Fusion of accelerometer with pressure sensor to get the vertical velocity

jremington:
Please read the material in the link, and make sure that you understand it before firing off such questions.

Maybe I did not understand your point before. I was only puzzled why you sent exactly that link.

Even small errors in the orientation estimate will produce extremely high errors in the measured acceleration, which translate into even larger errors in the velocity and position estimates. Without nicer rate gyros (FOG or Ring-Laser, for example) or without the addition of an external reference like GPS, accurate dead-reckoning is usually not possible.

This is the reason for my question.

jremington:
It would be a good idea for you to estimate, in actual practice, the errors in the individual operations before planning a grand fusion scheme.

I will do that. Thanks.
I am not yet planning a fusion. I want to understand the steps I should take before working on it. Maybe that's the wrong strategy.
As I said, I will borrow the book you recommended tomorrow and have a read through that.

CrossRoads:
We pilots already have Vertical Speed Indicators in the plane fed from a Static port on the side of the plane (or 2, one one each side).
More modern setups also feed the tube into a digital display and it appears as a rolling tape display on a screen.
You can see the current altitude on the right, with an indicator to its right of the rate of change in feet per second in this Garmin G5 example.

Yes, that's correct, but A/C without an ADAHRS, e.g. old Cessna's, won't be able to output this and you will have a mechanical type.
Also if the A/C has an ADAHRS, the FAA or EASA would not necessarily allow a retrofit device to tap the data. And also if the FAA or EASA allows it, Garmin or Dynon will not (I have already asked them). So since I am only considering smaller GA A/C, EASA ELA1 and ELA2 type, new types of certification specifications are available in the US and in Europe that gives a simplified and cheaper certification for a device that does not interfere with the safety of the flight. This is known as NORSEE in the US and CS-STAN in Europe.
Examples of NORSEE certified devices are the Levil BOM and I also think that the AoA Vane from alphasystems has a NORSEE certification.

Many "old Cessnas" (like mine, built 1973), that fly IFR (and even those that don't), are changing to electronic displays as vacuum pumps fail and some maintenance action is needed. Certificated airplanes need instruments that are certified. Experimental, and light sport and perhaps the types you mention can get by with other equipment; often times this looks like the same equipment but is Not certified for Certificated aircraft and is lower cost.
I haven't really followed the market since I updated my panel, I'm sure plenty of examples like this can be found:

G5s.JPG

Another good example, and maybe what you are attempting, is WingBug from Wingbug.com


I've been thinking of getting one to give my copilot a set of instruments to look at.

G5s.JPG

I am familiar with the wingbug. Its basically a cheaper Levil BOM, however, levil BOM generates its own power. I am not trying to replicate these two since they cannot get a certification in Europe. I have spoken with the person who is responsible in EASA and she told me that devices, like outerpods, have an influence on the safe operation of the A/C. Here the US has a different opinion. However, AoA vanes are certified for these A/C types.

As I mentioned, the issue with these electronic instruments is that tapping into the data is not allowed. Therefore, a realtime estimation of the turbulence intensity is impossible. Another issue is that if the A/C do not have an AoA vane, then the estimation has to be done using the A/C response function. This is different for every A/C and it is a very poor estimation.

I put the definition of ELA1 and 2 in the picture below. Your A/C might fit into this category.

Experimental A/C are not too popular in Europe since the running costs here are usually higher and renting it out is not allowed. Also I believe there are more restrictions on Exerimentals here than in the US. However, I am interested in a Kitfox. That's something I would like to own after my studies. For now, I'm sticking to renting the Piper archer.

So, I read more on the Kalman filter, and after estimating the errors, I tried converting the Sensor body frame to the NED frame using the rotation matrix. The issue here was that from the data I collected using my iPhone, I couldn't tell if it worked. So I decided to implement it into the Kalman filter on MATLAB and it wasn't great. So, I realized, the best way to test the conversion to NED frame was on the Arduino. That's where I realized that I would have to invert some of the axis to make sure it works. So now I have that.

My question, for the GPS, is that I have to convert the latitude and longitude to meters.

  1. Would it be sufficient to assume that all latitudes, from the equator to the poles, have the exact same distance per degree, or does it have to be more precise?
  2. Is it sufficient to convert the Longitudes with respect to the circumference of the small circle that lies on that latitude, namely:

long(in km) = deltaLong6371cos(lat)*pi/180

I need the vertical velocity so that I can calculate an estimate of the vertical wind in a turbulent atmosphere

This is exactly what is calculated in sailplane total energy variometers. Subtract the aircraft performance (requires airspeed, power and glide ratio) from the derivative of the altitude and you have what the air mass is doing. It’s been done mechanical and then electrically for close to fifty years. Plenty of prior art to research.

I don't think that would work for powered airplanes. I cannot and will not tap into the RPM of the aircraft.

The idea that I'm trying to implement is in page 7:
https://www.researchgate.net/publication/337640129_Estimating_Eddy_Dissipation_Rate_with_QAR_Flight_Big_Data