You should certainly fight this. Without any video footage or clock speed evidence, it will be hard for them to find you guilty.
I was on my way to the movies a few years ago with a friend we both drove our cars. At a specific light we accelerated from zero to the legal limit at a faster than usual rate, and with aftermarket exhaust / intake, it makes a lot more sound.
A min later we see cop lights far behind. We continue cruising at highway speed as it approaches but my friend freaks out and starts to go fast in hopes that the cop won't catch up. The cop passes me slowly making hand gestures (he did not go in my lane or behind me to pull me over). Keep going past me I figured he went after my friend. I keep going and then I pass my friend pulled over by that cop. I kept going to the movie I had purchased tickets for.
I see the movie and go home. Turns out the police showed up at my house to arrest me for evading police, racing, careless driving, reckless driving, unsafe lane changing.
Few days later I received 3 summons in the mail. Reckless, careless and the unsafe lane changing.
So after my attorney spoke to prosecutor and 2 court dates adjourned, I pleaded guilty to Unsafe driving violation. Zero points and had to pay the fine.