Polarimetric Calibration of the Ingara Bistatic SAR

Transcription

1 Polarimetric Calibration of the Ingara Bistatic SAR Alvin Goh, 1,2 Mark Preiss, 1 Nick Stacy, 1 Doug Gray 2 1. Imaging Radar Systems Group Defence Science and Technology Organisation 2. School of Electrical & Electronic Engineering University of Adelaide

2 Bistatic SAR experiments Reciprocity s hv = s vh in monostatic but not bistatic: potentially more information in bistatic measurements Supplement Ingara X-band full-pol. airborne SAR with stationary full-pol. ground-based receiver on 15 metre high tower Airborne Tx & Rx Tx-to-Rx azimuth separation angle φ Radius z Altitude Orbit Synch. using GPS 1PPS; operate at fixed 65 Hz PRF Operate in circular spotlight-sar mode: orbit radii 3 6 km; altitudes 1 36 m; incidence angles Simultaneously collect 6 MHz bandwidth fullpol. monostatic and bistatic data over wide variety of angles Groundbased Rx x Imaged scene y Airborne Tx & Rx antenna Beechcraft 19C Ground-based Rx-only antenna 2

3 Polarimetric measurement model is in which O = o hh o hv R = o vh o Polarimetric measurement model O = R S T + N r hh r hv S = r vh r o = P s + n P = Y M A K s hh s hv T = s vh s t hh t hv N = By rewriting O, S, N as o = (o hh, o hv, o vh, o ) T, s = (s hh, s hv, s vh, s ) T, n = (n hh, n hv, n vh, n ) T, we obtain where Measurements Receive distortion Target scattering t vh t Transmit distortion n hh n hv n vh n Noise 1 v w vw z 1 wz w M = A = u uv 1 v uz u z 1 α 1 α 1 K = k 2 k k 1 in which Y = r t k = r hh /r α = t hh r /t r hh u = r vh /r hh, v = t vh /t, w = r hv /r, z = t hv /t hh Absolute scaling factor Channel-imbalance parameters Cross-talk ratios Polarimetric calibration involves estimation of k, α, u, v, w, z (leaving Y to radiometric calibration). 3

4 For a distributed-target, can calculate covariance matrices Distributed-target methods 1 o hh 2 o hh o* hv o hh o* vh o hh o* o hv 2 s hh 2 s hh s* hv s hh s* vh s hh s* s hv 2 n hh 2 n hh n* hv n hh n* vh n hh n* n hv 2 C o = o hv o* hh o vh o* hh o vh o* hv o hv o* vh o hv o* o vh 2 o vh o* o 2 C s = s hv s * hh s vh s * hh s vh s* hv s hv s* vh s hv s* s vh 2 s vh s* s 2 C n = n hv n* hh n vh n* hh n vh n* hv n hv n* vh n hv n* n vh 2 n vh n* n 2 o o* hh o o* hv o o* vh s s * hh s s * hv s s * vh n n* hh n n* hv n n* vh whereupon C = C o -C n = P C s P H Covariance matrix of distributed-target is commonly postulated to have the simple form: C s = σ 11 * β β β β σ 41 σ 41 σ 44 from s hv = s vh (scattering reciprocity) s ii s ij = s ii s ji = (azimuthal symmetry) This provides the basis for calculating α, u, v, w, z from an input covariance matrix C: Ainsworth TL, Ferro-Famil L, Lee J-S, 26, Orientation angle preserving a posteriori polarimetric SAR calibration, IEEE Trans. Geosci. Remote Sens., 44(4): Klein JD, 1992, Calibration of complex polarimetric SAR imagery using backscatter correlations, IEEE Trans. Aerosp. Electron. Syst., 28(1): Lopez-Martinez C, Cortes A, Fabregas X, 27, Analysis and improvement of polarimetric calibration techniques, Proc. IGARSS 27, Barcelona, Spain, p Quegan S, 1994, A unified algorithm for phase and cross-talk calibration of polarimetric data - theory and observations, IEEE Trans. Geosci. Remote Sens., 32(1):

5 Distributed-target methods 2 Examine a variety of methods: K: use eigenvector of C (Klein 1992) Q: use linear-approximations to C (Quegan 1994) A: transform C into postulated C s form while accommodating non-zero azimuthal slope (Ainsworth et al. 26) Ka: K with improved estimation of α Qi: Q with iterations (Lopez-Martinez et al. 27) Az: A with enforced azimuthal symmetry Compare accuracy using numerical simulations: Set σ 11 = σ 44 = db, σ 41 = -1 db, β = -12 db, Y = k = 1 Randomly assign < u, v, w, z <.1,.5 < α < 1.5, σ 41, α, u, v, w, z < 2π Results with full noise-compensation, i.e. C = C o - C n Channel-imbalance α Cross-talk w (u, v, z similar) α - α α w - w w 5 Ka has lowest α-estimation error Az has lowest cross-talk estimation error

6 Calibration-target methods Model for calibration target measurements when cross-talk is negligible (or already corrected) is o hh = Y k 2 α s hh o hv = Y ks hv o vh = Y kα s vh o = Y s (noise assumed negligible) Hence, from measurements of a depolarising target with known s vh /s hv, we can estimate α via α = o vh /o hv s vh /s hv With a previously-obtained estimate of α, and measurements of a target with known s hh /s, we can estimate ±k via k = ± o hh /o α s hh /s (1) From measurements of a depolarising target with known s hh /s vh or s hv /s, we can also estimate k via k = o hh /o vh s hh /s vh k = o hv /o s hv /s (2) We can also just use (2) to resolve the sign ambiguity in (1). For bistatic system, direct-path signal can also be used in lieu of calibration target. 6

7 Polarimetric calibration Distributed-target methods: Az Ka Calibration targets Direct-path signal t hh r u = r vh /r hh v = t vh /t w = r hv /r z = t hv /t hh α = t r hh k = r hh /r Collection geometry for calibration data: Aircraft flight path Calibration targets Small bistatic angle β Gnd-based Rx Airborne Tx & Rx Distributed target 3.5 km 6.5 km 7

8 Monostatic VV (uncalib.) Distributed-target measurements 1 Bistatic VV (uncalib.) Power-lines View of site from ground Rx Local view of terrain December 28 Region used for covariance calculations Grazing angle of groundbased Rx 2 March 28 March 28 images Runs 1-7: Airborne Rx (monostatic) Runs 8-2: Ground-based Rx (bistatic) 8

9 Measured covariance matrix Distributed-target measurements 2 C o = o hh 2 o hh o* hv o hh o* vh o hh o* o hv o* hh o hv 2 o hv o* vh o hv o* o vh o* hh o o* hh o vh o* hv o o* hv o o* vh o vh 2 o vh o* o 2 On-diagonal covariances (real-valued) Off-diagonal covariances (complex-valued) o 2 o hh 2 o vh 2 Air Rx Gnd Rx o hh o* hv o hh o* vh Air Rx Gnd Rx o hv 2 o hh o* o hv o* vh o hv o* o vh o* 9 March 28 data

10 Air Rx (monostatic) Calibration target measurements 1 Gnd Rx (bistatic) Tilt ϕ =-22.5 Hay bales D1 Trihedral D1: tilted 25 cm dihedral S = D2: upright 25 cm dihedral S = 1-1 H D4 D2 D3 H: 112 cm hemisphere March 28 SAR images Hemisphere k = ± o hh α o Trihedral Tilt ϕ =+22.5 S = 1 1 Upright dihedral Tilted dihedral k = ±j o hh α o α = o vh /o hv o hh o hh k = ±j = tan 2ϕ = - α o o vh o hv o cot 2ϕ D4: tilted 54 cm dihedral S = D3: upright 54 cm dihedral S = 1-1 1

11 Calibration target measurements 2 D1: s hh /s = -1 s hv /s = +1 s vh /s = +1 Air Rx Gnd Rx o hh /o o hv /o D2: s hh /s = -1 s hv /s = s vh /s = o vh /o D3: s hh /s = -1 s hv /s = s vh /s = D4: s hh /s = -1 s hv /s = -1 s vh /s = -1 H: s hh /s = +1 s hv /s = s vh /s = 11 March 28 measurements

12 Direct-path signal measurements Direct-path signal measurements supplement the set of calibration target measurements. Scattering matrix of direct-path signal is S = -cos ϕ -sin ϕ -sin ϕ cos ϕ Estimate channel-imbalance from α = o vh /o hv k = ±j o hh o hh o vh o hv o and/or k = tan ϕ = - cot ϕ α o Aircraft flight path Level flight and pitch down ~7 Groundbased Rx (add 4 db attenuators) Direct-path signal Elevate antenna ~9.5 Stand-off ~32 km Rotate antenna by angle ϕ Level flight Pitch down o hh /o o 12 hv /o o vh /o December 28 measurements

13 Cross-talk estimation March 28 data December 28 data Recall: u = r vh /r hh v = t vh /t w = r hv /r z = t hv /t hh Rx only Tx only Air Rx Gnd Rx Expect same v & z in air and ground data but different u & w. u v w z For each run, initial cross-talk ratio u, v, w, z estimates obtained using method Az. Take median of distributions to obtain final calibration parameters: u (air) : median of u estimates from air data only u (gnd) : median of u estimates from ground data only v (air), v (gnd) : median of pooled v estimates from air and ground data w (air) : median of w estimates from air data only w (gnd) : median of w estimates from ground data only z (air), z (gnd) : median of pooled z estimates from air and ground data where median of set of complex z n is taken as: median( { Re(z n ) n } ) + j median( { Im(z n ) n } ) 13

14 α estimation March 28 data December 28 data Initial α estimates from individual runs Air Rx Ground Rx Distrib.-target D1 D4 Direct-path Final calibration solution: α (air) : median of air estimates α (gnd) : median of ground estimates 14

15 k estimation March 28 data December 28 data Initial k estimates from individual runs Air Rx Gnd Rx D1 D2 D3 D4 H Direct-path Final calibration solution: k (air) : median of air estimates k (gnd) : median of ground estimates 15

16 Post-calibration target measurements D1: s hh /s = -1 s hv /s = +1 s vh /s = +1 Air Rx Gnd Rx s hh /s D2: s hh /s = -1 s hv /s = s vh /s = s hv /s s vh /s D3: s hh /s = -1 s hv /s = s vh /s = D4: s hh /s = -1 s hv /s = -1 s vh /s = -1 H: s hh /s = +1 s hv /s = s vh /s = 16 March 28 measurements

17 Distributed-target co-/cross-polar covariances s hh s* hv 2 Air Gnd Air Gnd s s * hv 2 Before cal. Before cal. After cal. After cal. s hh s* vh 2 s s * vh 2 Before cal. Before cal. After cal. After cal. 17 March 28 measurements

18 Distributed-target cross-polar measurements March 28 data December 28 data Air Gnd Before cal. Before cal. Air Gnd s hv 2 s vh 2 After cal. After cal. After cal. Before cal. s hv s* vh Before cal. After cal. 18

19 Conclusion A method for polarimetric calibration employing distributed-target, calibration-target and direct-path signal measurements has been applied to the Ingara monostatic and bistatic data. High variability is present in calibration target measurements possibly related to large range of look angles (e.g. bistatic from 9 to 17 ): use Polarimetric Active Radar Calibrators (PARCs) in future? * Assumptions of distributed-target azimuthal-symmetry, i.e. s ii s ij =, may not be valid: validity of cross-talk calibration solution is uncertain. Fair agreement in α and k channel-imbalance estimates from distributed-target, calibration target and direct-path signal measurements is found. Application of calibration solution to measurements produces results generally more consistent with those expected of calibrated data. 19