It's not super far fetched to come to approximation, conservation of energy and all that, the main variability people in energy expenditure comes from activity.

Get population averages of base metabolic rate based on sex/weight/age etc. Get base heart rate. When heart rate increases due to activity,estimate what activity and intensity and use weight to estimate activity expenditure on top of base. A lot of assumptions of course which make these tend to be inaccurate but if the assumptions are right then methodology is not that unsound.