window.location.href = window.opener.href;
both will send GET parameters. The former will also send POST parameters (usually you get a pop-up box asking if you would like to re-send post parameters or not do the page reload at all (which can be annoying)).
To set what GET parameters should be used use among other things the
split()function on the string
splitArray = window.location.href.split("?");
window.location.href = splitArray;
and get parameters by splitting the second part of the
Adding opener after window will address the reload to the window which opened the current page: