Hash for use in embedded HMAC application
As cheaper alternatives to HMAC with modest security goals, consider:


SipHash—cheaper than MD5 because you don't have to pay for collision resistance; security is limited by the 64-bit output size
Maybe a Gimli-based PRF—Gimli is a new compact design
Derive a fresh key for each message, and use a one-time authenticator like a polynomial evaluation universal hash family such as Poly1305 or GHASH—extremely cheap to evaluate
Conceal a universal hash family output with a short-input, short-output PRF—faster than evaluating a generic long-input PRF


Of course, whether these actually provide security for your application depends on a lot more than the formal unforgeability properties of the cryptography.  No cryptography can prevent physical interference with the GNSS signals, for example!  With all of these systems, anyone who can verify log messages can also forge them—to separate the ability to verify from the ability to forge, you need public-key signatures, which are tremendously costlier.

To be clear: I don't suggest that you go out and invent new compositions of primitives right now along the lines I sketched above.  Rather, I suggest you spend effort now articulating your security model, so that you can focus your effort on implementing a design that confidently provides the security you're hoping for, rather than spend weeks micro-optimizing Poly1305 and SipHash for your AVR microcontroller, only to find that you actually need signatures, not authenticators.