Bluetooth connectivity issues after upgrading to iOS 8.2

Two days ago I upgraded to iOS 8.2 on both my iPad Air 2 and iPhone 5S. Since then I've experienced bluetooth connectivity problems on both devices that I hadn't seen before upgrading. The issues are also happening with peripheral devices I used before upgrading with no problems.

With my iPad, I use a bluetooth Logitech Ultrathin Keyboard to take notes in class. Starting two days ago after upgrading, the keyboard suddenly disconnects with no prompting at least every 5 minutes, usually more frequently and often multiple times per minute. The signal quickly reconnects after hitting a key (which is how I typically re-connect the keyboard after not using it for a while), but it's annoying to have the iPad keyboard pop up over my notes and to miss 3-4 seconds of typing while the keyboard reconnects. It's as if the keyboard is repeatedly sent into the standby mode it's in when I turn off bluetooth on my iPad, where it knows it should pair with my iPad but the two aren't connected until I hit a key on the keyboard.

With my iPhone, I use an Amazon Basics bluetooth receiver to connect audio to my speakers. Since upgrading, the audio signal sporadically sputters and cuts in and out. The signal hasn't completely dropped yet like it does with the keyboard, but the skips are annoying to say the least. My music continues to play as though it doesn't realize the issue, so it seems to be a problem with the bluetooth signal and not the internet signal or Pandora skipping.

Since these problems only appeared after upgrading to 8.2, I'm inclined to think the upgrade is the culprit. Is anyone else having these connectivity issues? If so, has anyone found a solution or workaround?

Thanks!