This principle is already sometimes used for determining the position of UAVs (e.g. Quadcopters). So absolute position is provided by GPS and short term movements can be calculated from accelerometers and other sensors.

Of course sensor data can only provide a relative position. After longer intervals of solely relying on the relative sensor-based position small errors can accumulate which makes "synchronization" with GPS necessary to retain accuracy.

The power consumption of computing the kalman filter is negligible compared to the power consumption of the gps module.

I thought that ios and android did this already for a long time.