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From: Alfred Bovin on 9 Mar 2010 15:02
Thanks for your reply.

>> What I fail to see is the difference between this approaches (except for
>> their mathematical apperances). Do you have any opinions on what to use
>> when my vechicle never leaves the surface of the Earth?
>
> Navigating with respect to a fixed earth seemed to be easiest to me. No
> matter what you do you'll be left with coordinate transforms that will
> make your head hurt. You can't avoid that -- just go with what you think
> will make your head hurt least.

When you say "fixed earth" do you mean a non-rotating coordinate system
attached to the center of the earth oriented at some fixed stars?
I admit that I'm already a little dizzy trying to vizualize these coordinate
systems, but I fail to see how this will be a good method.
If I describe the motion in this non-rotating frame then I'll not only get
the motion of my vehicle but also the rotation of the earth with respect to
this frame, right?

An approach which makes more sense to me is to have three coordinate
systems:
1) an inertial frame as explained above
2) an Earth frame with the same origin as the inertial frame but rotating
with the Earth
3) the body frame

Then as far as I understand it, the motion of the vehicle represented in
this Earth frame will then (ideally) only consist of the motion taken by the
vehicle.

The next problem is now to transform this motion given in the Earth frame to
the frame I use for the navigation (that is: the frame attached to the
position where the vehicle starts at time t = 0 as described in my initial
post).
If we now assume that I will not synchronize with any GPS information, then
I argue that if I'm not interested in an absolute position but only the
relative motion so to speak, then the initial alignment between the Earth
frame and the navigation frame doesn't matter. I may then simply say that at
time t = 0 the axes of the Earth frame is aligned with the navigation frame
without calculating any explicit rotation matrix.

Is this complete rubbish?


> With that IMU I don't think you have to pay attention to the earth's
> rotation -- IIRC the gyros on that have errors far in excess of 15
> degrees/hour, so any signal you'd get from the earth's rotation will be
> swamped by the gyro errors.

According to the data sheet the IMU has a gyro RMS output noise (worst case
configuration) of 0.6 deg/sec = 36 deg/hour, so you're right when saying
that the noise probably swamps the Earth's rotation. But if I don't model
the Earth's rotation then this will give an additional noise term, and the
combined error gets larger, right?


From: Alfred Bovin on 9 Mar 2010 15:11
"Vladimir Vassilevsky" <nospam(a)nowhere.com> wrote in message
news:BuSdnXH74Y3VNAjWnZ2dnUVZ_uydnZ2d(a)giganews.com...
>> I'll take the chance and ask this question here in the forum since
>> perhaps there are someone familiar with INS here.
>>
>> I'm trying to do some inertial navigation for (what perhaps will become)
>> an autonomous all-terrain vehicle with a strapdown inertial sensor (an
>> ADIS16350 from Analog Devices) with a 3-axis gyro and a 3-axis accel. I
>> have no previous experience with this stuff so I've been reading a bit in
>> "Strapdown inertial navigation technology" by Titterton and Weston.
>
> That won't work. The accuracy of ADIS is typical for MEMS sensors, i.e. ~1
> cm/c^2 or so. This is inadequate for innertial navigation.

Thanks for your reply.

I should say that this ADIS device came along with the platform from the
factory, and I want to experiment a little with it.

I realize now that, as you say, the performance is probably not good enough
to make reliable inertial navigation, but then I may have misunderstood
something fundamental regarding the usage of inexpensive MEMS IMUs.

When you say that the device is inadequate for innertial navigation, do you
then mean that it cannot be used in a system where it's the only sensor?

As I said, I have no previous experience with inertial navigation, but what
is the typical usage of such inexpensive devices as the one I have? Is it to
have short term navigation at a higher frequency than more reliable sensor
data is available (such as GPS)?

I of course also have odometry data available (10 Hz) and I'm experimenting
with motion estimates from a stereo camera system (around 6-7 Hz). Do you
think the IMU can be of any help/usage in this system?


From: Tim Wescott on 9 Mar 2010 15:13
Alfred Bovin wrote:
> Thanks for your reply.
>
>>> What I fail to see is the difference between this approaches (except for
>>> their mathematical apperances). Do you have any opinions on what to use
>>> when my vechicle never leaves the surface of the Earth?
>> Navigating with respect to a fixed earth seemed to be easiest to me. No
>> matter what you do you'll be left with coordinate transforms that will
>> make your head hurt. You can't avoid that -- just go with what you think
>> will make your head hurt least.
>
> When you say "fixed earth" do you mean a non-rotating coordinate system
> attached to the center of the earth oriented at some fixed stars?

I didn't state it well -- I found an earth-fixed, earth centered
coordinate system to work well for me. If you look at the references
this has the z axis going up through the north pole, the x axis exiting
the equator at 0,0 lat/lon, and the y axis following from the right-hand
rule.

So the frame rotates with the earth.

> I admit that I'm already a little dizzy trying to vizualize these coordinate
> systems,

Ha ha! Ha ha ha ha ha! (Keep it up and you'll be a bit manic, too).

> but I fail to see how this will be a good method.

For some it would be -- but as I said, that's not what I meant.

> If I describe the motion in this non-rotating frame then I'll not only get
> the motion of my vehicle but also the rotation of the earth with respect to
> this frame, right?

Yes you would; then you'd have to translate.

> An approach which makes more sense to me is to have three coordinate
> systems:
> 1) an inertial frame as explained above
> 2) an Earth frame with the same origin as the inertial frame but rotating
> with the Earth
> 3) the body frame

I'd leave off (1), just taking the earth's rotation into account in (2).

> Then as far as I understand it, the motion of the vehicle represented in
> this Earth frame will then (ideally) only consist of the motion taken by the
> vehicle.

The vehicle and the earth's rotation.

> The next problem is now to transform this motion given in the Earth frame to
> the frame I use for the navigation (that is: the frame attached to the
> position where the vehicle starts at time t = 0 as described in my initial
> post).

I'm not sure what you mean -- you want to establish a frame of reference
around the vehicle's starting point? Why?

> If we now assume that I will not synchronize with any GPS information, then
> I argue that if I'm not interested in an absolute position but only the
> relative motion so to speak, then the initial alignment between the Earth
> frame and the navigation frame doesn't matter. I may then simply say that at
> time t = 0 the axes of the Earth frame is aligned with the navigation frame
> without calculating any explicit rotation matrix.
>
> Is this complete rubbish?

That particular IMU has orders of magnitude worse performance than you
need for inertial-only navigation, unless you're only interested in
spans of time less than a second.

I'm not sure what orientation you're worried about, but the orientation
of the vehicle with respect to the earth is exceedingly important, lest
you mistake the direction of that 10m/s^2 gravity vector.

>> With that IMU I don't think you have to pay attention to the earth's
>> rotation -- IIRC the gyros on that have errors far in excess of 15
>> degrees/hour, so any signal you'd get from the earth's rotation will be
>> swamped by the gyro errors.
>
> According to the data sheet the IMU has a gyro RMS output noise (worst case
> configuration) of 0.6 deg/sec = 36 deg/hour, so you're right when saying
> that the noise probably swamps the Earth's rotation. But if I don't model
> the Earth's rotation then this will give an additional noise term, and the
> combined error gets larger, right?

Yes, the combined error gets larger. But if it doesn't get
_significantly_ larger then it doesn't matter. That's lower than I
expected; maybe you could benefit from paying attention to the Earth's
rotation.

Do pay attention to Vladimir's nay-saying, by the way -- that IMU is
probably marginal even for GPS-aided inertial navigation. It certainly
won't help you much through extended GPS dropouts, which you'll tend to
see on a ground-based vehicle.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
From: Tim Wescott on 9 Mar 2010 15:17
Alfred Bovin wrote:
> "Vladimir Vassilevsky" <nospam(a)nowhere.com> wrote in message
> news:BuSdnXH74Y3VNAjWnZ2dnUVZ_uydnZ2d(a)giganews.com...
>>> I'll take the chance and ask this question here in the forum since
>>> perhaps there are someone familiar with INS here.
>>>
>>> I'm trying to do some inertial navigation for (what perhaps will become)
>>> an autonomous all-terrain vehicle with a strapdown inertial sensor (an
>>> ADIS16350 from Analog Devices) with a 3-axis gyro and a 3-axis accel. I
>>> have no previous experience with this stuff so I've been reading a bit in
>>> "Strapdown inertial navigation technology" by Titterton and Weston.
>> That won't work. The accuracy of ADIS is typical for MEMS sensors, i.e. ~1
>> cm/c^2 or so. This is inadequate for innertial navigation.
>
> Thanks for your reply.
>
> I should say that this ADIS device came along with the platform from the
> factory, and I want to experiment a little with it.
>
> I realize now that, as you say, the performance is probably not good enough
> to make reliable inertial navigation, but then I may have misunderstood
> something fundamental regarding the usage of inexpensive MEMS IMUs.
>
> When you say that the device is inadequate for innertial navigation, do you
> then mean that it cannot be used in a system where it's the only sensor?
>
> As I said, I have no previous experience with inertial navigation, but what
> is the typical usage of such inexpensive devices as the one I have? Is it to
> have short term navigation at a higher frequency than more reliable sensor
> data is available (such as GPS)?
>
> I of course also have odometry data available (10 Hz) and I'm experimenting
> with motion estimates from a stereo camera system (around 6-7 Hz). Do you
> think the IMU can be of any help/usage in this system?
>
>
The IMU can _help_. In particular, the IMU plus a GPS receiver will
vastly increase the short-term accuracy of the GPS measurement. It
won't be good enough to resolve problems with multipath on the GPS, nor
will it carry you through a very long GPS dropout.

Odometry and visual data may help, but it's problematic -- how do you
tell the difference between a wheel slip and the sudden onset of GPS
multipath? In theory you could make a filter that would sort this out
(web search on "particle filter"); in practice you could spend a long
time dinking with such a filter without getting something that is robust
and practical.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
From: Rich Webb on 9 Mar 2010 15:32
On Mon, 08 Mar 2010 15:47:52 -0800, Tim Wescott <tim(a)seemywebsite.now>
wrote:

>Rich Webb wrote:

>> Unless you're using a specialized unit, your GPS fixes will be in WGS-84
>> latitude and longitude (assuming that's the fix source you'll be using)
>> so it's probably easiest to stick with that reference frame.
>>
>Trying to translate from your INS frame of reference into GPS's WGS-84
>frame will make your head hurt. Trying to write a system equation to
>express the motion of an accelerated, rotating body in the WGS-84 frame
>will make your head _really_ hurt. (Say "Coriolis". Say "Coriolis, ow
>ow ow").
>
>Translating both to earth-centered, earth-fixed, then back, will make
>your head hurt -- each way -- but both of those together may well make
>your head hurt less than _just_ trying to write a system equation that
>stays in WGS-84 coordinates. Particularly if you want your system to
>work close to the poles.

Yes, I've drifted away from the navigation equations in the last few
years (no pun intended (okay, that was a lie)) and do miss the mental
gymnastics but not so much the pain.

It sounds as if the OP doesn't want a GPS reference. If the problem is
local area navigation (e.g., something like Sparkfun's annual Autonomous
Vehicle Competition) then his best bet might be simply to stick with a
flat earth model and use odometry to estimate his sensor corrections.

--
Rich Webb Norfolk, VA
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