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Autonomous navigation airborne forward-looking synthetic aperture radar (SAR) observes the anterior inferior wide area with a short cross-track dimensional linear array as azimuth aperture. This is an application scenario that is drastically different from that of side-looking space-borne or air-borne SAR systems, which acquires azimuth synthetic aperture with along-track dimension platform movement. High precision imaging with a combination of pseudo-polar formatting and overlapped sub-aperture algorithm for autonomous navigation airborne forward-looking SAR imaging is presented. With the suggested imaging method, range dimensional imaging is operated with wide band signal compression. Then, 2D pseudo-polar formatting is operated. In the following, azimuth synthetic aperture is divided into several overlapped sub-apertures. Intra sub-aperture IFFT (Inverse Fast Fourier Transform), wave front curvature phase error compensation, and inter sub-aperture IFFT are operated sequentially to finish azimuth high precision imaging. The main advantage of the proposed algorithm is its extremely high precision and low memory cost. The effectiveness and performance of the proposed algorithm are demonstrated with outdoor GBSAR (Ground Based Synthetic Aperture Radar) experiments, which possesses the same imaging geometry as the airborne forward-looking SAR (short azimuth aperture, wide azimuth swath). The profile response of the trihedral angle reflectors, placed in the imaging scene, reconstructed with the proposed imaging algorithm and back projection algorithm are compared and analyzed.

Autonomous navigation airborne forward looking synthetic aperture radar (SAR) is a kind of imaging radar that obtains 2D image of the anterior inferior wide area of the platform [

Azimuth aperture is usually acquired by aperture synthesis with the platform movement (e.g., straight line movement in stripmap or spotlight working mode) in conventional SAR systems. For autonomous navigation airborne forward-looking SAR systems, the airborne can fly in an arbitrary flight path as the azimuth aperture is formulated by the cross-track dimensional linear array and not by the platform movement. Autonomous navigation airborne forward-looking SAR possesses an azimuth aperture with the length of only a few meters and illuminates an imaging scene spanning hundreds meters, or kilometers, in azimuth dimension (for example, the platform holds a linear array with a length of 3 m, which means the azimuth aperture is 3 m, the beam width of the array is 30 degrees, the straight line distance between the radar and the target is 500 m, and the imaging swath is 2 × 500 × tan(30/2) m = 270 m. It is obvious that the imaging swath is much larger than the azimuth aperture.) [

This paper focuses on the development of an autonomous navigation airborne forward-looking SAR imaging, with the combination of pseudo-polar formatting and an overlapped sub-aperture algorithm. The azimuth imaging is operated in space domain, which reduces the memory cost on the circumstances of imaging a wide azimuth area with a short azimuth aperture. The wave-front curvature phase error is compensated with overlapped sub-aperture algorithm, which guarantees imaging precision. The main operations in the proposed algorithm include complex matrix multiplication, interpolation, FFT/IFFT (Fast Fourier Transform/Inverse Fast Fourier Transform), which can be easily implemented in parallel. The proposed imaging method possesses the advantages of high precision, low memory cost, and moderate computation.

The remainder of the paper is organized as follows. In section 2, the imaging geometry of the autonomous navigation airborne forward-looking SAR is introduced. The echo signal model of the autonomous navigation airborne forward-looking SAR is illustrated in section 3. High precision imaging, with the combination of pseudo-polar formatting and an overlapped sub-aperture algorithm for the autonomous navigation airborne forward-looking SAR imaging is discussed in section 4. The validation and performance analysis of the proposed algorithm, with the GBSAR data sets, are presented in section 5. Finally, the conclusion and the current focus of our research are outlined in section 6.

As can be seen in the first image of

The azimuth aperture of the autonomous navigation airborne forward-looking SAR is formulated with the cross-track dimensional linear array. The linear array can be densely or sparsely configured at the bottom of the airborne platform. X axis is the azimuth dimension, which is in parallel with the linear array. Y axis is the radar range dimension. O is the origin. Range dimensional resolution is obtained with wide band signal compression and azimuth dimensional resolution is obtained with physical array aperture synthesis. The length of the aperture is L and the size of the imaging area is X_{0} in azimuth dimension and Y_{0} in range dimension. For autonomous navigation airborne forward-looking SAR system circumstance, the length of the azimuth aperture is much shorter than the azimuth-imaging swath (_{0} ≪ _{n}

The autonomous navigation airborne forward-looking SAR with linear array placed at the bottom of the platform is a multi-channel system. This multi-channel system usually works at a time-divided transmitting-receiving mode. The airborne platform movement during the time-divided transmitting-receiving procedure causes a Doppler shift to the echo signal. The Doppler shift effect can be compensated according to the method in [

In this section, the autonomous navigation airborne forward-looking SAR echo signal model is discussed. A chirp signal with carrier frequency _{c}_{r}_{P}_{n}

Range frequency domain echo signal can be obtained by performing range FFT. The obtained range frequency domain signal can be written as:
_{m}_{c}_{m}_{s}_{s}_{r}_{s}_{r}^{H}_{m}_{n}

According to the echo model in

With azimuth pseudo-polar formatting according to the relationship (_{c}_{m}_{n}_{c}x′_{n}_{n}

The wave front curvature phase error term defocuses the reconstructed image, if we require the azimuth defocus effect to be less than

Take maximum

According to

In autonomous navigation airborne forward-looking SAR circumstance, the condition in

Suppose the azimuth spacing interval is Δ_{n}_{n}

In autonomous navigation airborne forward-looking SAR circumstance, the condition in

Then β can be estimated as

The phase compensation term g(i) is applied to compensate the exponent term in

We perform IFFT along the i dimension and obtain:

We transform the azimuth image from matrix sample (i, k) to vector sample, n, according to the relationship in

An important advantage of the proposed pseudo-polar formatting and overlapped sub-aperture algorithm is that the resulting image shows an invariant resolution within the entire image scene. The resolution in pseudo-polar image is

The Ground Based SAR (GBSAR) system is widely used for slope area and glacier deformation monitoring for its low de-correlation compared with space-borne data [

The sketch view of the observed imaging scene is shown in

In order to obtain a high precision imaging result, the image reconstruction is operated with the proposed combination of pseudo-polar formatting and an overlapped sub-aperture algorithm. The azimuth synthetic aperture (256 azimuth samples) is divided into 30 overlapped sub-apertures, every sub-aperture contains 16 azimuth samples, and every two adjacent sub-apertures contain eight overlapped azimuth samples. The reconstructed image with the proposed algorithm is shown in

By comparing the reconstructed images in

In order to clarify the performance of the proposed imaging algorithm, we compare the range and azimuth dimensional profile response of the trihedral angle reflectors placed in the imaging scene reconstructed with the proposed imaging algorithm and back projection algorithm. The range and azimuth profile response of the trihedral angle reflectors labeled 1, 2, and 3 in the imaging scene is shown in

As is illustrated in the last part of Section 4, the reconstructed image in the pseudo-polar coordinate owns the same invariant azimuth resolution, which means that the main lobe of the trihedral angle reflectors’ azimuth profile is the same. The reconstructed image in the Cartesian coordinate owns variant azimuth resolution, which means the main lobe of the trihedral angle reflectors’ azimuth profile is different. From the imaging result shown in

In order to clarify the pseudo-polar and Cartesian coordinate azimuth response, we compare the azimuth resolution of the trihedral angle reflector in the pseudo-polar and Cartesian coordinate, which is shown in

We conclude with some minor suggestions regarding the practical use of this technique. The authors have implemented and extensively tested the proposed high precision imaging method with GBSAR experiments using Matlab (the Mathworks, MA, USA) and C/C++. The main computation operations in this algorithm include FFT/IFFT, complex matrix multiplication, and interpolation. Then high precision imaging result can be obtained in real time with parallel implementation. According to our experiences, the elapsed time for image reconstruction with the measurement parameters in the simulation is 0.3 second at Intel(R) Core(TM) i7 2600@3.40 GHz CPU platform.

Autonomous navigation airborne forward-looking synthetic aperture radar (SAR) observes the anterior inferior wide area with a short cross-track dimensional linear array as azimuth aperture. The short azimuth aperture wide azimuth swath application scenario is drastically different from that of side-looking space-borne, or air-borne, SAR system. The imaging geometry, echo signal model, and pseudo-polar formatting, and overlapped sub-aperture algorithm for autonomous navigation airborne forward-looking SAR imaging are illustrated. The range dimensional imaging is operated with wide band signal compression. The azimuth synthetic aperture is divided into several overlapped sub-apertures. Intra sub-aperture IFFT, wave front curvature phase error compensation, and inter sub-aperture IFFT is operated sequentially to finish azimuth high precision imaging. We demonstrate outdoor GBSAR experiments that possess the same imaging geometry as the airborne forward-looking SAR to validate the effectiveness and performance of our proposed algorithm. We also compare and analyze the profile response of the trihedral angle reflectors placed in the imaging scene reconstructed with the proposed imaging algorithm and back projection algorithm. The proposed algorithm possesses the advantage of high reconstruction precision, low memory cost, and medium computation complexity.

This work is supported by the National Natural Science Foundation of China Surface Program (Grant No. 61072112), and the National Natural Science Foundation of China Key Program (Grant No. 60890071). The authors would also like to thank the reviewers for their constructive comments.

Autonomous navigation airborne forward looking SAR imaging geometry.

The minimum reference range for ignoring wave front curvature phase error term according to

(

The sub-aperture division.

The flow diagram of the imaging algorithm with the combination of pseudo-polar formatting and overlapped sub-aperture algorithm.

(

Detail description of the imaging scene.

(

(

The profile response of the trihedral angle reflector labeled 1.

The profile response of the trihedral angle reflector labeled 2.

The profile response of the trihedral angle reflector labeled 3.

The trihedral angle reflector azimuth resolution comparison in the pseudo-polar and Cartesian coordinate.

Measurement parameters used in the experiment.

Carrier Frequency | 17.25 GHz |

Bandwidth | 500 MHz |

Range Sample Number | 4001 |

Azimuth Synthetic Aperture | 2.56 m |

Azimuth Sample Interval | 0.01 m |

Azimuth Sample Number | 256 |