building height estimation using multibaseline l-band...

Building height estimation using multibaselineL-band SAR data and polarimetric weighted

subspace fitting methods

Yue Huang, Laurent Ferro-Famil

SAPHIR team, IETRUniversity of Rennes 1, France

Jan 2009

Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF

Objectives of urban area analysis

I Estimate height locations ofscatterers

I Extract physical features ofscatterers

MB-PolinSAR approach

I MB-InSAR: heights, layover sources

I PolinSAR: physical features

Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods


MB-PolinSAR methods and limitations

I Classical methods (Capon, Beamforming): low resolution

I High Resolution methods (MUSIC, Det-ML, Stoch-ML)I Adapted to responses with specific statistical properties:

coherence, correlation, . . .I Irregularly sampled baseline: spurious sidelobes.

Proposed method

PolWSF: polarimetric weighted subspace fitting



Distributed Scatterer: Unconditional ModelCoherent Scatterer: Conditional Model

General array signal model (m sensors)

y = A(θ)x + n ∈ Cm

I y ∈ Cm: observed noisy data

I x ∈ Cd : source (reflected) signals (d elements)

I n ∈ Cm: additive noise

I m × d steering matrix

A(θ) = [a(θ1), . . . , a(θd)]

I a(θi ) m-element steering vector

I a(θi ) = a(zi ) with height zi

a(zi ) = [1, exp{jkz2zi}, exp{jkzmzi}]T




Unconditional MB-PolinSAR signal model

yu =d∑

i=1

√σixui � a(zi ) + n

I Valid for Distributed Scatterers with speckle affected responsesI Stochastic source signal

xi =√σixui with xui ∼ N (0, I)

I yu ∼ N (0,Ry)I σi , zi estimated from Ry




Conditional MB-PolinSAR signal model

yc =d∑

i=1

√σixcia(zi ) + n

I Valid for coherent scatterers: frequently encountered over urbanareas

I x =√σixci is deterministic (frozen) over N observations (looks)

I yc ∼ N (Ax, σ2nI )

I σi , zi estimated from Ax




Hybrid SAR signal model

I Mixture of coherent and distributed scattering contributions * (Saueret al: 2007)

y = yc + yu

=Pd1

i=1

√σi xci a(zi ) +

Pd2i=1

√σi xui � a(zi ) + n

I MUSIC: degraded performance for coherent scatterers

I Det-ML and Stoch-ML: partially sub-optimal techniques

Model adaptive method⇒ Weighted Subspace Fitting (WSF)



Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results

Characteristics of WSF

I Applicable to arbitary array structure

I Multi-dimensional optimization (MUSIC: 1-D optimization)

I Statistically efficient for correlated signals compared to MUSIC

I Optimal for coherent and distributed scatterersI Coherent scatterers

I CWSF (error) ≤ CDet−ML(error)I Asymptotically CWSF (error)→ CRLB

I Distributed scatterersI CWSF (error) = CStoch−ML(error)I CWSF (error)→ CRLB




WSF principle * (M. Viberg et al: 1991)

Subspace fitting problem

z, T = arg min ‖EsW1/2 − AT‖

2

F

I T: fitting matrix; W: weighting matrix; A: steering matrix;Es : signal subspace; En: noise subspace

I Objective: determine T that fits the steering matrix space to signalsubspace

I Subspace fitting cost function ‖EsW1/2 − AT‖2

F

Total Least-Square Solution

T = (AHA)−1AHEsW1/2

z = arg min tr{AH EnEHn AW}




WSF principle * (M. Viberg et al: 1991)

Various weighting matrix choices

I W = I → MUSIC

I W = Λs − σ2I = Λ→ Det-ML for coherent scatterers

Optimal weighting matrix: WSF

I Wopt = (AH EsΛsW−1S EH

s A)−1

I Estimation error covariance C(Wopt) ≤ C(W)

I C(Wopt) = C(Wstoch−ML) for distributed scatterers

⇒ WSF is optimally model adaptive




Extension to the fully polarimetric case

(z, Φ) = arg min tr{AH(z,Φ)EnEHn A(z,Φ)W}

Wopt = (AH(z,Φ)Es(Λs − σ2I)−2Λs EHs A(z,Φ))−1

Polarimetric steering vector and matrix

I a(z ,φ) = a1(z)φ1 + a2(z)φ2 + a3(z)φ3

I φ = [φ1, φ2, φ3]T : unitary target vector (4 parameters)

I For d sources, A(z,Φ) = [a(z1,φ1), . . . , a(zd ,φd)]

Optimization of POL-WSF estimation

I Originally search dimension = 5× d

I Analytic optimization solution over polarization space (see paper)Optimization algorithm maintained to 1× d search dimension




Simulations of distributed and coherent models

Distributed model Coherent model

SNR= 20dBDistributed model Coherent model

Source height (m) 0.0 15.0 0.0 15.0MUSIC 0.0 14.97 -27.9 -5.37WSF -0.1 14.96 0.06 14.85

MUSIC cannot localize coherent scatterers or too closely spacedcontributions




Urban zone in SAR image

I Acquired by E-SAR (DLR)

I L-Band (1.3 GHz)

I Resolution: 0.5 m × 2.5 m

I Fully polarimetric

I Dual-baseline InSARI Small baseline of 10 m

height of ambiguity: 55 m to 73 mI Large baseline of 40 m

height of ambiguity: 14 m to 18 m




Coherent and Distributed scatterers in SAR image*( L. Ferro-Famil et al: 2007)




SP-MUSIC vs SP-WSF tomograms (Model order=1)




SP-WSF tomograms (Model order=1)

Tomogram in slant range Tomogram in ground range




SP-MUSIC vs SP-WSF tomograms (Model order=2)




SP-WSF tomograms (Model order=2)

Tomogram in slant range Tomogram in ground range




FP-MUSIC vs FP-WSF tomograms (Model order=1)




FP-WSF tomogram (Model order=1)




Scattering mechanism α-FP-WSF (order=1)

α in slant range

α in ground range




Scattering mechanism α FP-WSF (order=2)

α in slant range α in ground range




Conclusion

I Building characterization using Polarimetric MB-inSAR methods:I Source discrimination, physical characterizationI Common HR estimation methods may reach serious limitations

I Proposed approach: Weighted Subspace FittingI Model adaptive : coherent and distributed scatterersI Compared to MUSIC

- WSF has no or very low sidelobes- WSF has a better resolution- WSF performs well on coherent signals

I Extension to the fully polarimetric caseI Analytical polarimetric optimizationI Computation cost equal to the single polarization caseI Refined characterization of building height and scattering

mechanisms


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