Analysis for Resolution of Bistatic SAR Configuration with Geosynchronous Transmitter and UAV Receiver

Table 4

Space-time analysis of GEO-UAV BiSAR.

Velocity ratio	Azimuth maximum coverage; (UAVSAR position in Ox axis)	Coherent accumulated time
		𝑇sar=𝑥−𝑥𝐴𝑉𝑅,𝑥∈𝑥𝐴,𝐿𝑅+𝑥𝐴,
𝑘=0	𝐶𝑎=𝐿𝑇 (𝑥𝑅=𝑥𝑅^(0))	𝑇sar=𝐿𝑅𝑉𝑅,𝑥∈𝐿𝑅+𝑥𝐴,𝐿𝑇−𝐿𝑅+𝑥𝐴,	(20)
		𝑇sar=𝑥−𝐿𝑇+𝐿𝑅−𝑥𝐴𝑉𝑅,𝑥∈𝐿𝑇−𝐿𝑅+𝑥𝐴,𝐿𝑇+𝑥𝐴.
𝑘∈(0,1)	𝐶𝑎=𝑉𝑅𝐿𝑇+𝑉𝑒𝑇𝐿𝑅𝑉𝑅−𝑉𝑒𝑇(𝑥𝑅=𝑥𝑅^(0))	𝑙(𝑥)=𝐿𝑇−𝑉𝑅−𝑉𝑒𝑇𝑉𝑅𝑥−𝑥𝐴,𝑇sar𝐿=min^𝑅𝑉𝑅,𝐿𝑇−𝑙(𝑥)𝑉𝑒𝑇,𝑥∈𝑥𝐴,𝑉𝑅𝐿𝑇𝑉𝑅−𝑉𝑒𝑇+𝑥𝐴,	(21)
		𝑉𝑙(𝑥)=^𝑅−𝑉𝑒𝑇𝑉𝑔𝑇𝑥−𝑥𝐴−𝑉𝑅𝑉𝑒𝑇𝐿𝑇,𝑇sar𝐿=min^𝑅𝑉𝑅,𝐿𝑅−𝑙(𝑥)𝑉𝑅,𝑉𝑥∈^𝑅𝐿𝑇𝑉𝑅−𝑉𝑔𝑇+𝑥𝐴,𝑉𝑅𝐿𝑇+𝑉𝑒𝑇𝐿𝑅𝑉𝑅−𝑉𝑒𝑇+𝑥𝐴.	(22)
𝑘∈(1,+∞)	𝐶𝑎=𝑉𝑅𝐿𝑇+𝑉𝑒𝑇𝐿𝑅𝑉𝑒𝑇−𝑉𝑅(𝑥𝑅=𝑥𝑅^(1))	𝑙(𝑥)=𝐿𝑅−(𝑉𝑒𝑇−𝑉𝑅)𝑥−𝑥𝐵𝑉𝑒𝑇,𝑇sar=𝐿𝑅−𝑙(𝑥)𝑉𝑅,𝑥∈𝑥𝐵,𝑉𝑒𝑇𝐿𝑅𝑉𝑒𝑇−𝑉𝑅+𝑥𝐵,	(23)
		𝑙(𝑥)=(𝑉𝑒𝑇−𝑉𝑅)𝑥−𝑥𝐵𝑉𝑅−𝐿𝑅𝑉𝑒𝑇𝑉𝑅,𝑇sar𝐿=min^𝑅𝑉𝑅,𝐿𝑇−𝑙(𝑥)𝑉𝑒𝑇,𝑉𝑥∈^𝑒𝑇𝐿𝑅𝑉𝑒𝑇−𝑉𝑅+𝑥𝐵,𝑉𝑅𝐿𝑇+𝑉𝑒𝑇𝐿𝑅𝑉𝑒𝑇−𝑉𝑅+𝑥𝐵.	(24)
𝑘<0	𝐶𝑎=𝑉𝑅𝐿𝑇+𝑉𝑒𝑇𝐿𝑅𝑉𝑅+𝑉𝑒𝑇(𝑥𝑅=𝑥𝑅^(1))	𝑙(𝑥)=𝐿𝑅−𝑉𝑅+𝑉𝑒𝑇𝑉𝑒𝑇𝑥−𝑥𝐵,𝑇sar𝐿=min^𝑅𝑉𝑅,𝐿𝑅−𝑙(𝑥)𝑉𝑅,𝑥∈𝑥𝐵,𝑉𝑒𝑇𝐿𝑅2𝑉𝑅+𝑉𝑒𝑇+𝑥𝐵,	(25)
		𝑉𝑙(𝑥)=^𝑅+𝑉𝑒𝑇𝑉𝑅𝑥−𝑥𝐵−𝑉𝑒𝑇𝑉𝑅𝐿𝑅,𝑇sar𝐿=min^𝑅𝑉𝑅,𝐿𝑇−𝑙(𝑥)𝑉𝑒𝑇,𝑉𝑥∈^𝑒𝑇𝐿𝑅(𝑉𝑅+𝑉𝑒𝑇)+𝑥𝐵,𝑉𝑒𝑇𝐿𝑅+𝑉𝑅𝐿𝑇𝑉𝑒𝑇+𝑉𝑅+𝑥𝐵.	(26)