ACCURATE OPTIMAL DOPPLER CENTROID ESTIMATION FOR SAR DATA

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ACCURATE OPTIMAL DOPPLER CENTROID ESTIMATION FOR SAR DATA. Andrea Monti Guarnieri Politecnico di Milano. Pietro Guccione Politecnico di Bari . IGARSS 2011 Vancouver, Canada July 27 th , 2011. Summary. Motivations and Rationale of the algorithm Target Model - PowerPoint PPT Presentation

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ACCURATE OPTIMAL DOPPLER CENTROID ESTIMATION FOR SAR DATAIGARSS 2011Vancouver, CanadaJuly 27th, 2011

Pietro Guccione Politecnico di Bari

Andrea Monti Guarnieri Politecnico di Milano

1EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalySummary Motivations and Rationale of the algorithm Target Model Problem Statement and the Maximum Likelihood estimation Results on simulated and X-band real data Conclusions

2IGARSS Symposium, Vancouver, CanadaJuly 27th , 20112EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalyMotivations /1Radiometric 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.3

IGARSS Symposium, Vancouver, CanadaJuly 27th , 20113EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalyMotivations /2We 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, CanadaJuly 27th , 20114EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalyTarget Model /1Synthetic 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, CanadaJuly 27th , 20115EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalyTarget Model /2Previous 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, CanadaJuly 27th , 20116EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalyProblem StatementIn 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 referencewhere 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 estimationfdc 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-Rao Bound of the estimate.7

IGARSS Symposium, Vancouver, CanadaJuly 27th , 20117EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalyAlgorithm Rationale8Stable PointScatterer estSpotlightAz FocusingAntenna IdealModelQuality FactorEvaluationClutterEstimationEvaluation fDCStable PointDBTarget spectralshape estNormalizeImagesTarget shapeDBAAPestimation

8EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalyStable Point Scatterer Estimation99This procedure performs the selection of a set of puntiform targetsstarting 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 point scatterer. Similarity of its spectrum with the model, i.e. the Azimuth Antenna Pattern. A quality factor is computed and target are sorted and thresholded w.r.t. it:

Stable PointScatterer 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).IGARSS Symposium, Vancouver, CanadaJuly 27th , 20119EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalySpotlight Azimuth Focusing /11010SAR 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.

IGARSS Symposium, Vancouver, CanadaJuly 27th , 2011Folded spectral supportAzimuth t-v filtering

10EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalyIGARSS Symposium, Vancouver, CanadaJuly 27th , 2011Spotlight Azimuth Focusing /2

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Extraction of slice of data(3x, 5x)PPS DBRange FocSLCSelectivewindowingAzimuth FFT &oversamplingselective windowing (on range compressed data to avoid interference of other targets nearby)

11EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalySpotlight Azimuth Focusing /3

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Ideal Target psd, SNR=20dB, null fDC, simulated for 5 antenna aperturesIGARSS Symposium, Vancouver, CanadaJuly 27th , 2011

Selective s-vfilterselective space-variant filter is applied to avoid the effect of replicaAzimuth stripmapfocusingCentral stripextractionSpotlight focusedPPS DB

Position of the ghosts of the central target12EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalyStarting from the model of target spectrum

we suppose that targets are white (we can weight this hypothesis by the quality factor) and initially we put also Doppler Centroid Estimation /11313For each image n, SAR data observations Zn,p are usually considered samples from a multivariate Gaussian; so their joint probability, conditioned to f 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.

IGARSS Symposium, Vancouver, CanadaJuly 27th , 201113EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalyDoppler Centroid Estimation /21414The 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

IGARSS Symposium, Vancouver, CanadaJuly 27th , 2011in agreement with results of Bamler (TGRS 1991).14EUSAR 2010. Aachen, Germany, June 9th, 2010Pietro Guccione, Politecnico di Bari, ItalyResults: fDC estimation /115

NameValueUoMCarrier frequency9,60E+09HzWavelength3,12E-02mAntenna length5,6mOff-nadir reference angle26,55degPRF3,06E+03HzPulse length40usecBandwidth119,8242188MHzSampling frequency146,25MHzSWL172,417094usecSimulated SNR20, 30 dBAntenna pointingRight, with yaw steeringOrbit propagatorNORAD4TMNumber of simulated apertures5Wrong fDC in spotlight focusing10Hz

is solved by exhaustive search. 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