获取android 授权省略了，上调用GPS部份代码吧。

implementation
 
uses androidapi.jni.JavaTypes, androidapi.jni.Location, FMX.helpers.android,
  androidapi.jni.GraphicsContentViewText, androidapi.jnibridge;
// context在android的content.context包
// ILocalObject在androidapi.jnibridge里
// sharedActivitycontext在fmx.helpers里
{$R *.fmx}
 
// 使用android的地理GPS定位函数
procedure TForm1.Button1Click(Sender: TObject);
var
  LocationManagerService: JObject;
  Location: JLocation;
  fLocationManager: JLocationManager;
 
  Lat: string;
  Lon: string;
  Alt: string;
begin
  if not assigned(fLocationManager) then
  begin
//获得Java对象
    LocationManagerService := sharedActivitycontext.getSystemService
      (TJcontext.JavaClass.LOCATION_SERVICE);
// 获得对象的java实例
    fLocationManager := tjlocationmanager.Wrap
      ((LocationManagerService as ILocalObject).GetObjectID);
     end;
//调用Java方法
  // use the gps provider to get current lat, long and altitude
  Location := fLocationManager.getLastKnownLocation
    (tjlocationmanager.JavaClass.GPS_PROVIDER);
    lat:=format('%2.6f',[location.getLatitude]);
    lon:=format('%2.6f',[location.getLongitude]);
    Alt := format('%2.6f',[location.getAltitude]);
    edit1.Text:=lat;
    edit2.Text:=lon;
end;
 
end.