ACCURATE OPTIMAL DOPPLER CENTROID ESTIMATION FOR SAR DATA Pietro Guccione Politecnico di Bari Andrea Monti Guarnieri Politecnico di Milano IGARSS 2011 Vancouver, Canada July 27th, 2011
Motivations and Rationaleof the algorithm
Problem Statement and the MaximumLikelihoodestimation
Results on simulatedand X-bandreal data
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Motivations /1 Radiometric calibration is a fundamental item in the processing of Synthetic Aperture Radar (SAR): it allows accurate measures of radar reflectivity.The determination of an accurate azimuth antenna pattern (AAP) and attitude -i.e. accurate Doppler centroid-, acquires particular relevance for calibration process. AAP estimation is actually performed using transponders:
they are high precision and geolocated devices that provide a fixed Radar Cross Section
require maintenance, accurate and complex calibration: so are expensive.
Provide the 1-way gain of the AAP
and require a sufficient background/target contrast: interference with the mission requirements.
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Motivations /2 We perform AAP (and AAP pointing) estimation using natural targets observation over a stack of SAR images. The natural targets we want to exploit are: 1) Sparse nearly over all the images, allowing a possible extraction of the AAP from all the acquired dataset; 2) Dense, i.e. many targets, especially in acquisition over cities or man-made objects, can be present in a single image, making the estimation robust; 3) Stable in time, (stability is required for a robust AAP estimation in a multi-image context) 4 Examples of persistent point scatterers (PPS) [… we use amplitude and phase of impulse response] IGARSS Symposium, Vancouver, Canada July 27th , 2011
Target Model /1 Synthetic Aperture Radar acquisition and focusing can be modeled as a complex source (the ground reflectivity) passed through a linear time-variant (LTV) system (the SAR impulse response) which smears out the energy of a single point scatterer. The inverse processing, said focusing, tries to focus the point scatterer response back to a single point. Model after focusing of SAR data: 5 SAR is pulsed in azimuth direction; this makes the spectrum folded. (Part of the clutter noise is then composed by the spectral replica that superimpose to the one of interest). IGARSS Symposium, Vancouver, Canada July 27th , 2011
Target Model /2 Previous model is more accurate if high-SNR and isolated point targets are considered (to avoid alias over sidelobes). For SAR data the effective azimuth bandwidth, which can be extended also over the main lobe, is greater than the actual sampling frequency. Since we want a proper representation of the antenna (i.e. without ambiguity), the sampling frequency must be increased. Azimuth oversampling can be performed before azimuth focusing with usual oversampling methods but accounting for the time-variant nature of the phase history. With the upsampling the complete history of the point scatterer is reconstructed after focusing, but spectral replica are generated (digital spotlight, Prati 1991) 6 IGARSS Symposium, Vancouver, Canada July 27th , 2011
Problem Statement In an AAP multi-image framework estimation, the problem can be stated as follows. We have available a stack of N images:
acquired by repeated geometry
properly co-registered w.r.t. a master reference
where a set of P targets have been properly selected on the basis of
their stability (i.e. they are present in all the images of the stack)
their whiteness(i.e. the spectrum is very similar to the ideal antenna shape, so they result very “point-shape”)
Doppler centroid Maximum Likelihood estimation δfdc is estimated as the optimal spectral shift of the target Power Spectral Density. All the almost-point targets in the image are exploited, as we suppose that the residual centroid is the same for them (this is the major assumption, valid over quite flat areas). The estimate shows to be more accurate than the traditional correlation-based methods and near to the theoretical Cramer-RaoBound of the estimate. 7 IGARSS Symposium, Vancouver, Canada July 27th , 2011
AlgorithmRationale 8 Stable Point Scatterer est Spotlight AzFocusing QualityFactor Evaluation Clutter Estimation Evaluation δfDC Target spectral shape est Normalize Images AAP estimation Target shape DB Antenna Ideal Model Stable Point DB
Stable Point ScattererEstimation 9 This procedure performs the selection of a set of puntiform targets starting from a SLC image. Targets are selected by passing the following tests:
High contrast.Their mean intensity is computed; then it is computed the power of the neighbor backstatterer. The higher is the ratio, the more probable is the target a pointscatterer.
Similarity of its spectrum with the model, i.e. the Azimuth Antenna Pattern. A quality factor is computed and target are sorted and thresholdedw.r.t. it:
Stable Point Scatterer est It is the normalized root mean square error of the target spectrum w.r.t. the ideal antenna, summed on all the frequencies. This similitude test is a sort of a Generalized Likelihood Ratio Test (GLRT). 9 IGARSS Symposium, Vancouver, Canada July 27th , 2011
Spotlight Azimuth Focusing /1 10 SAR acquisition is pulsed and the resulting azimuth spectrum folded. The effective azimuth bandwidth is greater than the actual sampling frequency. Azimuth oversampling is performed basically by adding N-1 zeros among each couple of samples in azimuth (after range compression) and by a time-variant filtering. With the upsampling the complete phase history of the point scatterer is reconstructed. Foldedspectralsupport Azimuth t-v filtering 10 IGARSS Symposium, Vancouver, Canada July 27th , 2011
Spotlight Azimuth Focusing /2 PPS DB Range Foc SLC Selective windowing Azimuth FFT & oversampling Extraction of slice of data (3x, 5x) selective windowing (on range compressed data to avoid interference of other targets nearby) 11 IGARSS Symposium, Vancouver, Canada July 27th , 2011
Spotlight Azimuth Focusing /3 Spotlight focused PPS DB selective space-variant filter is applied to avoid the effect of replica Selective s-v filter Azimuth stripmap focusing Central strip extraction Position of the ghosts of the central target IdealTarget psd, SNR=20dB, nullfDC, simulatedfor 5 antenna apertures 12 IGARSS Symposium, Vancouver, Canada July 27th , 2011
Doppler CentroidEstimation /1 Startingfrom the modelof target spectrum we suppose thattargets are white (we can weightthishypothesisby the qualityfactor) and initiallywe put also 13 For each image n, SAR data observations Zn,p are usually considered samples from a multivariate Gaussian; so their joint probability, conditioned to δf has a closed-form expression: The parameter estimation is carried out by maximizing the log-likelihood (LLH). Simplification: the covariance matrix is almost diagonal and its elements are basically the power spectrum density of the target. This leads to a very simple formulation of the LLH for each target: i.e. the power of the target whitened spectrum. 13 IGARSS Symposium, Vancouver, Canada July 27th , 2011
Doppler CentroidEstimation /2 14 The CRB of the estimate can be found by numerical computation, since for jointly circular Gaussian process its assumes a simple form numerically solved by means of sinc4 shape for the antenna PSD. Result is also dependent on the background clutter level w.r.t. the target power (i.e. SNR-1). The most relevant spectral contributions to the estimation are the ones with high derivative and low power, i.e. the spectral parts close to the nulls. In Stripmap case (aliased version of the antenna) we found that the limit for SNR->∞ is in agreement withresultsofBamler(TGRS 1991). 14 IGARSS Symposium, Vancouver, Canada July 27th , 2011
Results: fDCestimation /1 15 Simulatedtargets case MLequation issolvedbyexhaustivesearch.
High SNR case: covariance matrix is expected to be very good and we use the average of the spectra to estimate it
Low SNR case: we take the ideal model, i.e. the target ideal PSD, as the measures are unreliable
IGARSS Symposium, Vancouver, Canada July 27th , 2011
Results: fDC estimation /2 16 Cramer-Rao Bound results Repeated simulation allows to get the standard deviation of the estimate and compare it with the theoretical bound provided by the CRB. CRB forstripmap case, varying the SNR Experimentalresults on simulatedtargets, varying the SNR CRB forspotlight case, varying the SNR IGARSS Symposium, Vancouver, Canada July 27th , 2011
Results: fDC estimation /3 17 Real targets case CSK X-band data on ‘Milan lakes’ dataset The 12 best targets have been chosen: high quality factor (relative mean of MSE ≈0.043) and average SNR of 20.8dB. Joint LLH is achieved by a weighted sum, the weights being the quality factor values. Mission CSKS1_SLC_B_HI_03_HH_RA_SF_20080903051606 δfdc=40.75Hz IGARSS Symposium, Vancouver, Canada July 27th , 2011
Results: fDC estimation /4 Real targets case Validation of the fDC residual correction obtained by inspection on the CSK image:
peakness of point targets improved
Withoutcorrection Correctionofδfdc=40.75Hz -3dB res ≈ +10% PSLR ≈ +3 % IGARSS Symposium, Vancouver, Canada July 27th , 2011 18
Conclusions Robust (LLH based) estimation of Azimuth Antenna Pattern Pointing (Doppler centroid) for stripmap SAR data presented.
Based on natural point targets, with high SNR
Use of few targets, as long as they own good SNR
Antenna pointing estimation achieved with an accuracy of few Hz
Antenna pointing estimation better than traditional (stripmap) methods
Implement azimuth antenna pattern estimation after correction of residual fDC in a multi- image framework
Exploit the AAP estimation for a better radiometric calibration
Acknowledgements This work has been supported in the framework of ASI AO-1080, under the conditions as in ASI document DC-OST-2009-116. 19 IGARSS Symposium, Vancouver, Canada July 27th , 2011
Time-domain fine registration and phase alignment through the stack of images. [Phase alignment needed for fine azimuth peaks registration and possible residual focusing operator errors, or residual offset].
We exploit the measures of target spectrum over the stack, to average out the effect of the noise.
Determination of the spectral shape performed by a LMS polynomial approximation of the residual in the frequency domain, once that a model for the antenna is available and has been removed.
Lacking any kind of information (at initial step of iteration), we use as model for the antenna the weighted average of all the targets in all the images:
IGARSS Symposium, Vancouver, Canada July 27th , 2011
Appendix 2: antenna pattern estimation (preliminary) 21 Estimation of Azimuth Antenna is performed frequency by frequency on The join PDF, conditioned to the antenna as parameter The best value of the antenna model at that frequency is the one that maximizes the log-likelihood, We approximate the log-likelihood of N output as the sum of the log-likelihoods. For a high number of targets and images we have the same level of output accuracy of the strict ML formulation. IGARSS Symposium, Vancouver, Canada July 27th , 2011
Appendix 3: results (preliminary) 22 Simulated set of targets Target spectral shape have been achieved by distortion of ideal spectrum (value of 1 at all the f) with 3rdorder polynomial with random uniformly distributed coefficients. Since target amplitudes have been normalized, we express the target spectral shape as a deviation from the nominal value of 1 (or 0dB). At the first iterate the ideal antenna model has been used. IGARSS Symposium, Vancouver, Canada July 27th , 2011
Appendix 4: results (preliminary) 23 We simplified the LLH estimation by exploiting instead of to avoid the estimate of the covariance matrix of the observations. The problem has been divided in a subset of frequencies: for each subset we coherently summed (1) after correction for the estimated spectral shape, and looked for the most probable value of by exhaustive way. (1) (2) IGARSS Symposium, Vancouver, Canada July 27th , 2011