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This paper presents a novel method for estimating the absolute phase offset in interferometric synthetic aperture radar (SAR) measurements for digital elevation model (DEM) generation. The method is based on “phase-offset functions (POF),” relating phase offset to topographic height, and are computed for two different overlapping interferometric data acquisitions performed with considerably different incidence angles over the same area of interest. For the purpose of extended mapping, opposite viewing directions are preferred. The two “phase-offset functions” are then linearly combined, yielding a “combined phase-offset function (CPOF)”. The intersection point of several straight lines (CPOFs), corresponding to different points in the overlap area allows for solving the phase offset for both acquisitions. Aiming at increasing performance and stability, this intersection point is found by means of averaging many points and applying principal component analysis. The method is validated against traditional phase offset estimation with corner reflectors (CR) using real OrbiSAR-1 data in X- and P-band.

SAR interferometry is a well-known technique used to generate a Digital Elevation Model (DEM), which converts the absolute interferometric phase data into height data [

The absolute interferometric phase estimation is often solved by using ground control points (GCPs) within the scene or through the use of an already calibrated area. Automatic methods have also been proposed, based on spectral diversity [

This paper describes a method to estimate the phase-offset value automatically using a pair of unwrapped interferometric phases, whose data have been acquired in opposite flight directions and with an overlap area between the tracks. For a selected point in the overlapped area, a function relating phase-offset value to height value, called here

SAR Interferometry is based on the measurement of the phase difference from the complex-valued resolution elements of two co-registrated images, acquired by two separated antennas (baseline B) as shown in _{m} in _{unw}

The phase-offset value, represented by _{off}_{abs}

The proposed method to estimate the phase-offset value for an InSAR airborne system is based on the following assumptions: the interferometric SAR images are generated in zero-Doppler geometry [_{1} as the reference (

Assuming a flat-earth geometry, for sake of simplicity, the terrain height can be represented by:

From the _{1}.

The proposed method is based on the acquisition mode shown in _{p}_{abs1}_{abs2}

_{p}_{off 1}_{off 2}

Considering that _{θ}_{ph}_{p}_{off 1}_{off 2}

In order to build up the phase-offset function, we first consider the absolute phase value of a generic point _{i}_{p}_{p}_{p}_{p}_{1}_{2}

The slant range distances, _{1}_{2}_{i}_{p}_{p}_{p}_{1}_{1}_{1}_{1}_{i}_{p}_{p}_{p}_{2}_{2}_{2}_{2}_{1}_{1}_{1}_{1}_{2}_{2}_{2}_{2}_{i}_{p}_{p}_{p}_{unwPi}_{unw i}

The phase-offset value of _{i}_{p}_{p}_{p}_{p}

The phase-offset value found in _{i}_{p}_{i}_{min}_{max}_{i}_{i}_{min}_{max}

Attributing a height for _{i}_{min}_{max}_{i}_{min}_{max}

Considering that the true height _{t}_{i}

- Firstly, as the _{min}_{max}_{i}_{off 1} × Φ_{off 2} for the point _{i}_{θ}_{ph}_{i}^{i}_{off 1} with respect to ^{i}_{off 2}, where the term _{θ}_{ph}_{θ}_{ph}

- Secondly, considering another point _{k}_{i}_{k}_{k}_{off 1} × Φ_{off 2} for the point _{k}

- Finally, as the _{i}_{k}_{off 1} × Φ_{off 2}, they have different angular coefficients, ensuring an intersection point between them, from where the phase-offset values for both acquisitions can be estimated, as illustrated in _{off 1} × Φ_{off 2}, shown in _{off 1}_{off 2}

In order to get an accurate estimation of the phase-offset values, instead of two points, a set of points in the overlapped area, with different range positions, can be used to produce a set of _{off 1} × Φ_{off}, with a common intersection point. Due to noise presence in the interferometric unwrapped phase, or to abrupt variation of the phase, the common point of the intersection is not unique but has a cluster of points, very close together, from where the phase-offset values can be estimated.

_{unw1}_{unw2}_{1}_{2}

To illustrate the processing step that generates the _{1} and _{2} for a selected point in the overlapped area, shown in _{comb}_{off 1} × Φ_{off 2}.

Carrying out the same operations for a set of points in the overlapped area, a set of functions _{comb}_{max}_{min}_{h}

The _{comb}

In order to make it easier to determine the intersection point of the _{comb}

_{comb}_{off}_{1} and _{off}_{2}. From these estimated phase-offset values, the absolute interferometric phase for both acquisitions can be determined by using the

This method works basically in two iterations. Firstly, the coarse phase-offsets values are estimated using a height interval [_{max} − _{min}] and a height step _{h}_{off}_{1} and _{off}_{2} (_{DEM}_{12}, of both acquisitions (

An important issue regarding the accuracy of the phase-offset estimation using the proposed method, is the number of points selected in the overlapped area used to build up the

The performance of the proposed method regarding the size of the overlapped area in range direction was checked by changing the overlap percentage in a range direction, varying from 20% to 90% of the swath width. For each fixed percentage, the algorithm was executed ten times. For each execution, the points used by the algorithm were randomly distributed in the overlapped area within a fixed range. The phase-offset mean values and standard deviations for the X-band of the first acquisition for each fixed percentage used are shown in

It can be noted from

The presented method validation was carried out in a test site area in the south-west of Brazil, Cachoeira Paulista, São Paulo state, using data from the OrbiSAR-1 system in X- and P-bands, with the parameters shown in

To evaluate the performance of the presented method, firstly, the corner reflectors were used to estimate the phase-offset values, followed by the absolute phase determination and the DEM generation for X- and P-bands. The same procedure was performed using the proposed method to estimate the phase-offset values, considering an overlapped area of approximately 60% of the swath width and a coherence threshold of 0.6 for X-band and 0.5 for P band. About 80 points randomly distributed in the overlapped area were used to build up the

The quality of the results regarding the estimate of the phase-offset values, the first based on corner reflectors at the scene and the second based on the proposed method, are presented in

The X-band and P-band DEMs generated with both phase-offset estimation methods were evaluated in 16 GCPs measured with GPS survey: the results are shown in

The results shown in

The height derived from the interferometric phase is very sensitive to phase errors. According to [_{ϕu}_{n}

The standard phase error and the phase uncertainty with 95% of confidence level, according to [_{ϕ}_{ϕ}

The advantage of not using corner reflectors (GCPs) to estimate the phase-offset values on forested areas is tremendous. Dispensing the reflectors can lead not only to lower costs but it can also diminish the environmental impact associated with corner reflector deployment. In certain regions, like the dense Amazon forest or in fluvial regions, access to appropriate areas to deploy the reflectors can be difficult. Based on that, a test was performed in the Amazon rainforest area characterized by quite flat relief, without the use of corner reflectors. Several tracks were flown so that they crossed each other to compute the DEM difference in the intersection areas. The data were acquired with the same characteristics shown in

The method for phase-offset estimation, based on phase-offset functions presented in this work, has good potential for operational application, as it does not require the presence of GCP or

The results presented in

The potential for mapping rainforest area was checked and the results are presented in

The results presented in

The authors are grateful to Antonio Miguel Vieira Monteiro, Fabio Furlan Gama and Leonardo Sant’Anna Bins from INPE, for their fruitful suggestions. The authors would also like to express special thanks to the reviewers whose comments improved the quality of the manuscript.

Representation of the interferometric phase components.

Acquisition mode of airborne InSAR system for systematic mapping.

Positioning of the point _{i}_{1} and _{2} in Cartesian coordinates.

(_{i}_{k}_{i}_{k}_{i}_{k}_{off 1} × Φ_{off 2} are used to estimate the phase-offset values _{off 1}_{off 2}_{i}_{k}

Processing sequence for phase-offset estimation.

OrbiSAR-1 X-band InSAR data; (

Example of the

Example of the

Standard deviation of the phase-offset values

OrbiSAR-1 data: (

DEMs of OrbiSAR-1 X-band data for all tracks generated through the use of the proposed method for phase-offset estimation in the Amazon test site.

Performance regarding the percentage of the area used in range direction.

20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | |
---|---|---|---|---|---|---|---|---|

Mean value [rd] | 1.05 | 0.97 | 0.98 | 0.99 | 0.99 | 0.97 | 0.99 | 1.00 |

Std. dev. [rd] | 0.06 | 0.04 | 0.03 | 0.03 | 0.03 | 0.03 | 0.02 | 0.05 |

OrbiSAR-1 System-flight parameters.

Wavelength (λ) [m] | 0.031228 | 0.713791 |

Flight altitude (H) [Km] | 5.6 | 5.6 |

Incident angle (θ)—mid swath [deg] | 50 | 50 |

Normal Baseline (Bn)—mid swath [m] | 2.16 | 35.3 |

Swath width [Km] | 7.0 | 7.0 |

Chirp bandwidth [MHz] | 200 | 50 |

DEM spatial resolution [m] | 2.0 | 2.0 |

Phase-offset error between the two phase-offset estimation methods.

Mean difference [rd] | 0.047 | 0.051 |

Std. dev. [rd] | 0.0152 | 0.0191 |

DEM error in relation to 16 GCPs in the test site area measured with GPS survey.

Mean: _{h} |
1.1127 | 0.7641 | 1.1378 | 0.8265 |

Std. dev.: _{h} |
1.4720 | 0.6999 | 1.4709 | 0.7094 |

Statistics regarding the phase-offset estimation error of the proposed method for X- and P-band.

Wavelength: (λ) [m] | 0.0313918 | 0.713791 |

Measurement (GCPs) : (N) | 16 | 16 |

Mean phase error : _{ϕ} |
0.0470 | 0.0510 |

Phase Std. dev. _{ϕ} |
0.0152 | 0.0191 |

Phase uncertainty (95%): Max(|_{ϕu} |
0.0508 | 0.0558 |

Mean height error: _{h} |
0.327 | 0.702 |

Height Std. dev. _{h} |
0.059 | 0.203 |

Height uncertainty (95%): Max(|_{hu} |
0.445 | 1.108 |

Computed statistics between the DEMs in the intersection areas of all tracks.

Mean value of the difference: _{DEM} |
0.520 | 0.640 |

Std. dev. of the difference: _{DEM} |
3.170 | 2.520 |

Std. dev. of the range slope: _{rg} |
0.003 | 0.360 |

Std. dev. of the azimuth slope: _{az} |
0.008 | 0.310 |

Height standard error: _{he} |
1.124 | 1.127 |

Height uncertainty (95%): Max(|_{hu} |
2.768 | 2.904 |