Background surface coherent filtering procedure in connection with Slow-moving target velocity estimation problem for Synthetic Aperture Radar in Spotlight Mode
This paper is devoted to consideration of new algorithmic approach for coherent background signal compensation in context with exact velocity vector estimation problem for slow-moving target (SMT) having nonzero radial velocity component.
The following situation is examined here: two (or more) spaceborne narrow-beam steering decametric antennae (which are based on the spaceship and shifted along the way) are working synchronously in Narrow-Beam Spotlight Mode (i.e. switching simultaneously their directivity patterns). Each antenna is both emitting and receiving, all others antennae are only receiving. Moments of LFM-pulse emitting are shifted by time for different antennae. Time shift value equals to half of LFM-pulse repetition interval. Each antenna has two shifted by time receiving strobs. Each of repetition intervals contains two disjunct receiving strobs exactly, such scheme is possible due to very small width of SAR beam by angle of elevation (half of nominal value). Another possible variant – very small width of SAR beam by azimuth (half of nominal value) and low repetition frequency (two nominal values).
High spaceship velocity value (60007000 m/s for heights 400500 km) requires usage of high interferometrical base value (50100 m) for along-way interferometry to achieve high-fidelity solution of SMTD problem. Antennae system of above considered type allows to simulate the situation with three phase receiving centers in simplified two-antennae system situation, each antenna is having only one phase center (both receiving and emitting). Such antennae system provides the simple solution of wide range of problems in connection with SMT-problem in various difficult situations (dim targets and bright backgrounds, MT and background have the same texture signs, etc.) without usage cumbersome three-antennae spaceborne systems.
The triple of phase center simulation is being executed in the following way for discribed above two-antennae system. ADC exits of these antennae provide three complex digital holograms as follows. ADC exit of 1-st receiving strob of 1-st antenna will derivate the 1-st digital hologram (signal emited by 1-st antenna and received by 1-st antenna). ADC exit of 2-nd receiving strob of 2-nd antenna will derivate the 2-nd digital hologram (signal emited by 2-nd antenna and received by 2-nd antenna). ADC exit of 1-st receiving strob
of 2-nd antenna will derivate the 3-rd digital hologram (signal emited by 1-st antenna and received by 2-nd antenna). The triple of holograms will coorrespond to the triple of «virtual» receiving phase centers.
Three complex two-dimensional (range and way) holograms are being transformed into three digital complex radar images («disturbed» by signal reflected by the background) by using two-dimensional convolution algorithm with the common reference function.
The following step is coherent background surface filtering and dedication of pure complex radar images, using a few of algebraic operations on complex values for each image pixel.
SMT detection (SMTD) «phase-difference» method (based on fact that two different pure complex SAR target images, obtained from discrete sampled signals from shifted along the way phase centers by fast-convolution algorithm of synthesis using common reference function for each signal, differ one from another by nonzero phase value only in case of moving targets having nonzero radial velocity component) is complemented in current paper with algorithm for radial velocity component estimation.
Radial velocity estimation algorithm is based on on study of dependance law variations of phase augment value (i.e. phase difference value between two different SMT images) from antenna shift value (along the way); these variations are caused by frequency band variations. Noted above filtering procedure of getting complex «phase-difference» SMT-images of slow-moving targets (having nonzero radial velocity component) is beeng executed in this algorithm twice for two partial frequency «sub-bands» (having different frequency carrier values but the same width) of the whole working frequency band. Each partial sub-band is being cut (by range in spectral domain) from two-dimensional hologram spectra on stage of synthesis. Then the comparison (by phase value) procedure is being executed for each pair of SMT-images (synthesed using different partial sub-bands for each moving target). Phase variation value for each detected moving target (i.e. for each pair of «phase-difference» SMT-images) gives (accounting phase center shift along the way values and sub-band frequencies) the value of radial target velocity.
Audible formulae and charts are being put here in the paper for each algorithm, computer simulation results (both graphic and numeric) are being put here too