Where are the abs sensors ?

Abs sensor is in front at the brake pads driver side

Sensors are not subject to malfunction due to dirt the pick up is based on magnets and wheel spin , the tone wheel is clogged eith rust that could cause slight problems , abs set by air gab between sensor and tone wheel ,if possible drive short distance ,then disconnect battery wait 30 sec. reconnect , if this doesn't work you may have a problem in master cylinder.

A seniors light may indicate several possible issues however I would look at the least cost fixes first which if it's not the problem you have serviced items which may throw up a future issue 1- It's possibly the contacts behind the discs. These can be pulled apart and sprayed with WD-40. If this fails then a general clean down of the wheel speed sensor will be next. Again behind the disc this is the second element if the first item to which is integral to the ads function.. These steps will normally fix this problem remember you need to clean both front sensors. A more serious indicator may be a reduction in the brake pressure system upon which correct functioning of the abs depends. I would bank on the problem resting to sensors or bad connections.

ABS sensors are part of your brake system. There is one in the brake pads on each wheel. If the ABS light is on, it usually means that your car has sensed a dangerous situation and has deployed the ABS system to help you stop safely. If only the ABS light is on, then one may be gunked up, or you need to have your brakes checked. If you've had any other work done around the wheels, apparently, they can be bumped quite easily. This repair is not very expensive, if you have a good local mechanic. or brake shop.
On the other hand, if the ABS AND brake lights are on, and you hear a constant beeping, there's is a good chance that your ABS control module has gone out. Unfortunately, this is an extremely common problem with Audis of this era. Many VWs use the same part, and they were recalled (but Audis weren't). There is a grey market where you can picked them up a somewhat cheaper, but the original ABS control module went for around $1700.
I hope it's a bad sensor!