def METHOD_NAME(grid_map, u, yaw):
    grid_map.dx += DT * math.cos(yaw) * u[0]
    grid_map.dy += DT * math.sin(yaw) * u[0]
    x_shift = grid_map.dx // grid_map.xy_resolution
    y_shift = grid_map.dy // grid_map.xy_resolution
    if abs(x_shift) >= 1.0 or abs(y_shift) >= 1.0:  # map should be shifted
        grid_map = map_shift(grid_map, int(x_shift[0]), int(y_shift[0]))
        grid_map.dx -= x_shift * grid_map.xy_resolution
        grid_map.dy -= y_shift * grid_map.xy_resolution
    # Add motion noise
    grid_map.data = gaussian_filter(grid_map.data, sigma=MOTION_STD)
    return grid_map