You can try this way :

  // If you dont need to call original method
    $.widget("ui.addresspicker", $.extend({}, $.ui.addresspicker.prototype, {
      _updatePosition: function(){
        // Do what you want to
      }
    }));

    // If you need to call original method
    var _updatePosition = $.ui.addresspicker.prototype._updatePosition;
    $.widget("ui.addresspicker", $.extend({}, $.ui.addresspicker.prototype, {
      _updatePosition: function(){
        // Do what you want to
        // Call original widget method  
        _updatePosition.apply(this, arguments);
      }
    }));