Sports watches can reportedly give an estimate of one's VO2max. Tracking changes in this number is useful for training (even if the absolute numbers turn out to be unreliable).
Can I track (improvements in) VO2max using just the data from a heart rate monitor, a cadence sensor, a speed sensor, and GPS data (distance, altitude), plus additional software on mobile or desktop? What does a sports watch have access to that could not be done with these data?
Can I track (improvements in) VO2max using just the data from a heart rate monitor, a cadence sensor, a speed sensor, and GPS data (distance, altitude), plus additional software on mobile or desktop?
No. You need a consistent source of power meter data (along with an HRM).
With consistent power meter data, something like Garmin connect will be able to estimate your VO2. In the case of Garmin Connect, it will alert you when the estimate changes.
if you only wants to see if there's any improvements in your VO2 max, then it is possible as the absolute number is not your main point, it is your relative (comparison) to the previous VO2 max on the same device. as to how, I also didn't have power meter back then, the similar setup as you (cyclocomp with GPS, cadence, HR). I'd go to a climb (preferably under 10 minutes, pretty steep so you won't deal with much aero drag and can go all out). try to go all out for 4 minutes (ofc. after warming up first get the HR to zone 3-4; [use HR zone calculator if you don't have your HR zones 1). then hit the climb all out for 4 minutes, pace your effort so your HR is at zone 5 at the later half of the climb and sustain it until the 4 minutes is up. the do the same effort after some training, and see the improvements of speed and distance from your 1st and 2nd effort. or, you can do the same climb with the same avg speed, then compare the HR differences between 1st and 2nd effort (it should decrease).
First, I'll provide one answer to the question. After the line break, I will raise the question of what your goal is - you may not need to be interested in your VO2max specifically.
If you at least have power data, it is possible to estimate VO2max from a 4 to 6 minute maximum fresh effort. If you are on Zwift, they already do this with your existing power data. Based on a 5-minute max effort where I averaged 295W, Zwift estimates that my VO2max is 57.3 mL O2/kg/min. Basically, an effort around this duration should put you at or near your VO2max.
If you Google, you may find some formulas. Andrew Coggan, a respected sports scientist, posted here that:
VO2max in L/min = 0.0108 x power (W) + 0.007 x body mass (kg)
I believe that power is the average power during a 5-min max effort for this formula. Different durations may have different formulas. Also note that the formula provides liters per minute, not mL, and it's not normalized to body weight. When I input my 5-min power, multiply my result by 1,000 to convert L to mL, and then divide by my current body weight, my 5-min effort corresponds to an estimate of 56.47 mL O2/kg/min, close to the Zwift estimate.
There are some assumptions that go into these estimates.
First, you have to assume your power meter is accurate. If you have a modern smart trainer or a good dual-sided power meter, you are probably good enough, but it is possible for a unit to come out of calibration. Of the major power meter brands, Shimano power meters are the only ones that have been tested to be systematically inaccurate, which is incredibly disappointing but is outside the question scope.
Second, I believe the formulae assume a fixed gross mechanical efficiency. That is, you're measuring watts generated at the crank or the trainer flywheel. Your body has to burn fuel to generate that power. It is not 100% efficient. In fact, one study I cited in this answer found that trained male cyclists average 21.9% gross efficiency with a standard deviation of 1.7 percentage points - that is, 95% of the population this sample represents should have GEs from 18.4% to 25.4%. Thus, Zwift is really reporting the midpoint of a range of possible VO2max values. Zwift's estimate has the caveat "Assumes a fixed cycling efficiency", and I believe this is what they mean. I suspect the GE assumption is baked into the constants in the formula, so I don't know how to re-estimate a plausible range for myself. Consumers can't easily measure GE. You could measure it in a VO2max test if you also measure power to the bike, but then you already have VO2max directly measured.
Third, I don't have a background in exercise physiology, but I believe this bit is accurate. We know that anaerobic metabolism contributes to 4-6 min efforts, especially at the start of the effort. If you are an anaerobic-dominant athlete, the formula-based VO2max estimate may be high. You can often get a general sense of your anaerobic capabilities based on how you do in sprints or very short max efforts (<2 min) in group rides or races. I know that I have good anaerobic power. So, my purported VO2max estimate is also biased upward, and I don't know by how much.
Also, readers should consider why they need to measure/approximate their VO2max. Are you looking to maximize longevity? Per the discussion in this answer, for most adults who want to maximize longevity and who don't need to get high athletic performance, it is likely sufficient to do long slow distance workouts. You can add whatever intervals you want, but it might not be necessary to improve longevity.
If you are a cyclist and you want to improve your performance in short-duration efforts, then you can track your 5-min power as discussed in that answer. It can be seen an imperfect but reasonable proxy for VO2max, as discussed above. Or you can just take it at face value.
Unlike running, bicycles are inherently very efficient, therefore with cycling the power lost to speed related items (height gain and drag) varies much more than running. Faster speeds mean wind (power required to maintain a speed is roughly a square of air speed) and hills (gentle inclines) affects results far more than running. Garmin can guestimate VO2Max running provided the runner is on a moderately flat course and its lowish wind. On a cycle, a slight incline or slight wind can easily make a big difference to required power to maintain a speed. Therefore, cycling Vo2Max can only be guesstimated if actual power is measured. Running varies much less and therefore it is possible to guestimate Vo2Max with useable consistency.
A good example that is easy to understand is imagine if you were guestimating Vo2Max with two clones riding a bike. One was in the lead, the other drafting the entire ride. Same speed, same distance, same height change yet very different Vo2Max. If you did this with runners, you would get a different Vo2Max, but it would be much closer.
It's worth pointing out that an otherwise popular product will not help. The Apple Watch will estimate your VO2max for only outdoor walking, outdoor running, and hiking, but not for cycling—not even if you have a power meter.
At least some Garmin Edge devices have for some time estimated VO2max — using software by Firstbeat.
Quoting a comment by Weiwen Ng, lest you miss it:
There is a portable VO2 analyzer, which directly measures O2 consumption but doesn't require a lab. I don't know of any reviews of its accuracy. It's also a bit expensive.