Is there a cryptographic method to add noise to a plaintext instead of actually encrypting it? I'm looking for a cryptographic technique that instead of permuting a cleartext, would add noise to the cleartext to obfuscate the true text among a bunch of garbage.  For example,  a list of 10 numbers would be combined with a list of 90 random ones with the goal of making the true set of numbers difficult to recover.

I need an attacker to believe that the message is not encrypted. I'm trying to obfuscate a set of GPS coordinates that need to be submitted to a third party but the original route needs to be recoverable with only a key.

Is there a principled way to do this?  One idea is to use a secure PRNG to generate the 'noise' and, assuming there is no collisions, regenerate the noise on the receiver side and filter to decrypt.  Any pointers to other techniques would be appreciated.
You first need to consider your adversary and what are your goals for this mechanism.

This kind of mechanism appears less effective than proper cryptographic means:


having secure PRNG means that both ends of the message exchange have access to some proper cryptographic means
Adding noise means that the information exchange is less efficient: there is much more information to exchange
Even when garbage is added, some cryptanalysis techniques could be effective in retrieving the true text from the garbage.


The principled way (in my humble opinion) would be to use proper cryptographic primitives. Otherwise, you risk getting your system efficiently attacked by attacker who know the system (Kerckhoffs' principle).

Steganography

Steganography is about encoding and hiding message so that only sender and recipient should detect existence of the message. Steganographic techniques often involve adding various materials to make it easier to detect the message. I recommend studying steganographic techniques (in case you do not follow advice on just using cryptography) because there you may find partial aid for your problem.

Format preserving encryption

If the target is to make it look like it has not been encrypted, one possibility is to use format preserving encryption for encryption instead of adding garbage.