Regrettably, you do tend to get what you pay for. The unit you
linked to is intended for things like video game controllers, such
as the Nintendo Wii wireless controller. By itself, a tri-axial
accelerometer does not constitute an IMU. You need turn rate
information in addition to accelerations, and you need a method of
combining those signals into a useful inertial reference, which
means sampling them simultaneously and fusing them in your Kalman
filter at a sufficient sampling rate to minimize the integration
error. That particular instrument is a high noise device, as well
as having no temperature compensation. While it certainly could be
of use for obtaining information such as pitch and roll angle of
your vessel (within the instrument repeatability), it is not
sufficiently accurate to derive meaningful navigation information
from.
As far as a sub moving in a current, all accelerometers will measure
zero (+/- their accuracy limits) when in an inertial reference frame
(i.e. your sub) which is traveling at constant velocity.
Integrating an acceleration signal over time gives you the velocity,
and integrating once again gives you displacement. To illustrate,
imagine a support ship keeping station at a particular GPS
location. Your sub is on deck, and while the accelerometer signal
is oscillating due to the ship's roll, the average is zero.
Therefore, the velocity is zero, and net displacement is zero. Now,
have the ship drop your sub over the side into a slight current. As
soon as you are disconnected from the crane, the sub begins to
accelerate as the water force starts to overcome the sub's inertia.
At some point, the acceleration reaches a peak value and then
decreases, until the sub is traveling at the same speed as the
current, at which point the acceleration is zero. The velocity,
however, is not zero, since integrating the acceleration over the
time interval between setting the sub free and reaching the speed of
the current results in some positive value. With the acceleration
at zero, the velocity is now some constant value, and the
displacement, being an integral of velocity (now a non-zero value),
will continue to increase over time. Now, actuate your thrusters to
"put on the brakes", with respect to the ground below. You
accelerate in the other direction, slowing from the water current
speed to zero speed with respect to ground. Again, the acceleration
increases from zero, peaks, and drops to zero again (albeit in the
negative direction this time). Integrating that signal over time,
the velocity reduces from its previous constant value to zero, and
the displacement, being the integral of velocity, stops changing.
The displacement now has a constant value equal to the distance you
have traveled since you left the ship - in essence, dead reckoning
(distance = velocity * time). Your absolute position is simply the
last known good position (GPS reading at the ship), plus the
accumulated displacement estimate. The quality of this estimate
depends on the quality of the instrumentation, as well as the time
over which the error has been accumulating. If you come to a stop
over ground, but the integration error is such that the resultant
velocity is not exactly zero, then the displacement will continue to
increase over time, despite the fact that you are, in fact,
motionless with respect to ground. To correct this with an external
signal, you could surface to obtain a GPS position and velocity
(i.e. eliminating the errors), or similarly, determine this on the
bottom with sonar. The higher the quality of your IMU
instrumentation, the longer you can rely on the dead-reckoning
position estimate before the error becomes unmanageable.
-Sean
On 12/02/2011 4:21 PM, Alan James wrote:
Hi Sean,
There's a triple axis
accelerometer on the Cytron Robotics site. Needs additional
analogue to digital converter.
Cost RM $109, that's probably
less than $40- US. Have bought stuff off them & it's been
good quality.
Will these units cope when your
sub is moving in a current?
Regards Alan
----- Original Message -----
Sent: Sunday, February 13,
2011 9:59 AM
Subject: Re:
[PSUBS-MAILIST] Navigation
A few years ago I experimented with an inertial navigation
system I created using a 3DM-GX1 sensor from Microstrain. I
think the newest model is the 3DM-GX3 now - would have to
experiment to see what accuracy gain there is in the new model.
In any case, this is a three axis accelerometer which
incorporates 3 magnetometers and 3 rate gyros. The
magnetometers are supposed to be used to measure the ambient
magnetic field and use this as a quasi-constant input to correct
the gyro bias. Unfortunately, the magnetometers are affected by
external magnetic influences, such as large steel shipwrecks, so
the instrument is least accurate when you tend to need it. The
instrument measures acceleration directly. Integrating this
signal over time gives you your present velocity, and
integrating over time once again gives you your displacement
(position) in xyz space. In my experiment (conducted on a
surface vessel), I started with a known position obtained from
GPS, then shut off the GPS signal and simply added the position
variations as calculated from the 3DM-GX1 to determine my
current position. This is, in fact, exactly how military
submarines do it, only their inertial navigation units comprise
extremely accurate (and consequently, extremely expensive)
hardware to minimize the integration error. This is the crux of
the inertial navigation problem - you are essentially
determining your position through dead-reckoning, using the last
known good position, and applying corrections from your IMU
instrument. The problem is that error creeps into the
integration, and since you have to integrate twice, the error
starts to get significant. In my experiment, as soon as the GPS
was shut down, the error started to accumulate, so that the
uncertainty in the calculated position grew with time.
Eventually, you reach a point at which the error in your
calculated position renders the position useless for the purpose
of navigation. The solution? Either spend big bucks on a more
accurate IMU, or periodically correct the calculated deviations
with another input. There are several possibilities for this:
1) Doppler sonar - limited to low speeds at which the sonar
reading is accurate, but this is more accurate than inertial
navigation when it is implemented. Doing this would limit the
inertial navigation error to that accumulated during the descent
from the surface to a range from the bottom at which the doppler
sonar becomes effective.
2) Depth transducer - It occurred to me that since you do know
with reasonable accuracy your depth in the water column (and
thus your velocity in the Z direction), you could use this as a
correction input (i.e. do not allow integrated velocity values
in Z direction to exceed this measured velocity, and rein in the
X and Y velocities accordingly). I have no idea what effect
this might have on accuracy without trying it.
3) Acoustic methods - widely used in industry, but require
surface or seafloor based transmitters. (reference LBL &
SBL navigation). If you have no need to operate independently
of surface support, then acoustic navigation alone may meet your
requirements, but this does require some hardware and so may end
up being more expensive than an IMU for small submersible
navigation at your required accuracy - depends on what you need.
I would be inclined to try and find a low-cost doppler sonar for
bottom navigation, supplemented by an inertial unit that isn't
hugely expensive. One advantage of the IMU is that it will
output pitch, roll and yaw angles, so you could use the output
to control, for example, a trim tank system to keep a level
keel.
As I recall, the 3DM-GX1 cost somewhere in the neighborhood of
$1400.00. I would be happy to look into developing a turnkey
PSub inertial navigation solution, but I'd need a 3DM-GX3 (or
similar) IMU to play with, as well as data acquisition hardware
that runs at an appropriate frequency to capture the IMU output
with minimal error. At present, I can't afford to buy these
things for a hobby R&D project, although I might reexamine
this at a later date when my situation changes.
-Sean
On 12/02/2011 10:43 AM, Recon1st@aol.com wrote:
Jim I think navigation would be a good topic for this
group to discuss. I for one am at a loss for a
solution.
I so like my gps system on my surface support boat I
want
something decent under water.
How does the military do it? Lots of money I am sure
but seems something better than a compass could be
done.
I am leaning towards a tracking beacon on the sub and
get nav directions from support boat.
Dean
In a message dated 2/12/2011 11:42:17 A.M. Central
Standard Time, kocpnt@tds.net
writes:
Hi All,
I am beginning rebuilding Bionic Guppies
electronics/electrical systems. I am planning on
again using an aircraft directional gyro for
navigation.
Before I go down this road does anyone have a
better/different idea?
Also, Dan Lance, I believe that you were quite
pleased with OTS communication system.
Can you confirm this, and if so provide contact
info for a good supplier.
Best Regards,
Jim K
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