I think it would be trivial to replace evade their patents. They've phrased all of their claims around using averages (over time windows) of different sensor values.

I can describe the following inventions which would not infringe upon "Traumatic nightmare detection and intervention" (Patent 10765831).

. A method of detecting and intervening in traumatic nightmares, the method comprising:

    monitoring a user by collecting data from at least one of an accelerometer, a gyroscope, or a heartrate sensor of at least one device worn by the user;

    determining the sum of the data values for each of the at least one of the accelerometer, gyroscope, or heartrate sensor over a first period of time and detecting traumatic nightmares or precursors thereof based on a combination of the summed values; and

    causing an intervention based upon detection of a traumatic nightmare or precursor thereof;

    wherein detecting traumatic nightmares or precursors thereof based on a combination of the summed values comprises summing combinations of the summed values over a second period of time greater than the first period of time; and

    wherein summed values for each of the at least one of the accelerometer, gyroscope, or heartrate sensor are determined over a plurality of first periods of time, and the summed values corresponding to the plurality of first periods of time are summed over the second period of time.

A sum cannot be considered an average because it is not representative of the numbers in a list - it is in fact far greater than any number in the list.

Yet, for time windows containing a constant number of values, this should work just as well as the Nightware algorithm. There are plenty of other work-arounds for those patents.

Easy to avoid the letter of the patent, but not easy to avoid getting sued anyway and having to defend yourself.

They'd also have to be able to serve you with the lawsuit, which is far from easy if you post the code anonymously online.

I don't a judge will care much about your argument that a sum is different from an average for patent infringement considerations.

A judge absolutely would care about that. The actual claim language, not the patent description, defines what is patentable. Accidentally including specificity in the claim beyond what is needed to overcome rejections will absolutely kill the enforcability of the patent.

Luckily it's a software patent so someone outside the USA can just copy it and exclude the jurisdictions where software patents are still a thing.

Well it's really a patent for a method which includes both software and hardware (the sensors). It still might be an Art 84 rejection but I don't know enough about the EPO to say. They haven't filed any international patents, though, so it would not at all be enforceable in Europe even if it was patentable subject matter.

The sensors themselves are nothing special, the first patent was filed for a standard Android smartwatch. There is no new hardware, it's just an algorithm for a software system that happens to talk to hardware.

In the USA it's an improvement patent (see 35 U.S.C. 101). Because the algorithm is novel and involves steps that rely on hardware, you can patent the combination of hardware and process. Not sure if Europe views it the same way.

Presumably though if you built a version in Europe they wouldn't have jurisdiction or grounds to sue?