Q: Why GPS consumes battery power?
A: GPS is expensive because it is a very slow communication channel — you need to communicate with three or four satellites for an extended duration at 50 bits per second. There is no time division as it is in other communication mechanisms, necessitating powering the antenna for the duration of any communication. Besides that, while the GPS is on, the system cannot enter a sleep state. Mobile devices, such as Android and iPhone, achieve their battery life largely because they can aggressively and quickly enter into and exit from sleep states. GPS prevents this.
GPS's battery draining behaviour is most noticeable during the initial acquisition of the satellite's navigation message: the satellite's state, ephemeris, and almanac. Each satellite acquiring takes from 12 to 30 seconds, but if the full almanac is needed, it can take up to 12 minutes. During all these actions, your phone is unable to enter a deep sleep. A-GPS (Assisted GPS) partially solves the issue by sending the navigational message to your mobile device over your cellular data network or even Wi-Fi. As the bandwidth of either of these greatly dwarves the 50bps of the GPS satellites, the time spent powering the GPS antenna or avoiding deep sleep is greatly reduced.