Took me some time but I’ve found a more reliable way than relying on hasPermanentMenuKey() which doesn’t work for newer phones like the HTC One which have no menu key but do have home & back keys so don’t need (or show) the soft navigation bar. To get around this try the following code which checks for a back button too:
boolean hasMenuKey = ViewConfiguration.get(context).hasPermanentMenuKey();
boolean hasBackKey = KeyCharacterMap.deviceHasKey(KeyEvent.KEYCODE_BACK);
if(!hasMenuKey && !hasBackKey) {
// Do whatever you need to do, this device has a navigation bar
}