Can we Predict the Trajectory of a hypersonic missile?

I'll deal here with "classic" hypersonic missiles which travel through the upper reaches of the atmosphere and stay aloft by generating lift and operate under continuous thrust.

Such missiles are maneuverable, unlike ballistic missiles whose post-boost phase coasting trajectories can be mapped in real time and for which precise intercept courses can therefore be plotted. This means that when a defensive missile launch against a hypersonic missile is detected, it can quickly change course in response and avoid the incoming missile. It is in this sense that the hypersonic missile's trajectory is "unpredictable".

Also note this does not mean it is "undetectable"; it just means it is much harder to shoot down than a ballistic missile.

Of course the missile's trajectory is predictable if you know everything about its thrust, position, and momentum at all times since its launch. The problem is that someone who launches a hypersonic missile generally does not inform the opposing missile defense systems, "Hey, I launched a missile at this time and place, and here is its full thrust profile and flight plan!" Generally, that is information that someone launching a missile does not want their target to know.

So these parameters must be measured by the missile defense system. The problem with hypersonic missiles is that these measurements are hard to make, for three main reasons:

1. Unlike an ICBM, which travels a roughly parabolic trajectory, a hypersonic missile can change course mid-flight. This means that information that was valid a few seconds ago may no longer be valid now.

2. Unlike an ICBM, which goes briefly into space, a hypersonic missile spends its time flying at low altitude, below the radar horizon, so accurate measurements aren't possible until it's much closer.

3. Unlike an ICBM, which generally spends some time in a near vacuum where it's the only radar-reflecting object around, a hypersonic missile heats the surrounding atmosphere into plasma. Plasma absorbs radio rather than reflecting it, which makes it much harder to bounce a radar pulse off of it.