I have a few friends/acquaintances that work (or are looking for work) in this field and all of them have graduate degrees with research specifically focused on vehicle controls, autonomy, and mapping. Most of the work on the autonomy systems will probably require something similar, since it is still a research heavy field.
There are software systems within autonomous (and non-autonomous) vehicles that won't require such a specific academic background, but they would probably require some level of experience with embedded systems or systems programming.
Within the research community, ROS (http://www.ros.org) seems to be the standard platform. So perhaps put ROS on something and play around with it? You have to start somewhere.
High end SoC vendors generally don't care about you until you're buying millions of devices. If you can't find it on Digikey/Mouser/etc you're probably not going to get your hands on these parts without an in with one of the big name suppliers or the SoC vendor itself. However, in the case where you are shopping for millions of devices - say you're looking for the centerpiece of a new smartphone, its not unusual for them to fly a team of applications engineers to you to facilitate getting the part into your system.
Of course, merely procuring the part itself is just the beginning. The early revisions of a SoC (and in many cases even small microcontrollers) can have fairly extensive errata sheets (basically a list of known hardware bugs). If you aren't a first class customer (usually based on order volumes), this is a world where you can spend weeks to months wondering why your code doesn't work only to find out that it legitimately was a hardware problem in the silicon.
Trying to source displays is also a nightmare for relatively low volume (<100K) designs.
Richard Lyons - Understanding Digital Signal Processing
Focuses more on explaining the concepts behind the math than presenting a wall of theorems. Given that math is the language of DSP though, there's still a reasonable amount of math.
It assumes the reader has an EE or similar background, but I think it's still fairly approachable regardless. Given that my own background is in EE/embedded systems though, I'm not sure what my opinion counts for there.
There are software systems within autonomous (and non-autonomous) vehicles that won't require such a specific academic background, but they would probably require some level of experience with embedded systems or systems programming.
If you're starting from scratch, many of them have recommended the following book as an approachable introduction to the field: http://www.amazon.com/Introduction-Autonomous-Mobile-Intelli....
Within the research community, ROS (http://www.ros.org) seems to be the standard platform. So perhaps put ROS on something and play around with it? You have to start somewhere.