Here is an app that might exist, but if not, should be created:
An emergency button on your lock screen. One touch would bring up an emergency menu of "I'm in trouble and need the police." or "I am having a medical emergency and need assistance" or "Cancel".
Hitting the first two options would automatically dial 911 and repeat a message with the type of emergency (police related or medical related), give your location and your name. The app would automatically turn on your phone's GPS and Mobile Data connection (whatever was needed to make the call and provide the information) and keep repeating same until the call was disconnected.