Refining intrinsic params in PnP Ransac using divide and conquer?

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I'm working with a set of non-coplanar point correspondences making the cameracalibration method unsuitable for extracting intrinsic params.

Could I instead supply an estimated focal length to the pnp method and then use divide and conquer running pnp with different focal lengths to hone in on the correct focal length by comparing reprojection errors? (I know the aspect ratio and lens distortion is negligible, so I effectively only have a single unknown intrinsic param: X focal length, from which Y focal length can be derived)

I guess my question is: Am I guaranteed to have a single, local minimum reprojection error in the range of focal lengths, or could there be more than one "trough" in the focal length-projection error curve?

Thanks.