Реализация перемещения маркера

В ранних версиях Android – практически вручную, в более поздних – с помощью встроенных в SDK средств, вроде ValueAnimator и ObjectAnimator:

public class MarkerAnimation {
    static void animateMarkerToGB(final Marker marker, final LatLng finalPosition, final LatLngInterpolator latLngInterpolator) {
        final LatLng startPosition = marker.getPosition();
        final Handler handler = new Handler();
        final long start = SystemClock.uptimeMillis();
        final Interpolator interpolator = new AccelerateDecelerateInterpolator();
        final float durationInMs = 3000;
        handler.post(new Runnable() {
            long elapsed;
            float t;
            float v;
            @Override
            public void run() {
                // Calculate progress using interpolator
                elapsed = SystemClock.uptimeMillis() - start;
                t = elapsed / durationInMs;
                v = interpolator.getInterpolation(t);
                marker.setPosition(latLngInterpolator.interpolate(v, startPosition, finalPosition));
                // Repeat till progress is complete.
                if (t < 1) {
                    // Post again 16ms later.
                    handler.postDelayed(this, 16);
                }
            }
        });
    }
    @TargetApi(Build.VERSION_CODES.HONEYCOMB)
    static void animateMarkerToHC(final Marker marker, final LatLng finalPosition, final LatLngInterpolator latLngInterpolator) {
        final LatLng startPosition = marker.getPosition();
        ValueAnimator valueAnimator = new ValueAnimator();
        valueAnimator.addUpdateListener(new ValueAnimator.AnimatorUpdateListener() {
            @Override
            public void onAnimationUpdate(ValueAnimator animation) {
                float v = animation.getAnimatedFraction();
                LatLng newPosition = latLngInterpolator.interpolate(v, startPosition, finalPosition);
                marker.setPosition(newPosition);
            }
        });
        valueAnimator.setFloatValues(0, 1); // Ignored.
        valueAnimator.setDuration(3000);
        valueAnimator.start();
    }
    @TargetApi(Build.VERSION_CODES.ICE_CREAM_SANDWICH)
    static void animateMarkerToICS(Marker marker, LatLng finalPosition, final LatLngInterpolator latLngInterpolator) {
        TypeEvaluator<LatLng> typeEvaluator = new TypeEvaluator<LatLng>() {
            @Override
            public LatLng evaluate(float fraction, LatLng startValue, LatLng endValue) {
                return latLngInterpolator.interpolate(fraction, startValue, endValue);
            }
        };
        Property<Marker, LatLng> property = Property.of(Marker.class, LatLng.class, "position");
        ObjectAnimator animator = ObjectAnimator.ofObject(marker, property, typeEvaluator, finalPosition);
        animator.setDuration(3000);
        animator.start();
    }
}

Взято отсюда.