000 feetat 3.3 ft/s after 5 min.
Simulated log-likelihood surfacefor an aircraft descending to 3700feet at -3.3 ft/s after 5 min.
Simulated log-likelihood surfacefor an aircraft descending to 3700feet at -3.3 ft/s after 5 min.
• Target altitude rate adds different Doppler shift components to each micro-multipath, depending on the target range rate and altitude.
• Modification of the micro-multipath model permits joint estimation of altitude andaltitude rate to discriminate aircraft in ascent, descent, or level flight.
• Target altitude rate adds different Doppler shift components to each micro-multipath, depending on the target range rate and altitude.
• Modification of the micro-multipath model permits joint estimation of altitude andaltitude rate to discriminate aircraft in ascent, descent, or level flight.
11
Altitude Rate Estimation Results with Aztec Data
16:00 16:30 17:00 17:30 18:00 18:30 19:00 19:30 20:00 20:30 21:00 21:30 22:00−2
0
2
4
6
8
10
12
GPS Time
Alti
tude
(th
ousa
nds
of fe
et)
Altitu
de R
ate
(ft/s)
Time (minutes)
AZTEC track 15390 dz/dttrue
= −5.5 ft/s, dz/dtest
= −1.1 ft/s
0 1 2 3 4 5
−6
−4
−2
0
2
4
6
Norm
alize
d Lik
eliho
od
−50
−40
−30
−20
−10
0
Time (minutes)
Initia
l Altit
ude
(kft)
AZTEC track 15390, z0,true
= 10.1 kft, z0,est
= 8.2 kft
0 1 2 3 4 5
5
10
15
20
25
30
35
40
Norm
alize
d Lik
eliho
od
−50
−40
−30
−20
−10
0
• ROTHR-VA data collected 11/97 of a GPSground-truthed Aztec flight SW of Puerto Ricohad both ascending and descending legs.
• ROTHR-VA data collected 11/97 of a GPSground-truthed Aztec flight SW of Puerto Ricohad both ascending and descending legs.
• Time-evolving log-likelihood of initial altitude (left) and altitude rate (right) of descentfrom 10 kft. at approximately -5 ft/s.
• Time-evolving log-likelihood of initial altitude (left) and altitude rate (right) of descentfrom 10 kft. at approximately -5 ft/s.
• Correct altitude rate obtained when initiated with previous MFAE altitude estimate.Currently working on approaches for resolving possible altitude-rate ambiguities.
• Correct altitude rate obtained when initiated with previous MFAE altitude estimate.Currently working on approaches for resolving possible altitude-rate ambiguities.
12
OTH Target Localization in Ground Coordinates
0
5001000 1500
2000
2500Ground Range (km)
0
100
200
300
400
Heig
ht (k
m)
0 2 4 6 850
100
150
200
250
300
350
Plasma Frequency (MHz)
Heigh
t (km
)
• The process of making slant-track-to-raymode and slant-track-to-targetassignments and determining target ground locations is called mode linking andcoordinate registration (CR).
• Conventional CR methods assume perfect knowledge of the down-range ionosphereand are prone to large localization errors when the ionospheric model is uncertain.
• The process of making slant-track-to-raymode and slant-track-to-targetassignments and determining target ground locations is called mode linking andcoordinate registration (CR).
• Conventional CR methods assume perfect knowledge of the down-range ionosphereand are prone to large localization errors when the ionospheric model is uncertain.
• In contrast to line-of-sight microwave radars, skywave HF radars require apropagation model to convert multipath delays to a target location estimate.
• In contrast to line-of-sight microwave radars, skywave HF radars require apropagation model to convert multipath delays to a target location estimate.
13
Target Localization with an Uncertain Ionospheric Model
• Ionosonde measurements provide spatially and temporally incomplete information aboutthe downrange ionosphere.
• A statistical ionospheric model is obtained by treating plasma frequency profileparameters as random variables with mean and covariance derived from sounder data.
• Monte Carlo raytracing through a random ionospheric model gives the probabilitydistribution function (PDF) of slant-coordinates for each ground location.
• Ionosonde measurements provide spatially and temporally incomplete information aboutthe downrange ionosphere.
• A statistical ionospheric model is obtained by treating plasma frequency profileparameters as random variables with mean and covariance derived from sounder data.
• Monte Carlo raytracing through a random ionospheric model gives the probabilitydistribution function (PDF) of slant-coordinates for each ground location.
1 2 3 4 5 6 7 8 9 10 11 12
100
150
200
250
300
Plasma Frequency (MHz)
Hei
ght (
km)
Plasma Frequency Profile Realizations
1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 30001000
1500
2000
2500
3000
Ground Range (km)
Sla
nt R
ange
(km
)
Bistatic CR curves, DIR 200, 22Sep1998−1953
−EL−F1L−F1H−F2L−F2H
14
Deterministic versus Statistical CR and Mode Linking
• Statistical CR/mode linker block diagram• Statistical CR/mode linker block diagram
• Deterministic CR/mode linker block diagram• Deterministic CR/mode linker block diagram
Compute PDF ofRaymodes
Clustering inSlant Space
Hypothesize Slant-Track-to-Target Assignments
ML Mode Assignmentand CR
Evaluate MAPHypothesis Sequence
Ionospheric modelstatistics
SlantTracks
Possible raymodes from previous dwell for each hypothesis
Delay
Clusteringin Ground Space
Hypothesize Slant-Track-to-Raymode-to-Target Assignments
Evaluate Chi-squareHypothesis Test
SlantTracks
Possible raymodes from previous dwell for current hypothesis
Delay
CR
Compute CR TableIonospheric model
realization
15
Maximum Likelihood Mode Assignment and CR
• Each slant observation is modeled as a doubly-stochastic random variable whosedistribution is determined by both the probability that it corresponds to a particularraymode type and its variability conditioned on its raymode family.
x F r nj k s k sj k j k, , ,( )= +
• Given the Doppler-ordered observations, xj k, , the MLE of target ground position, rk, and
associated raymodes, sj k, , in the presence of slant track jitter, nsj k, is obtained by:
arg max log ( | , , , ) log Pr( | , ), , , , , ,p x x s s r s s rj k j k j k j k k j k j k kj
K
− − −=
+∑ 1 1 11= B
where raymode transition probabilities, Pr( | , ), ,s s rj k j k k−1 , and the output probability
distribution parameters are estimated from Monte Carlo raytracing through a statisticalionospheric model.
• A fast recursive dynamic programming method is used to compute this ML estimate.
16
MLCR Results with the Puerto Rico Beacon Data
• Ground range error histograms from ROTHR-VA, minimum variance (MV) CR with3-D raytracing, and MLCR for Puerto Rico beacon at 2193 km range using real data.Average absolute miss distance (AVMD) reported in normalized coordinates.
• Ground range error histograms from ROTHR-VA, minimum variance (MV) CR with3-D raytracing, and MLCR for Puerto Rico beacon at 2193 km range using real data.Average absolute miss distance (AVMD) reported in normalized coordinates.
−1.5 −1 −0.5 0 0.5 1 1.50
10
20
MV−
Rada
r
AVMD = 0.45BIAS = 0.34
−1.5 −1 −0.5 0 0.5 1 1.50
10
20
MV−
3D AVMD = 0.31BIAS = 0.08
−1.5 −1 −0.5 0 0.5 1 1.50
10
20
ML
Miss Distance in normalized units
AVMD = 0.20BIAS = 0.04
17
Statistical CR and Mode Linking Features
• Statistically models the ionosphere to achieve greater robustness to uncertainty indownrange environmental conditions. In contrast, for example, current deterministicapproach may lead to large errors if strongest raymode incorrectly predicted.
• Estimates the correlation between slant tracks due to ionospheric variability underdifferent hypothesized raymode assignments to improve mode linking. In contrast, forexample, current approach assumes independence among bistatic EE, EF, and FFraymodes which during an F-layer TID could prevent tracks from being linked.
• Uses Doppler ordering of slant tracks to assist in raymode assignments. This exploitsraymode elevation angle information useful for slant-track-to-raymode assignment.
• Maximum a posteriori probability (MAP) decision criteria based on estimated PDF’s ofslant-track observations under different hypotheses. This extends conventionalminimum variance test to provide a more accurate criteria for mode linking decisions.
• Chooses mode linking decision which optimally weights time history of decisions withcurrent slant track data. In contrast, existing mode linker makes a hard decision after alimited observation time.
18
Scenario for Multi-Target Multi-Mode Mode Linking
• Ionospheric Modeling
Frequency (MHz)
Grou
p Dela
y (ms
)
22−SEP−1998 19:53:07.16
2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Frequency (MHz)
Grou
p De
lay (m
s)
22−SEP−1998 19:53:07.16, Sector 3
200
5 10 15 20 250
500
1000
1500
2000
2500
3000
3500
4000
4500
0 10 20 30 40 50 60 70 80 901600
1700
1800
1900
2000
2100
2200
28771
Time (minutes)
Sla
nt R
ange
(km
)
28781
28789
28817
28820
28846
28855
28856
28860
28883
28884
28895
28936
28946
28953
28966
29002
29034
29050
29085
29086
29092
29122
29123
2912429129
2919029248
29261
29284
29289
29313
Slant Ranges, DIR 200, 22Sep1998−1946 to 2110
• Typical QVI and WSBI with prediction from CREDO ionospheric model for 9/22/98 data.• Typical QVI and WSBI with prediction from CREDO ionospheric model for 9/22/98 data.
• Slant tracks from DIR 200 from1946 to 2110 Z used to evaluatemode linker performance. Noteseveral occurrences of possiblemultipath arrivals.
• Slant tracks from DIR 200 from1946 to 2110 Z used to evaluatemode linker performance. Noteseveral occurrences of possiblemultipath arrivals.
19
MAP vs. ROTHR Geographical Displays
−73 −72.5 −72 −71.5 −71 −70.5 −7018
19
20
21
22
23
24
25
C102
C1502
FWL774
NASA806NASA817
SLM655
2878028781
28839 28846
28884
2905029084
29086
29092
29124
29187
29247 29289
Longitude (0.1 deg ~ 10 km (5.4 nmi))
Latit
ude
(0.1
deg
~ 1
1 km
(5.9
nm
i))
DIR 200, 22Sep1998−1946:2111
FAAROTHR
−73 −72.5 −72 −71.5 −71 −70.5 −7018
19
20
21
22
23
24
25
28781
28817
28846
28855
28856
28884
28895
2905029085
29086
29092
2912229123
29124
29190
29261
2928429289
Longitude (0.1 deg ~ 10 km (5.4nmi))
Latit
ude
(0.1
deg
~ 1
1 km
(5.9
nmi))
C102
C1502
FWL774
NASA806NASA817
SLM655
FAAML CRTA
• MAP ground tracks vs. FAA data for1946-2110 Z.
• MAP ground tracks vs. FAA data for1946-2110 Z.
• Current ROTHR ground tracks versusFAA data for 1946 to 2110 Z.
• Current ROTHR ground tracks versusFAA data for 1946 to 2110 Z.
• Observe that MAP ground tracks exhibit smoothness comparable to ROTHR without a“hard-wired” ground track jump limit and while retaining the ability to revise mode linkingdecisions as more slant-track data becomes available.
• Observe that MAP ground tracks exhibit smoothness comparable to ROTHR without a“hard-wired” ground track jump limit and while retaining the ability to revise mode linkingdecisions as more slant-track data becomes available.
20
Multi-Target Multi-Track Mode Linking Example
−72 −71.8 −71.6 −71.4 −71.2 −71 −70.8 −70.6 −70.4 −70.219
19.2
19.4
19.6
19.8
20
20.2
20.4
20.6
20.8
21
28817
28846
28856
28895
Longitude (0.1 deg ~ 10 km (5.4nmi))
Latit
ude
(0.1
deg
~ 1
1 km
(5.
9nm
i))NASA806
NASA8172884628839
NASA806 and NASA817, DIR 200, 22Sep1998−1946:2111
• NASA806 and NASA817flights from 9/22/98 whereMAP assigns the four tracksto the two targets to gives asmuch as a 3:1 accuracyimprovement over ROTHR.
• NASA806 and NASA817flights from 9/22/98 whereMAP assigns the four tracksto the two targets to gives asmuch as a 3:1 accuracyimprovement over ROTHR.
FAA = RedMAP = Blue
ROTHR=Green
F ligh ts N A S A 806 and N A S A 817 D IR 200
S lan t ID M A P G round ID M A P M ode M A P M is s D is tanc e R O TH R G round ID R O TH R M ode R O TH R M is s D is tanc e(m ed ian nm i) (m ed ian nm i)
28817 28817 F 2L-F 2L 6 .2 28846 F 2L-F 2L 15 .028846 28817 E -F 2L 6 .2 28846 F 2L-F 2L 15 .028856 28856 F 2L-F 2L 6 28839 F 2L-F 2L 18 .428895 28856 E L-F 2L 9 .9 no t pu t to g round n /a n /a
21
Multi-Mode Single Target Example
−71.3 −71.2 −71.1 −71 −70.9 −70.8 −70.7 −70.6 −70.5 −70.4 −70.320.7
20.8
20.9
21
21.1
21.2
21.3
21.4
21.5
21.6
2928429289
Longitude (0.1 deg ~ 10 km (5.4nmi))
Latit
ude
(0.1
deg
~ 1
1 km
(5.
9nm
i))
FWL774
29289
FWL774, DIR 200, 22Sep1998−1946:2111
• FWL774 flight from 9/22/98where MAP correctly links twotracks to give a 2:1 accuracyimprovement over ROTHR.
• FWL774 flight from 9/22/98where MAP correctly links twotracks to give a 2:1 accuracyimprovement over ROTHR.
FAA = RedMAP = Blue
ROTHR=Green
F ligh ts F W L774 D IR 200
S lant ID M A P G round ID M A P M ode M A P M is s D is tanc e R O TH R G round ID R O TH R M ode R O TH R M is s D is tanc e(m ed ian nm i) (m ed ian nm i)
29284 29284 F 2L-F 2L 10.0 29281 (from D IR 199 ) F 2L-F 2L n /a29289 29284 F 1L-F 2L 10.0 29289 F 2L-F 2L 18.5
22
Conclusions
• Complex multipath propagation conditions can be modeled and exploited to providenew capabilities, such as altitude estimation, to existing radars.
• Matched-field altitude estimation (MFAE) exploits the complex fading characteristic ofunresolved multipath to achieve a median absolute error of less than 3000 feet withtypically no more than 10 revisits on the target.
• Our current extensions of MFAE include target depth estimation with active sonar.
• Statistical modeling of the ionosphere facilitates target ground localization which ismore robust to uncertainties in the down-range electron density profile.
• Comparison of statistical mode linking/CR with conventional methods using largedatasets will by facilitated by near-term ionospheric modeling upgrades to ROTHR.
