jimserac@yahoo.com wrote:
> Correlious wrote:
>
> >With Sonar, as any other mechanism, you'll have to watch out for
> >multipath fading effects!
>
>
> Sorry, my question was meant to be completely theoretical
> and not to involve the physics of sonar.

You have to deal with the physics of the application you sketch.
You said you wanted to use sonars as measurement devices.
You will have to deal with the physics of sonars to get this
system to work. You reformulate the application a bit below.
Be aware that the difference between an idealized/trivialized
textbook example and a working real-world application, is the
physics of the application.

> Let me restate more clearly - I have a situation where a robot gets
> some sort of time duration information from a remote robot
> and this time duration is a linear function of distance.
> The bigger the time duration number, the farther away is the
> remote robot.

What robot knows this number? The master, as in radar? The slave,
as with GPS? Both? Do you intend to organize the information into
an overall "situation awareness map"? How would you exchange
the information between robots?

> So my question is, in setting up the Kalaman filter state equations,
> do I make this time duration number itself be the measured variable or
> do I make it be distance (which, obviously, is a function of time).

Time and distance are (in the naive model) proportinal quantities,
x = ct, and it ought not matter which one you use if you know the
sound velocity c. If the sound velocity varies with time or space,
you will have trouble. And you will need to take the physics of
the sonar into account in your model, whether you like it or not.

What is the purpose of the exercise? To learn Kalman filters?
To organize a control system? Is this academic? Are you involved
with designing a real-life application?

It is basically impossible to answer your questions without knowing
what you try to do, and why. Only when analyzing the complete
application (purpose, technical resources, physical and other
constraints) may it be possible to decide exactly which method of
doing things will be better than others.

In your clarification you are basically reducing the position
estimation problem to a very generic (trivial?) one, depending
merely on the equations of motion and little else. Why don't you
re-formulate the "physical application" of your system to that
of tracking aircraft or objects in free space? You might find
one or two papers on the subject, it might even have appeared
in a textbook or two by now. I think somebody (Wiener himself?)
had a go at this around 1943-44, in order to hit the V1 rockets
with AA artillery.

Rune

In my opinion, and I'm not an expert, you would calculate a position estimate 
from the durations and use the Kalman filter on the position estimate and 
maybe on the distance measurements of the distances from the various robots as 
well.  Errors in the distance estimate and the calculated position derived 
therefrom would be modeled as measurement noise in the Kalman filter position 
estimate.

If you are going to use RF ranging signals, you might want to look into 
continous pseudorandom code correlation as a distance measurement technique.  
NASA uses (used to use) this technique to measure the distance to spacecraft.

In article <1121699075.436129.119380@g14g2000cwa.googlegroups.com>, 
jimserac@yahoo.com wrote:
>So my question is, in setting up the Kalaman filter state equations,
>do I make this time duration number itself be the measured variable or
>do I make it be distance (which, obviously, is a function of time).
>
>Thanks
>Jim
>

John Herman wrote:

>To exxpand on Rune's suggestion, you might arrange for the slave robots to be
>able to transmit the ranging signal to all the other robots.  This
>"sing-around" technique is used to locate underwater sensors..

Yes, thanks, I'm considering this very idea.
Also, I'm considering the possibility of adding a wireless
cellular frequency chip which would give more accurate distancing.

However, my original question was meant to be theoretical pertaining to
the
kalman filter .

Assume a robot gets some sort of  elapsed time number which is a
function of the distance of some remote robot.   Do not even worry
about directionality.
The larger the elapsed time for the return ping (or whatever) to get
back to
the master robot, the farther away the slave robot is.   So distance is
a linear function of time.

How do I set up the Kalman state equation?   Do I make time be the
measured variable
or do I computer the distance from the time each iteration and then
plug that into
the state equation as the "reading" to be filtered?

Thanks
Jim

T

Correlious wrote:

>With Sonar, as any other mechanism, you'll have to watch out for
>multipath fading effects!


Sorry, my question was meant to be completely theoretical
and not to involve the physics of sonar.

Let me restate more clearly - I have a situation where a robot gets
some sort of time duration information from a remote robot
and this time duration is a linear function of distance.
The bigger the time duration number, the farther away is the
remote robot.

So my question is, in setting up the Kalaman filter state equations,
do I make this time duration number itself be the measured variable or
do I make it be distance (which, obviously, is a function of time).

Thanks
Jim

Rune Allnor wrote:
> In what scenario would these robots operate? In an open area?
> Inside an enclosure, like in an arena with high walls around or
> inside a room?
>
> If there is a use for a Kalman filter in here, it would be for
> merging tracking individual positions into a track. Getting that
> far needs not be easy. The problem is "false" echos and multipath
> reflections from various objects in the area.

Sorry, my question was meant to be completely theoretical
and not to involve the physics of sonar.

Let me restate more clearly - I have a situation where a robot gets
some sort of time duration information from a remote robot
and this time duration is a linear function of distance.
The bigger the time duration number, the farther away is the
remote robot.

So my question is, in setting up the Kalaman filter state equations,
do I make this time duration number itself be the measured variable or
do I make it be distance (which, obviously, is a function of time).

Thanks
Jim


Rune Allnor wrote:
> jimserac@yahoo.com wrote:
> > I've got a stationary robot (the master) which sends a sonar ping
> > (4 times per second)
> > to locate several mobile robots.
> >
> > The mobile robot(s),
> > upon sensing the master's ping, sends a return ping.
> >
> > The mobile robots are usually from 10 to 40 feet
> > from the master and move about at 2 to 3 miles per hour.
> >
> > The master robot checks the elapased time from when it sent
> > the ping to when the ping returns and from this information
> > it judges the distance.
> >
> > But, there is a good deal of inaccuracy, interfering objects,
> > reflections, i.e. noise.
> >
> > I think this is a candidate for Kalman filtering.
> >
> > Do I make the elapsed time be the measured variable and then
> > invoke the machinery of Kalman, after figuring out the noise matrices,
> > and then out pops the distance (the desired resultant of the Kalman
> > filtering)?
> >
> > It's not clear how to:
> > a. Set up the state equation.
> > b. Set up either the measurement noise or the process noise matrices.
> >
> > Would this example be considered a one dimensional Kalman filter?
>
> In what scenario would these robots operate? In an open area?
> Inside an enclosure, like in an arena with high walls around or
> inside a room?
>
> If there is a use for a Kalman filter in here, it would be for
> merging tracking individual positions into a track. Getting that
> far needs not be easy. The problem is "false" echos and multipath
> reflections from various objects in the area. Depending on the
> degrees of freedom in the problem, I'd mount some beacons in the
> operation area, and have the slave robots determine their own
> positions by triangulating with respect to the beacons, and then
> report their positions to the master.
> 
> Rune

To exxpand on Rune's suggestion, you might arrange for the slave robots to be 
able to transmit the ranging signal to all the other robots.  This 
"sing-around" technique is used to locate underwater sensors..

In article <1121586421.391657.48840@o13g2000cwo.googlegroups.com>, "Rune 
Allnor" <allnor@tele.ntnu.no> wrote:
>
>
>jimserac@yahoo.com wrote:
>> I've got a stationary robot (the master) which sends a sonar ping
>> (4 times per second)
>> to locate several mobile robots.
>>
>> The mobile robot(s),
>> upon sensing the master's ping, sends a return ping.
>>
>> The mobile robots are usually from 10 to 40 feet
>> from the master and move about at 2 to 3 miles per hour.
>>
>> The master robot checks the elapased time from when it sent
>> the ping to when the ping returns and from this information
>> it judges the distance.
>>
>> But, there is a good deal of inaccuracy, interfering objects,
>> reflections, i.e. noise.
>>
>> I think this is a candidate for Kalman filtering.
>>
>> Do I make the elapsed time be the measured variable and then
>> invoke the machinery of Kalman, after figuring out the noise matrices,
>> and then out pops the distance (the desired resultant of the Kalman
>> filtering)?
>>
>> It's not clear how to:
>> a. Set up the state equation.
>> b. Set up either the measurement noise or the process noise matrices.
>>
>> Would this example be considered a one dimensional Kalman filter?
>
>In what scenario would these robots operate? In an open area?
>Inside an enclosure, like in an arena with high walls around or
>inside a room?
>
>If there is a use for a Kalman filter in here, it would be for
>merging tracking individual positions into a track. Getting that
>far needs not be easy. The problem is "false" echos and multipath
>reflections from various objects in the area. Depending on the
>degrees of freedom in the problem, I'd mount some beacons in the
>operation area, and have the slave robots determine their own
>positions by triangulating with respect to the beacons, and then
>report their positions to the master.
>
>Rune
>

jimserac@yahoo.com wrote:
> I've got a stationary robot (the master) which sends a sonar ping
> (4 times per second)
> to locate several mobile robots.
>
> The mobile robot(s),
> upon sensing the master's ping, sends a return ping.
>
> The mobile robots are usually from 10 to 40 feet
> from the master and move about at 2 to 3 miles per hour.
>
> The master robot checks the elapased time from when it sent
> the ping to when the ping returns and from this information
> it judges the distance.
>
> But, there is a good deal of inaccuracy, interfering objects,
> reflections, i.e. noise.
>
> I think this is a candidate for Kalman filtering.
>
> Do I make the elapsed time be the measured variable and then
> invoke the machinery of Kalman, after figuring out the noise matrices,
> and then out pops the distance (the desired resultant of the Kalman
> filtering)?
>
> It's not clear how to:
> a. Set up the state equation.
> b. Set up either the measurement noise or the process noise matrices.
>
> Would this example be considered a one dimensional Kalman filter?

In what scenario would these robots operate? In an open area?
Inside an enclosure, like in an arena with high walls around or
inside a room?

If there is a use for a Kalman filter in here, it would be for
merging tracking individual positions into a track. Getting that
far needs not be easy. The problem is "false" echos and multipath
reflections from various objects in the area. Depending on the
degrees of freedom in the problem, I'd mount some beacons in the
operation area, and have the slave robots determine their own
positions by triangulating with respect to the beacons, and then
report their positions to the master.

Rune

With Sonar, as any other mechanism, you'll have to watch out for
multipath fading effects!

If you want to get absolute distance you won't be able to do it with
that. At best it will give you a radius, not a directional vector.
Also, you won't be able to resolve multipath effects unless you start
to get real complex and track distances and drop out all the sudden
changes in distance. You can also have the robots sync what they know
of distances w/ each other but again you'll need a directional vector
for that.

The multipath problem is not solveable w/ any filters!

The way cellphones get around this is use very accurate timing signals
-- that are compared from multiple towers to figure out true distances.
Very complex stuff.

I've got a stationary robot (the master) which sends a sonar ping
(4 times per second)
to locate several mobile robots.

The mobile robot(s),
upon sensing the master's ping, sends a return ping.

The mobile robots are usually from 10 to 40 feet
from the master and move about at 2 to 3 miles per hour.

The master robot checks the elapased time from when it sent
the ping to when the ping returns and from this information
it judges the distance.

But, there is a good deal of inaccuracy, interfering objects,
reflections, i.e. noise.

I think this is a candidate for Kalman filtering.

Do I make the elapsed time be the measured variable and then
invoke the machinery of Kalman, after figuring out the noise matrices,
and then out pops the distance (the desired resultant of the Kalman
filtering)?

It's not clear how to:
a. Set up the state equation.
b. Set up either the measurement noise or the process noise matrices.

Would this example be considered a one dimensional Kalman filter?

Thanks
Jim Pannozzi