For True Innovation ...
Ditch the budget. First of all, as per this Financial Times article, there is no correlation between R&D spend and innovation success. Secondly, as per this Harvard Business Review blog post, fixing an innovation budget puts your people into a mindset that their innovation is limited to the budget they have. Third, and most important, while you can budget the cost of product development (based on what the market is expected to bear), you can't budget the cost of innovation. That relies as much on inspiration as it does perspiration.
Plus, and this is key, you can't "innovate" a new product until you know what is, and is not, doable. That's why it's ridiculous to tie the research and development budgets together. They should be separate. While the two units should come together regularly to collaborate on research directions (i.e. "this is what we'd like to build, what's possible") and product directions (i.e. "this is what we've [sort-of] figured out, what do you think you can use and sell, and we'll focus on improving that"), research should be free from distracting day-to-day product development, market, and associated budget constraints so they can focus on figuring out what can be done and, once development has identified certain capabilities as currently marketable, how (cost) efficiently it can be done.
Now, I'm not saying Research shouldn't have a budget, as it should, but that budget should be at the department level, and not the researcher / research project level, and it should be up to the director(s) to figure out how best to allocate it on an on-going basis. For instance, if a team requests a purchase of a new piece of hardware that would be generally applicable to multiple research projects, then even if it exceeds the typical hardware investment, the director(s) can choose to allow the purchase and then spend less elsewhere. But if a certain costly request would not be generally applicable, the director(s) can choose to deny the request and urge the investigator(s) to innovate a more cost effective way to obtain what is needed for an experiment or investigation. In other words, we need to return to the innovation lab model, where productive researchers and true innovators aren't spending all their time worrying about budgets ... because when you're worrying about budgets, you're not getting anything done. GE understood that, and that's why they did so well for so many years. Not only did they give their top people the budgets they needed to be effective, but they paid also paid their top people very well so they wouldn't have to worry about money in their personal life. While "what can we do for 20% less" is inspiring, nothing kills an innovation mindset faster than if the team is constantly stressed about money.