No need for jQuery, you can do this with pure JavaScript in most "modern" browsers, i.e.:
if (window.location.href === "http://examplesite.com/test.html") {
window.history.pushState("object or string", "Title", "http://examplesite.com/test.html?aa_campaign=f45632");
}
The pushState() method
pushState() takes three parameters: a state object, a title (which is
currently ignored), and (optionally) a URL. Let's examine each of
these three parameters in more detail:
state object — The state object is a JavaScript object which is associated with the new history entry created by pushState(). Whenever
the user navigates to the new state, a popstate event is fired, and
the state property of the event contains a copy of the history entry's
state object.
The state object can be anything that can be serialized. Because Firefox saves state objects to the user's disk so they can be restored
after the user restarts the browser, we impose a size limit of 640k
characters on the serialized representation of a state object. If you
pass a state object whose serialized representation is larger than
this to pushState(), the method will throw an exception. If you need
more space than this, you're encouraged to use sessionStorage and/or
localStorage.
title — Firefox currently ignores this parameter, although it may use it in the future. Passing the empty string here should be safe
against future changes to the method. Alternatively, you could pass a
short title for the state to which you're moving.
URL — The new history entry's URL is given by this parameter. Note that the browser won't attempt to load this URL after a call to
pushState(), but it might attempt to load the URL later, for instance
after the user restarts the browser. The new URL does not need to be
absolute; if it's relative, it's resolved relative to the current URL.
The new URL must be of the same origin as the current URL; otherwise,
pushState() will throw an exception. This parameter is optional; if it
isn't specified, it's set to the document's current URL.
SRC : https://developer.mozilla.org/en-US/docs/Web/Guide/API/DOM/Manipulating_the_browser_history
if (window.location.href.indexOf("http://examplesite.com/test.html"))