Multiposition Synthetic Aperture Radar (MPSAR) 

              Alexander V Ksendzuk 

3. Multiposition SAR. Geometry.

As we can see from equation (3.1) input signal is modulated by time delay behaviour . This time delay for each points of the surface  depends on range history for both receiver  and transmitter, Fig. 3.1.

Figure 3.1. Time delay in arbitrary bistatic pair in MPSAR.

Signal Groups in Multiposition SAR

For further investigation it is useful to separate time delay

                   (3.1)

into constant  and variable  parts in time domain

 ,                                         (3.2)

where

         ,                  (3.3)

. (3.4)

Analysis of (3.3), (3.4) allows to investigate Doppler frequency of the signal in bistatic pair , which was scattered from surface point :

,   (3.5)

.(3.6)

Behavior of the Doppler frequency shift as spatial function are shown in Figure 3.2.

Figure 3.2. Doppler frequency as the space functions of the relative receiver/transmitter velocity.

Dependence of the ,  of surface coordinates for given bistatic pair we’ll call field of average delays  and field of delta-delays .

Analysis of the field of average delays  and field of delta-delays  is the principle of the gradient analysis of multiposition SAR. This analysis allow to select spatial configuration, radar scene etc by criteria based on resolution.

Analysis of the  and  allows to investigate spatial resolution, unambiguity measurements intervals and optimize attitude of the multiposition SAR .

Fundamental advantage of the optimization in comparison with “direct analysis of the space ambiguity functions (point target responses)” is ultimate speed. For this example proposed Gradient Optimization takes 50 seconds and optimization based on space ambiguity function analysis takes 56 days!

An example of the optimal selection of the radar scene (footprint of the transmitters/receivers antennas intersection) for the multiposition synthetic aperture radar, spatial configuration (attitude and velocity vector are given) is shown in the Fig. 3.3.

Figure 3.3. Spatial configuration of the MPSAR to be optimized.

Figure 3.4. Fields  and .

Figure 3.5. Optimization based on absolute gradient values allows to select area with good resolution in azimuth and/or range

Figure 3.6. Optimization based on angle between gradients allows to select zone where shape of the high resolution zone is given and with usage of absolute gradient values- shape and area of  the high resolution zone are given

Conclusion

Investigation of the geometry of the multiposition SAR is necessary step to understand signal structure.

Based on this analysis proposed gradient analysis allows to select best constellation in case of multiposition SAR or to select the best relative position and velocity in bistatic SAR which provides maximal resolution in given direction (directions) and/or maximal interval of the unambiguity measurements.

Ultimate advantage of the proposed gradient optimization method is characterizes by little computation costs. This gives possibility to use this analysis in the on-board remote sensing systems.

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