Both setInterval and requestAnimationFrame don't work when tab is inactive or work but not at the right periods. A solution is to use another source for time events. For example web sockets or web workers are two event sources that work fine while tab is inactive. So no need to move all of your code to a web worker, just use worker as a time event source:
// worker.js
setInterval(function() {
postMessage('');
}, 1000 / 50);
.
var worker = new Worker('worker.js');
var t1 = 0;
worker.onmessage = function() {
var t2 = new Date().getTime();
console.log('fps =', 1000 / (t2 - t1) | 0);
t1 = t2;
}
jsfiddle link of this sample.