filter_sub_menu.php

<?php
function theme_wp_nav_menu_sub_menu_objects( $sorted_menu_items, $args ) {
    if ( isset( $args->sub_menu ) ) {
        $root_id = 0;

        //var_dump($sorted_menu_items);

        // find the current menu item
        foreach ( $sorted_menu_items as $menu_item ) {
            if ( $menu_item->current ) {
                // set the root id based on whether the current menu item has a parent or not
                $root_id = ( $menu_item->menu_item_parent ) ? $menu_item->menu_item_parent : $menu_item->ID;
                break;
            }
        }

        $menu_item_parents = array();

        foreach ( $sorted_menu_items as $key => $item ) {
          if ( $item->current_item_ancestor ) $menu_item_parents[] = $item->ID;
            // init menu_item_parents
            if ( $item->ID == $root_id ) $menu_item_parents[] = $item->ID;

            if ( in_array( $item->menu_item_parent, $menu_item_parents ) ) {
                // part of sub-tree: keep!
                $menu_item_parents[] = $item->ID;
            } else {
                // not part of sub-tree: away with it!
                unset( $sorted_menu_items[$key] );
            }
        }

        return $sorted_menu_items;

    } else {
        return $sorted_menu_items;
    }
}