Range Doppler algorithm for bistatic missile-borne forward-looking SAR

Focusing bistatic synthetic aperture radar (SAR) data in frequency domain requires two-dimensional (2D) point target reference spectrum (PTRS). Lofield's bistatic formula (LBF) and the Method of Series Reversion (MSR) have been introduced recently to compute PTRS of bistatic SAR. In this paper, flrstly we generalize the original LBF (OLBF) by introducing the Doppler contribution functions of transmitter and receiver. Thus, OLBF and its derivatives (e.g., extended LBF) can be viewed as special forms of the generalized LBF with constant Doppler contributions. Based on this, secondly the ideal LBF (ILBF) with no computing error, except the error resulting from the principle of stationary phase, is also presented. The ILBF reveals that the theoretical PTRS of bistatic SAR consists of only two monostatic terms, but it does not include bistatic deformation term in comparison with OLBF. It supplies us with a target when we deduce the PTRS for bistatic SAR. Finally, to get the precise analytical PTRS for general bistatic SAR, an approximated ILBF (AILBF) is proposed. It expresses the Doppler contributions of the transmitter and receiver as power series and can approach the ILBF very well. AILBF can keep the precision as MSR and inherit a simple form from LBF. In addition, error limit for the validity of bistatic PTRS is also given. The results in this paper can be used to develop imaging algorithms for extreme bistatic (e.g., spaceborne/airborne) and high squint (e.g., bistatic forward-looking) cases.

As having the imaging ability of area in front of flight direction, forward-looking synthetic aperture radar (SAR) has become a hot topic in areas of SAR research. Nevertheless, existing imaging algorithms of forward-looking SAR are all based on the assumption that the platform is moving in low velocity. When this assumption is not satisfied, the imaging result of existing algorithms will show focus out effect and deviation of imaging position from real position. Aiming at this problem and taking airborne forward-looking SAR system using single transmitting and multiple receiving antennas as the research object, this paper analyzes the feasibility of forward-looking SAR imaging of high velocity platform, and proposes a forward-looking SAR imaging algorithm suitable for high velocity platform according to its spatial geometry and the model of echo signal. Finally, the raw echo data of an array of point targets is simulated, and the focused images are obtained using the algorithm proposed in this paper. Imaging results demonstrate the validity of the algorithm. (6 pages)

In this paper, an omega-K imaging algorithm to focus the raw data of translational invariant (TI) bistatic synthetic aperture radar (BSAR) is proposed. The method utilizes a point target reference spectrum of generalized Loffeld's bistatic formula (GLBF). Without the bistatic deformation term, GLBF is the latest development of Loffeld's bistatic formula. It is comparable in precision with the method of series reversion (MSR), but it has a much simpler form than MSR and a similar form to a monostatic case. Based on the spatial linearization of GLBF, the Stolt transformation relationship is derived. The method can consider the linear spatial variation of Doppler parameters, which is always ignored in previous publications about bistatic omega-K algorithms. This method can handle the cases of TI BSAR with high squint angles and large bistatic degrees. In addition, a compensation method for the phase error caused by the linearization is discussed. Numerical simulations and experimental data processing verify the effectiveness of the proposed method.

An effective focusing approach for azimuth invariant bistatic SAR processing

The speed and direction of a missile shifts sharply in the dive phase, making the azimuth frequency modulation (FM) rate change with the azimuthal position, leading to azimuth ambiguities and image distortion. To solve this problem, a modified nonlinear chirp scaling (NLCS) algorithm was adopted to compensate for the azimuth FM rate. First, the geometric configuration and echo signal model of the spaceborne missile bistatic synthetic aperture radar (SAR) were built, and then the Doppler frequency correction was performed, and the 2-D spectrum of the signal was derived by the method of series reversion. Next, range migration correction and range compression were finished in the 2-D frequency domain. Following this, a modified NLCS algorithm was proposed to solve the space variance of Doppler phase problem. After compensating for the azimuth FM rate, the azimuth compression focusing was completed and the imaging result was obtained. Finally, by comparing the calculation amount, imaging effect, and performance index with the traditional NLCS algorithm, it can be concluded that the algorithm reduced the calculation amount by 1.0128 × 108 floating point operations per second (FLOPs) compared with the traditional NLCS algorithm, and the azimuth focusing effect of the edge point was greatly improved. Its resolution, peak sidelobe ratio (PSLR), and integrated sidelobe ratio (ISLR) were improved by 0.87 m, 3.32 dB, and 1.79 dB, respectively, which proved the effectiveness and feasibility of this method.

The bistatic SAR has forward-looking imaging capabilities if a opportunistic illuminator is selected to form the synthetic aperture. This would enable it to perform some inspection tasks that traditional SAR cannot perform. The system resolution of a bistatic SAR is related to its configuration. Due to the special configuration of the bistatic forward-looking SAR, the traditional system trajectory design method is no longer applicable. Therefore, a trajectory design method used for bistatic forward-looking SAR is proposed in this paper. First, the original trajectory of the receiver is determined according to the system which is always cannot be changed. Then, the slant range and the pitch angle of the transmitter are determined at each time. Next, the resolution of the transmitter under different squint angles at different times is calculated. Then, the available area of squint angle is obtained by drawing the results into a diagram. Finally, a position curve of the squint angle that is contained within the available area is found, and then the position of the transmitter and the resolution are calculated based on the position curve. The method can make the resolution of the forward-looking SAR system meet the requirements at all times under the condition that the changes to the original trajectory are at the minimum. The simulation results verify the validity of the proposed method.

Bistatic Synthetic Aperture Radar (BSAR) with GPS transmitter is in a focus of consideration. Bistatic topology, satellite transmitter of opportunity and stationary receiver, combined with inverse synthetic aperture radar (ISAR) technology with GPS P code modulated waveform for imaging of a moving are presented. Kinematical equations and mathematical model of the deterministic BSAR signal are created. It is proven that the signal formation and image reconstruction can be regarded as direct and inverse space transforms. Stages of image reconstruction, including phase correction, cross-correlation range compression and Fourier transform azimuth compression are defined. The effectiveness of models and algorithms are illustrated with results of numerical experiments.

In this paper, we develop a range Doppler algorithm (RDA) for the tandem bistatic synthetic aperture radar (BiSAR) configuration. The key step is to use an analytical tandem bistatic spectrum. The proposed algorithm is able to handle reasonably high squint by compensating secondary range compression in the two-dimensional wavenumber domain, and is more robust to focus bistatic data compared with Neo's RDA based on the spectrum of method of series reversion (MSR) in the tandem configuration particularly when the baseline-range ratio is large. The effectiveness of the proposed algorithm is verified by simulations.

In this paper, an effective moving target imaging approach is proposed for the geosynchronous-low earth orbit (GEO-LEO) bi-static multi-channel SAR system, which is robust for the fast moving target with Doppler centroid ambiguity. We discover that the baseline can be approximately regarded as a constant in chirp Fourier transform domain for the GEO-LEO bi-static multi-channel SAR system. Hence, the corresponding baseline compensation can be achieved in the azimuth chirp Fourier transform domain for the clutter. Then, the clutter can be well-suppressed and the moving target is extracted. After that, the moving target imaging approach is developed with the baseband Doppler centroid estimation and Doppler ambiguity number estimation. Finally, the theoretical investigations and the proposed approach in this paper is validated by experiments.

Recently, three-dimensional (3-D) millimeter-wave (mm-Wave) Forward-Looking Synthetic Aperture Radar (FLoSAR) has emerged as a promising technology for applications such as self-landing, navigation, and collision-avoidance in a deteriorated vision environment. The FLoSAR images targets when the radar platform is moving in the forward direction. The advantage of operating at mm-Wave comes from potentially exploiting its unlicensed, wide bandwidth for high-resolution imaging. Simultaneously, high angular resolution is difficult to achieve in FLoSAR because objects located symmetrically along the flight direction have the same range and Doppler history. Additionally, at mmWave, GPS accuracy is insufficient to obtain platform position at subwavelength level leading to challenges in providing motion compensation in the reconstructed images. In this work, we investigate the autofocusing by modeling it as a sparse deconvolution problem. The radar measurements correspond to a convolution of unknown radar image with an impulse function that has unknown focusing errors. In particular, we exploit the sparse nature of the target scenario and compare the results with the phase gradient autofocus method.

Chapter 1 - Overview of bistatic SAR

Focusing on the issue of echo data acquire approach in bistatic SAR system. In this paper, the key technology of echo sampling window synchronization is introduced, the effect of echo sampling window synchronization error to the echo data and image performance are analyzed, an adaptive echo sampling window synchronization approach based on amplitude demodulation and phase compare is proposed, which could automatically adapt for the echo pulse repeat interval(PRI), and establish a high accurate synchronized echo sampling window, then a high precise phase bias compare algorithm for the proposed approach is introduced. At last the performance and residual error for the presented approach are analyzed to illustrate the efficiency of the proposed approach. This paper provides a theoretical and engineering reference for the design of echo sampling window synchronization in bistatic SAR system.

With appropriate geometry configurations, bistatic Synthetic Aperture Radar (SAR) can break through the limitations of monostatic SAR on forward-looking imaging. Thanks to such a capability, bistatic forward-looking SAR (BFSAR) has extensive potential applications. However, the current BFSAR imaging algorithms always involve the time-consuming interpolation to carry out range migration correction. This paper develops a Chirp Scaling type imaging algorithm, which just needs the complex multiplication and FFT, for BFSAR with two parallel moving stations. The simulation results validate the effectiveness of the method.

A novel autofocus method for synthetic aperture radar (SAR) image is studied. Based on a quadratic model for the phase error within each sub-area (narrow strip × sub-aperture) after a wide range swath is subdivided into narrow range strips and long azimuth aperture into sub-apertures, an objective function for estimation of the error is derived through the principle of minimum entropy. There is only one unknown variable in the function. With the Chebyshev approximation, the function is approximated as a polynomial, and the unknown is then solved using the method of series reversion. Curve-fitting methods are applied to estimate phase error for an entire scene of the full-swath by full-aperture. Through simulations, the proposed method is applied to restore the defocused SAR imagery that is well focused. The restored and original images are almost identical qualitatively and quantitatively. Next, the method is implemented into an existing SAR data processor. Two sets of SAR raw data at X- and Ku-bands are processed and two images are formed. Well-focused and high-resolution images from plain and rugged terrain are obtained even without the use of ancillary attitude data of the airborne SAR platform. Thus, the studied method is verified.

Performance analysis of Bistatic Synthetic Aperture Radar (SAR) characterized by arbitrary geometric configurations is usually complex and time-consuming since system impulse response has to be evaluated by bistatic SAR processing. This approach does not allow derivation of general equations regulating the behaviour of image resolutions with varying the observation geometry. It is well known that for an arbitrary configuration of bistatic SAR there are not perpendicular range and azimuth directions, but the capability to produce an image is not prevented as it depends only on the possibility to generate image pixels from time delay and Doppler measurements. However, even if separately range and Doppler resolutions are good, bistatic SAR geometries can exist in which imaging capabilities are very poor when range and Doppler directions become locally parallel. The present paper aims to derive analytical tools for calculating the geometric resolutions of arbitrary configuration of bistatic SAR. The method has been applied to a hybrid bistatic Synthetic Aperture Radar formed by a spaceborne illuminator and a receiving-only airborne forward-looking Synthetic Aperture Radar (F-SAR). It can take advantage of the spaceborne illuminator to dodge the limitations of monostatic FSAR. Basic modeling and best illumination conditions have been detailed in the paper.