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Assessing BIOMASS Radiometric Stability using Permanent Scatterers

Marco Manzoni, Francesco Salvaterra, Claudio Maria Prati, Stefano Tebaldini

arXiv:2610.37400v1eess.SPeess.IV

TL;DR

Limited BIOMASS stacks and sparse P-band calibration targets complicate relative radiometric monitoring amid changes in scene backscatter. The paper combines amplitude-based permanent-scatterer selection with gain estimation; Nairobi and Córdoba results show estimated variations generally around 0.1 dB outside a processing anomaly.

  • Problem

    P-band calibration targets are difficult to deploy and sparse, while BIOMASS typically has only seven repeat-pass images per area, constraining conventional and PS-based monitoring.

    Source: §I · p. 1

  • Method

    The approach models stable scatterer amplitudes across acquisitions and estimates relative image gains using amplitude-based PS detection and iterative estimation.

    Source: A. Signal model · p. 2, B. Incoherent detection · p. 3

  • Results

    Nairobi’s estimated gain variations were generally within 0.1 dB excluding an acquisition affected by an RFI-mitigation defect; Córdoba estimates oscillated on the order of 0.1 dB.

    Source: A. Nairobi - Kenya · p. 6, B. C´ordoba - Argentina · p. 8

  • Takeaways & Limitations

    PS-based relative gain estimates can help assess radiometric stability and serve as an early warning indicator of hardware or software malfunctions.

    Source: D. Incoherent estimation · p. 4, §IV · p. 9

    Interpretation depends on temporal and angular stability of selected scatterers, and estimated gains do not provide an absolute radiometric reference.

    Source: §IV · p. 9

Abstract

from arXiv · show

Monitoring the relative radiometric stability of the European Space Agency's BIOMASS P-band synthetic aperture radar (SAR) requires separating instrumental and processing effects from temporal changes in the scene backscatter. This study investigates the use of permanent scatterers (PSs) as opportunistic references for estimating residual radiometric gains without dedicated calibration targets. The PS-based calibration (PSCal) framework combines amplitude-based scatterer selection with iterative maximum-likelihood gain estimation. Simulations assess detection and estimation performance under the limited number of acquisitions available in BIOMASS stacks, highlighting the importance of stringent selection thresholds and the dependence of estimation accuracy on scatterer abundance and signal-to-noise ratio. The approach is applied to datasets over Nairobi, Kenya, and Cordoba, Argentina. Over Nairobi, PSCal identifies an approximately 1 dB radiometric anomaly subsequently traced to a defect in radio-frequency interference mitigation, while the remaining acquisitions exhibit estimated gain variations generally within 0.1 dB. Over Cordoba, twelve acquisitions spanning two mission phases separated by approximately eight months yield residual gain variations on the order of 0.1 dB despite pronounced changes in the scene backscatter and acquisition geometry. Results were observed to be consistent with measurements from the BIOMASS Calibration Transponder (BCT) installed in New Norcia (Australia). These results demonstrate the potential of carefully selected P-band PSs to complement dedicated calibration infrastructure for relative radiometric monitoring and the detection of processing anomalies.

I. INTRODUCTION

BIOMASS needs relative radiometric monitoring, but P-band calibration targets are difficult to deploy and its short stacks constrain permanent-scatterer calibration. The paper frames PS observations through a model that separates image gains from stable target amplitudes.

I. INTRODUCTION

  • P-band calibration infrastructure is costly and sparse, limiting long-term and global radiometric monitoring; naturally occurring permanent scatterers offer a complementary reference.The long wavelength makes corner reflectors large and transponders specialized, while BIOMASS typically provides only seven repeat-pass images per area.Source: §I · p. 1
  • BIOMASS stacks typically contain only 7 images, and combining stacks is constrained by footprint overlap and viewing-angle differences that limit consistently identifiable scatterers.Jointly selected scatterers must remain stable over time and across sampled geometries.Source: §I · p. 1

SIMULATED PERFORMANCES

  • The paper recaps the theory for permanent scatterers and radiometric-gain estimation before its detailed analysis of the approach.The cited background for that theory is –.Source: §II · p. 2

A. Signal model

  • The signal model treats image gains as acquisition-dependent and spatially uniform, while each permanent scatterer’s amplitude remains constant across acquisitions.Setting the first image gain to 1 resolves the common multiplicative ambiguity, making estimated gains relative to that image.Source: A. Signal model · p. 2

B. Incoherent detection

The incoherent detector selects candidates from amplitude histories, using the dispersion index as a stability measure. Short stacks bias estimated DI upward, motivating stringent thresholds and an additional brightness criterion.

B. Incoherent detection

  • The dispersion index provides a figure of merit equivalent to the GLRT, while normalized DI maps that measure to a range from 0 to 1.DI is based on temporal mean and standard deviation of pixel amplitude; high reflectivity with small fluctuations marks a suitable candidate.Source: B. Incoherent detection · pp. 2–3
  • For a 7-image stack, an estimated DI threshold of 16 corresponds to a true DI of approximately 14, illustrating the upward bias at high DI in short stacks.The bias grows as the stack shrinks and as true DI increases; incoherent detection is used to avoid phase estimation with few acquisitions.Source: B. Incoherent detection · p. 3
  • An additional brightness screen selects the brightest 2% of pixels or requires σ0 > −17 dB, 10 dB above the −27 dB NESZ.Source: B. Incoherent detection · p. 3

C. Detection performances

In simulations of the incoherent detector, raising the NDI threshold reduced false alarms but increased missed detections. At NDI 0.99, missed detection depended sharply on SNR.

C. Detection performances

  • Increasing the NDI threshold reduced false alarms at the cost of increasing missed detections.Source: C. Detection performances · p. 3
  • At NDI 0.99, false-alarm probability was approximately 10^-5; missed-detection probability fell from approximately 80% at 12 dB SNR to 0.1% at 18 dB.The simulation used a 12-image stack and varied SNR from 12 to 20 dB.Source: C. Detection performances · p. 3

D. Incoherent estimation

The incoherent estimation procedure alternates maximum-likelihood estimates of PS amplitudes and noise variances with gain updates until convergence. The resulting gains are relative and can support radiometric-stability assessment and anomaly warning.

D. Incoherent estimation

  • The algorithm iteratively estimates PS amplitudes and noise variances, then updates gains until convergence.PS amplitudes are estimated by maximizing the likelihood; gain updates use the likelihood derivative.Source: D. Incoherent estimation · p. 4
  • Estimated gains are relative and remain ambiguous up to an unknown common multiplicative factor.Resolving the ambiguity requires a constraint, such as residual gains averaging to unity, or an externally calibrated reflector.Source: D. Incoherent estimation · p. 4
  • Relative gain estimates can assess radiometric stability and serve as an early warning indicator of hardware or software malfunctions.Source: D. Incoherent estimation · p. 4

E. Estimation performances

Simulations show that estimation accuracy improves with higher SNR and more PSs, while the Cramér–Rao bound quantifies their trade-off. In Nairobi, the third acquisition's radiometric anomaly was traced to the RFI mitigation strategy.

E. Estimation performances

  • A 0.1 dB standard deviation requires roughly 150 PSs at 15 dB average SNR, or about 400 PSs at 10 dB.The CRB highlights the trade-off between the mean SNR and number of detected PSs.Source: E. Estimation performances · p. 4
  • The third Nairobi acquisition, dated 31 May 2025, exhibits a radiometric anomaly traced to the RFI mitigation strategy during processing.The strategy distorted the signal spectrum and consequently altered the acquisition's radiometry.Source: Figure 5 · p. 5
  • Approximately 0.35 dB error for 50 PSs at 8 dB SNR falls to near 0.05 dB for 500 PSs at 20 dB SNR.Across experiments, estimate standard deviations approach the CRB at high SNR.Source: E. Estimation performances · p. 5

III. REAL DATA ANALYSIS

The real-data analysis applies PSCal to selected commissioning and tomographic-phase datasets to assess scatterer availability, radiometric stability, and processing anomalies. The processing includes coregistration and dispersion-index computation across polarimetric channels and span.

III. REAL DATA ANALYSIS

  • Selected test cases from commissioning and tomographic phases assess PS availability and PSCal's potential for anomaly detection and long-term stability assessment.Source: §III · p. 5
  • The study downloads calibrated Level-1A images from MAAP, which already include polarimetric corrections.Source: §III · p. 5
  • A two-step coregistration combines geometric alignment with local cross-correlation before computing dispersion index for each polarimetric channel and span.Span is defined from the amplitudes of VV, VH, HV, and HH.Source: §III · p. 5

A. Nairobi - Kenya

In Nairobi, PSCal identifies a roughly 1 dB anomaly in the third acquisition and distinguishes it from subsequent scene-wide amplitude changes. In Córdoba, estimates remain around 0.1 dB despite substantial scene brightening and changes in acquisition geometry.

A. Nairobi - Kenya

  • 735 SPAN, 184 HH, and 334 VV PS candidates were selected in Nairobi using a minimum dispersion index of 16 and a minimum σ0 threshold.No candidates were detected in the cross-polarized channels; the source states the threshold as “minimum σ0 of 7 dB.”Source: A. Nairobi - Kenya · pp. 5–6
  • Approximately 1 dB separates the first and third Nairobi acquisitions in PSCal estimates, while later scene-median decline is absent from those estimates.The third acquisition’s anomaly was subsequently attributed to a defect in the initial RFI-mitigation implementation; excluding it, estimated gains generally vary within 0.1 dB.Source: A. Nairobi - Kenya · p. 6, Figure 6 · p. 6

B. C´ordoba - Argentina

  • The Córdoba stacks’ longer observation period, differing geometries, and reduced footprint overlap require jointly selected scatterers to remain stable over time and viewing geometries.The first five acquisitions have approximately zero relative baseline; the seven tomographic acquisitions span up to approximately 4 km within their sub-stack.Source: B. C´ordoba - Argentina · pp. 6–7
  • Incoherent-detector selection yielded 105 PS candidates in SPAN, 21 in HH, and 29 in VV; none were detected in cross-polarized channels, and PS density was much lower than in the previous case.The minimum dispersion index was 12.5, corresponding to approximately 19 dB SNR, and minimum σ0 was −17 dB.Source: B. C´ordoba - Argentina · pp. 7–8
  • About 0.1 dB: Córdoba PSCal gain variations remain on this scale despite pronounced scene brightening and do not follow the scene-median trend.The stack combines two sub-stacks separated by approximately eight months and a normal baseline of approximately 40 km.Source: B. C´ordoba - Argentina · pp. 6–8, Figure 10 · p. 8

C. Qualitative BIOMASS Calibration Transponder (BCT) comparison

The BCT comparison supports the plausibility of PSCal gain variations at a qualitative level, not as direct validation. The conclusion presents PSCal as a complementary relative-monitoring tool while bounding its interpretation by scatterer stability and the absence of an absolute reference.

C. Qualitative BIOMASS Calibration Transponder (BCT) comparison

  • A few tenths of a decibel: BCT and PSCal fluctuations are comparable in magnitude during the overlapping period, though PSCal shows larger excursions.The comparison uses different sites, techniques, and acquisition dates; offset correction removes the possibility of assessing absolute radiometric agreement.Source: C. Qualitative BIOMASS Calibration… · p. 8, Figure 11 · p. 9
  • The BCT comparison is a qualitative consistency check, not direct validation of individual PSCal gain estimates.BCT-derived gains may also reflect fluctuations in transponder response, potentially over- or underestimating instrument variability.Source: C. Qualitative BIOMASS Calibration… · p. 8

IV. CONCLUSION

  • PSCal is presented as a complementary tool for monitoring relative radiometric response and detecting processing anomalies, not as an absolute radiometric reference.The conclusion’s real-data results include the Nairobi anomaly and Córdoba gain variations on the order of 0.1 dB.Source: §IV · p. 9

APPENDIX BIAS ON THE ESTIMATE OF THE DISPERSION INDEX

This appendix examines bias in the dispersion-index estimate using the moments of independent, identically distributed amplitudes and a first-order Taylor expansion. The supplied passages state that the estimator is biased but do not give the size or direction of that bias.

APPENDIX BIAS ON THE ESTIMATE OF THE DISPERSION INDEX

APPENDIX RELATIONSHIP BETWEEN INCOHERENT DISPERSION INDEX AND SNR IN SAR IMAGES

This appendix models a complex SAR pixel with signal and noise, then relates the incoherent-amplitude dispersion index to SNR. The supplied passages describe the derivation’s steps but do not state its final relationship.

APPENDIX RELATIONSHIP BETWEEN INCOHERENT DISPERSION INDEX AND SNR IN SAR IMAGES

  • The derivation begins with a complex SAR pixel whose deterministic signal amplitude is A and whose noise is circular complex Gaussian.The total mean noise power is then considered.Source: APPENDIX RELATIONSHIP BETWEEN… · p. 9
  • SNR is defined as the ratio between signal power and total complex noise power.The derivation then considers the incoherent amplitude image.Source: APPENDIX RELATIONSHIP BETWEEN… · pp. 9–10
  • The appendix expands the amplitude R to first order around A and compares the resulting expression with the SNR expression.This comparison is used to obtain a relationship involving the incoherent dispersion index.Source: APPENDIX RELATIONSHIP BETWEEN… · p. 10
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