Method Of Series Reversion Research Articles

An Analytical Method of Updating the Range Derivatives and a Simple Image Registration Method for the MSR-Based Range Doppler Algorithm

Based on the method of series reversion, Neo developed a quite accurate range Doppler algorithm (RDA). In performing this RDA, the range derivatives need to be updated along the range. In this letter, first, we will give an analytical method to update the range derivatives for this RDA. The proposed method mainly exploits two points the first is the introduction of a reference vector on the ground plane of the bistatic geometry, and the second is the use of the principle of series reversion. Second, based on this new method of updating the range derivatives, we present a simple image registration method for mapping the focused image onto the ground plane, which needs a 1-D interpolation only in the range direction. Third, a motion compensation method is also proposed.

Bistatic SAR Data Focusing Using an Omega-K Algorithm Based on Method of Series Reversion

This paper deals with an omega-K algorithm for focusing bistatic synthetic aperture radar (SAR) data. The key of the proposed algorithm is the derivation of a frequency mapping function by using Neo's method of series reversion. The registration of the focused image onto the ground plane is discussed in detail, which is based on a conclusion that the targets whose instantaneous Doppler frequencies at zero azimuth time are the same as that of the reference target at zero azimuth time will all be focused at the reference target's azimuth position in the focused image. The range invariance region size, which the proposed algorithm can process, is also determined in this paper. The proposed algorithm can handle extreme bistatic configurations with wide apertures and large squint angles. The effectiveness of the proposed algorithm is confirmed by simulation results. Although developed for the azimuth-invariant case, the proposed algorithm can be readily extended to the azimuth-variant case, as long as we divide the SAR data into blocks in the azimuth direction so that each block of SAR data can be assumed quasi-stationary in the azimuth direction.

An effective focusing approach for azimuth invariant bistatic SAR processing

This paper proposes a processing method to extend monostatic imaging algorithms for the azimuth invariant bistatic SAR (BISAR) data where the transmitter and the receiver move on parallel tracks with equal velocities. The bistatic range history is approached by a polynomial of the azimuth time. Based on this model, an analytic 2-D signal spectrum derived by the method of series reversion is utilized and a simple one-to-one mapping between the transmitter and the receiver closest ranges is established. In this way, efficient monostatic imaging algorithms which operate in the 2-D frequency domain or the range-Doppler domain are easily modified to handle the BISAR data. In this paper, a chirp scaling algorithm for the BISAR is developed as an application of the new method. By implementing two key operations, range cell migration correction by a chirp scaling, and azimuth compression by a curve fitting technique, this algorithm is able to process the azimuth invariant BISAR data. Simulation results are presented to demonstrate the validity and the efficiency of the proposed algorithm.

A Comparison of Point Target Spectra Derived for Bistatic SAR Processing

The existence of a double hyperbola in the bistatic range equation makes it difficult to find an exact analytical solution for the 2D point target spectrum. Several approximate solutions for the spectrum have been derived and used to focus bistatic synthetic aperture radar data. In this paper, we establish the relationship between three independently derived bistatic point target spectra. The first spectrum is Loffeld's bistatic formula, which consists of a quasi-monostatic and a bistatic phase term. The second spectrum makes use of Rocca's smile operator, which transforms bistatic data in a defined configuration to a monostatic equivalent. The third spectrum is derived using a power series - called the method of series reversion (MSR). The MSR spectrum is the most general among the three. This paper shows that this spectrum can be reduced to the same formulation as the former two when certain conditions are met. In addition, a new approximate spectrum is derived using a Taylor series expansion about the two stationary phase points of the transmitter and receiver. We also give an alternative geometrical proof of the relationship between Rocca's smile operator and Loffeld's bistatic deformation term. The accuracies of the point target spectra are demonstrated using simulations of an X-band bistatic airborne radar with a fixed baseline.

Processing of Azimuth-Invariant Bistatic SAR Data Using the Range Doppler Algorithm

This paper discusses bistatic synthetic aperture radar processing (complex image formation) using the Range Doppler Algorithm. The key step is to use an analytical form of the signal spectrum derived by the method of series reversion. The spectrum is used for secondary range compression (SRC), range cell migration correction, and azimuth compression. The algorithm is able to focus the azimuth-invariant bistatic configuration where the transmitter and receiver platforms are moving in parallel tracks with identical velocities. Moreover, the algorithm is able to handle reasonably high squints and wide apertures because SRC can be performed in the 2-D frequency domain.