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NutCracker

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Switchblade is a loitering munition, not a drone.
Thats just semantics.
You brought up 50km number. And called it "drone yourself and now telling me whats drone and whats LM.

No, since drones cover about 50km 1-way distance, even an error of 1% will be 0.5km which is huge for the tiny drone camera to pan and search. Since drones are slow moving, there is huge time window of half an hour for the nature's forces like turbulence, windspeed variations etc to act on them and drift it away. That is why loitering munitions attached to rockets are way better since rockets move fast, there is minimal time window for nature's forces to act and they can be more accurate.
You are just total Reatard who is debating for the sake of it.
 

Samej Jangir

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Thats just semantics.
You brought up 50km number. And called it "drone yourself and now telling me whats drone and whats LM.



You are just total Reatard who is debating for the sake of it.
My bad here regarding switchblade. It is a drone & loitering munition both. However, it does not change anything about other aspects. Its maximum speed is 100 & it takes at least 30mins to reach 50km which is long enough for nature's forces to act.

Let me give an example of MEMS INS of Honeywell:
1716280772210.png

Out of the 3 models, the first one is most accurate. So, I will take that:
It is a 6 directional IMU/INS with 3 direction of gyro & 3 direction of accelerometer.
Let us see the gyro deviation first:
Firstly, bias is the initial variation caused by various factors & can't be predicted : The gyro bias is 0.25 degree per hour standard deviation. Taking the standard deviation itself as the actual error, it would be 0.25degree of 0.0044 radian/hour.
Taking speed as 100kmph, distance 50km, time 0.5hr the deviation will be 0.0044*50*0.5 = 0.11km

Now, the random walk (Gyro ARW): 0.04degree/sqrt(hour). Since time is 0.5hr, sqroot is 0.71. So, the net ARW is 0.04*0.71 = 0.0284 degree or 0.0005 radian. Multiplying with 50km= 0.025km.

Net deviation in a direction is 0.135km

This happens in 3 directions. so we have to use formula sqrt(a^2 + b^2 + c^2) which gives minimum deviation of 0.235km

Next to accelerometer/velocity deviation:
The accelerometer bias deviation is hard to predict as it will depend on the maneuvering being done. As for velocity deviation, it is 0.03*0.71= 0.0213m/s
given the speed is 100kmph or roughly 28m/s, this will be ~0.6m/s. Over 30 minutes (1800s), the deviation would be nearly 1km.

The deviation from accel & gyro have to be added as sqrt( a^2 + b^2), we get 1.1km.

The operating conditions will be harsher than specified which can make its performance deviate even more.

Even assuming that the gyro & accelerator deviations are consolidated and recitified, we can expect at least 1% or 0.5km error at the least.

Since complex calculations & assumptions are involved, it is possible that I have erred. If there is any errors you can find from my side, let me know
 

SwordOfDarkness

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dont ins have drift error ? how much do they cost anyway .
It has, but not enough to be relevant in this case.
Cost varies, based on your requirements for error. Roughly from <100 Rs to 3-5 k.

No, since drones cover about 50km 1-way distance, even an error of 1% will be 0.5km which is huge for the tiny drone camera to pan and search. Since drones are slow moving, there is huge time window of half an hour for the nature's forces like turbulence, windspeed variations etc to act on them and drift it away. That is why loitering munitions attached to rockets are way better since rockets move fast, there is minimal time window for nature's forces to act and they can be more accurate.
Firstly, 500m uncertainty over 50 km is perfectly fine for any drone operation.

Secondly, "the nature's forces like turbulence, windspeed variations etc" are all also included in imu readings and this offer no extra error than normal. Apart from some sort of serious vibration issue, these type of forces are not an issue for localisation with imu alone.

Plus, it's not some unknown factor. The drone itself can know the expected uncertainty in its position and search accordingly if you are super concerned about searching a particular area. (If you have some idea about python programming you can try to look up codes for libraries like robotics-toolbox and mess around with simulations.)
 

SwordOfDarkness

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My bad here regarding switchblade. It is a drone & loitering munition both. However, it does not change anything about other aspects. Its maximum speed is 100 & it takes at least 30mins to reach 50km which is long enough for nature's forces to act.

Let me give an example of MEMS INS of Honeywell:
View attachment 254107
Out of the 3 models, the first one is most accurate. So, I will take that:
It is a 6 directional IMU/INS with 3 direction of gyro & 3 direction of accelerometer.
Let us see the gyro deviation first:
Firstly, bias is the initial variation caused by various factors & can't be predicted : The gyro bias is 0.25 degree per hour standard deviation. Taking the standard deviation itself as the actual error, it would be 0.25degree of 0.0044 radian/hour.
Taking speed as 100kmph, distance 50km, time 0.5hr the deviation will be 0.0044*50*0.5 = 0.11km

Now, the random walk (Gyro ARW): 0.04degree/sqrt(hour). Since time is 0.5hr, sqroot is 0.71. So, the net ARW is 0.04*0.71 = 0.0284 degree or 0.0005 radian. Multiplying with 50km= 0.025km.

Net deviation in a direction is 0.135km

This happens in 3 directions. so we have to use formula sqrt(a^2 + b^2 + c^2) which gives minimum deviation of 0.235km

Next to accelerometer/velocity deviation:
The accelerometer bias deviation is hard to predict as it will depend on the maneuvering being done. As for velocity deviation, it is 0.03*0.71= 0.0213m/s
given the speed is 100kmph or roughly 28m/s, this will be ~0.6m/s. Over 30 minutes (1800s), the deviation would be nearly 1km.

The deviation from accel & gyro have to be added as sqrt( a^2 + b^2), we get 1.1km.

The operating conditions will be harsher than specified which can make its performance deviate even more.

Even assuming that the gyro & accelerator deviations are consolidated and recitified, we can expect at least 1% or 0.5km error at the least.

Since complex calculations & assumptions are involved, it is possible that I have erred. If there is any errors you can find from my side, let me know
From a rough glance your calculations seem all over the place, and I'll work it out myself and post here once I get back.

But just to point out, that the calculations are still pointless, as the main error accumulation is with velocity(like over 90%), and there are ways to fix it. Even in gyro error that you are quoting, the error in horizontal plane will be virtually zero with magnetometer reading.

Long story short, many ways exist to have robust INS, it's just a lot more convenient and cheaper to have gps as a consumer manufacturer.
 

Samej Jangir

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How did you end up with 0.6m/s from 28m/s , you divided by approx 50 ?

0.0213m/s is not a ratio.
I did consider it as a ratio. Yes, I did err on the units as ratio has no units. But if it was not ratio, it would mean if one travels at 10kmph or 100kmph, it would be same error which is not reasonable. Random walk or drift is always a ratio
 

Samej Jangir

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From a rough glance your calculations seem all over the place, and I'll work it out myself and post here once I get back.

But just to point out, that the calculations are still pointless, as the main error accumulation is with velocity(like over 90%), and there are ways to fix it. Even in gyro error that you are quoting, the error in horizontal plane will be virtually zero with magnetometer reading.

Long story short, many ways exist to have robust INS, it's just a lot more convenient and cheaper to have gps as a consumer manufacturer.
I am not entirely sure of how accurate magnetometers are, whether they can face interference by electric cables etc. But if you take an example helicopter's crashing due to CFIT, we get to see that the pilot is unable to tell the exact location or altitude with accuracy. I am not sure if it is because helicopters don't have even basic units like the cheap MEMS INS which even mobile phones have or if it is due to their unreliability.
 

SwordOfDarkness

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I am not entirely sure of how accurate magnetometers are, whether they can face interference by electric cables etc. But if you take an example helicopter's crashing due to CFIT, we get to see that the pilot is unable to tell the exact location or altitude with accuracy. I am not sure if it is because helicopters don't have even basic units like the cheap MEMS INS which even mobile phones have or if it is due to their unreliability.
IFR CFIT? Can you quote an example please?

All the CFITs I've heard were VFR, in cases where VFR was not sufficient/pilot error. Even in CDS crash case.

Btw some of the discussion was quoted in chit chat thread, we can talk there ig.
 

Samej Jangir

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IFR CFIT? Can you quote an example please?

All the CFITs I've heard were VFR, in cases where VFR was not sufficient/pilot error. Even in CDS crash case.

Btw some of the discussion was quoted in chit chat thread, we can talk there ig.
True, it was VFR cases only. However, I am only wondering if even the VFR helicopters have basic instrumentations like altimeters, GPS etc? I am not sure here but it appears dumb to not have such basic tools which one can even get on Amazon for cheap.
 

SwordOfDarkness

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True, it was VFR cases only. However, I am only wondering if even the VFR helicopters have basic instrumentations like altimeters, GPS etc? I am not sure here but it appears dumb to not have such basic tools which one can even get on Amazon for cheap.
They are supposed to have, plus most importantly for avoiding this is radar for terrain warning. Usually crashes involve either multi system failure or pilots assuming the warnings are wrong.
 

SwordOfDarkness

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From a rough glance your calculations seem all over the place, and I'll work it out myself and post here once I get back.

But just to point out, that the calculations are still pointless, as the main error accumulation is with velocity(like over 90%), and there are ways to fix it. Even in gyro error that you are quoting, the error in horizontal plane will be virtually zero with magnetometer reading.

Long story short, many ways exist to have robust INS, it's just a lot more convenient and cheaper to have gps as a consumer manufacturer.
Copy pasting from chit chat thread

My calculations, tell me if there's some error
Gyro ARW - 0.04 deg/root(hr) = 0.00066deg/root(sec)= 0.000011 rad/root(sec)

Vel ARW - 0.03 m/s/root(hr) = 0.0005m/sec/root(sec)

Taking one Sigma for 70 percent chance.

dV= VRW*dT
dTheta=GRW*dT

dX=dV*dT+V*dTheta*dT
=VRW*root(T)*dT+GRW*V*root(T)*dT

Integrating, we get Xtotal=2/3*(VRW+GRW*V)*root(T)

So 0.66*(0.0005+0.000011*28)*root(1800^3)

Which is 40 m
For XY plane, we get 40*root(2)=less than 60m

I'm ignoring z here, not very relevant.
I've also not included error due to bias, as it can be corrected during initialisation, assuming low temp changes mid flight.

Remember, this is without any midway localisation or corrections from other sensors.

Even for 99% confidence interval this is just 150m. Though tbh, this is a pretty unnecessary level of accuracy, much better to buy a significantly cheaper sensor setup with 2x,3x error limit.

If you notice any errors in calculations/assumptions do let me know, will correct.
 
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Samej Jangir

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Copy pasting from chit chat thread

My calculations, tell me if there's some error
Gyro ARW - 0.04 deg/root(hr) = 0.00066deg/root(sec)= 0.000011 rad/root(sec)

Vel ARW - 0.03 m/s/root(hr) = 0.0005m/sec/root(sec)

Taking one Sigma for 70 percent chance.

dV= VRW*dT
dTheta=GRW*dT

dX=dV*dT+V*dTheta*dT
=VRW*root(T)*dT+GRW*V*root(T)*dT

Integrating, we get Xtotal=2/3*(VRW+GRW*V)*root(T)

So 0.66*(0.0005+0.000011*28)*root(1800^3)

Which is 40 m
For XY plane, we get 40*root(2)=less than 60m

I'm ignoring z here, not very relevant.
I've also not included error due to bias, as it can be corrected during initialisation, assuming low temp changes mid flight.

Remember, this is without any midway localisation or corrections from other sensors.

Even for 99% confidence interval this is just 150m. Though tbh, this is a pretty unnecessary level of accuracy, much better to buy a significantly cheaper sensor setup with 2x,3x error limit.

If you notice any errors in calculations/assumptions do let me know, will correct.
Error from bias is critical. It is about changes in temperatures, vibrations, tilt etc. It has a hour denominator because it is not fixed and not merely initial condition. Also, error in Z or any of other XY axes can't be ignored.

Just a math tip: Instead of complex differentials, you can use S = R(theta) when theta is very small (<0.01 radian) and the error in such cases is pretty low & can be ignored. It will make calculations simpler
 

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