Google keeps increasing the personalization of SERPs so it's hard to be very accurate on keyword rankings. You also want to take into account PPC & other universal serp add-ons that can push a #1 SEO ranking below the fold. Check out the older threads about SEO tools. I personally focus more in tracking traffic levels. I don't care if I rank #1, I care if the page is generating traffic that converts into profit for me.
We usually don't allow specific tools to be mentioned because it can turn into a spam/self promotion mess. We'll make an exception if anyone wants to share a specific tool - just make sure to mention the good & bad of the tool. Anything that looks too close to spam or self-promotion will be deleted.
Define 'accurate'. In the near past the problem was prominent rank checkers not allowing you to define a specific geolocation regarding searches, which is the major customisation factor.
As for the rest, it's hard to define a "#1", so anything that differentiates between organic, knowledge panels, shopping, news or any other listings should be good enough. Doing that, you're able to tell the difference between potential CTR rates and SEO efforts.
I've noticed dataforseo seem to provide rank checking results for a number of well-known rank checkers. They are worth a look. I may be wrong but it may require some programming experience to get results en-masse.
As others have said, getting exact keyword tracking data is difficult with increasingly more personalized search, so take this with a grain of salt. I personally use Semrush for a broad overview of keywords that generate meaningful traffic. This can tip me off to potential issues early on. I also use SEO PowerSuite Rank Tracker to get exact data on ALL of our keywords (~1 million). Rank Tracker lets you run SERP tracking through their servers, so you don't piss off Google, but it can still take a fair amount of time if you have an enterprise level site.