Update URL with new parameter value

I'm not sure about ways to improve performance, but I did notice a couple things.

Guaranteed Returns

If the specified key is already set to the specified value, your function does not return anything. Maybe this is the expected behavior, but I could see it being a problem if you used the function to directly update the URL.

window.location.href = changeURLParameter("thriggle","boring");
// If thriggle already == boring, this redirects you to /undefined

One way to fix that would be to simply remove the If statement if (aURLParams[sVariable] != sNewValue){...}.

Without that check, regardless of whether the parameter is already set to the specified value, it'll be overwritten with the desired value and the URL string will be returned.

Original Sin

window.location.origin does not exist in older versions of Internet Explorer (9 and down). If your user base doesn't overlap with those poor souls still using IE9, feel free to ignore this one, but otherwise you could do something like this:

var sOrigin = window.location.origin ? window.location.origin : window.location.protocol + "//" + window.location.host;
sNewUrl = sOrigin + window.location.pathname;

Edit: even better, as you noted in your followup comment, just update window.location.search directly and you won't have to deal with window.location.origin!

I'd say you should split the problem into separate pieces.

1. You want to add/change a parameter
2. So you need to get the current parameters
3. So you need to parse the current query string (aka location.search)
4. And then you need to pack the params back into a query string

Right now, you're doing all that in one function, but I'd split that up into several.

First the parsing: Now, this can is actually be quite tricky, depending on how deep you want to go. Firstly, there's the URL encoding scheme (a literal & becomes %26, etc.).

Then there's the fact that any key can occur any number of times in a query string (e.g. foo=1&foo=2), and how to handle that. Usually, you want to match the behavior of the server on this point. Often, the last value for the key "wins", while adding brackets to the key (e.g. foo[]=1&foo[]=2) is means it's interpreted as a foo = [1, 2] array. This is however an informal syntax, and different servers act differently. Point is, there's ambiguity at play.

Right now, I'll go with the naïve solution: Don't unescape params, don't parse arrays.

function getQueryParameters() {
  var queryString = location.search.slice(1),
      params = {};

  queryString.replace(/([^=]*)=([^&]*)&*/g, function (_, key, value) {
    params[key] = value;
  });

  return params;
}

I'm using replace here instead of splitting the string. Basically matching keys and values in the string, one pair at a time.

Next up, setting query parameters. Again, a naïve solution that assumes that values have been encoded properly already, and doesn't bother with arrays.

function setQueryParameters(params) {
  var query = [],
      key, value;

  for(key in params) {
    if(!params.hasOwnProperty(key)) continue;
    value = params[key];
    query.push(key + "=" + value);
  }

  location.search = query.join("&");
}

And so finally, to change a param, you can do something like

var params = getQueryParameters();

if(params.foo != "new value") {
  params.foo = "new value";
  setQueryParameters(params);
}

Again, this is all pretty simplistic, but it's mostly about the structure of it all.