My wife drives a 2014 Volvo XC60 with forward collision warning and in a year and a half and 16,000 miles, she's never had a false alarm. Good thing, too, as it also has an autobrake - meaning that it will automatically apply the brakes after warning you if you take no action and it thinks a collision is imminent. Reports of false alarms on the Volvo forums are rare. So it is possible to get this right.
Same here. I currently drive a 2013 S60 with city safety (full brake on collision detection ir camera based) and the adaptative cruise package with collision warning(radar in grill based).
While the city safety did engage 4 times in 2 years, it only did so twice for false positive :
1- was getting in my garage while the door was opening. Car went into panic mode and full brake applied because the door was over the hood, close to the sensor.
2- parked into a spot near a tree with low hanging branches(that would sit very close to the windshield when parked)
In all instances, the system only intervened because there were zero input from myself (steady accelerator or brake, no steering wheel movement)
Btw, this system only engage under 25mph.
The adaptative cruise is another beast : it frequently get messed up when turning on the highway while passing slower traffic. Parked cars also trigger the warning all the time...
You learn the workarounds : in a curve hit the gaz pedal a bit.
Bottom line : these 2 systems work differently and the accuracy is not the same. Tesla could separate both systems like Volvo did : use the always clean camera (behind the windshields wipers) for critical applications (i.e. full auto brake in emergency) and keep the radar and ultrasonic sensors for convenience features like TACC and collision WARNING.
I should get my 85D within 15days : I'll be able to compare it to Volvo's system.