You eliminate the power transformers (T1 in each) and and rectifier diodes (D2, D3 and D3, D4) and connect the regulators (IC3 in each) to the battery (through a small resistor and 15V zener to ground to suppress transients).
IC3 in the reciever is a 78L12, 12V regulator, which requires a minimum of 14.5V to work. This regulator will need to be replaced with a 12V low dropout regulator. Alternately the circuit could probably be modified to work with a lower voltage regulator such as a 78L09, 9V device.