User talk:Crazy Software Productions

From Wikipedia, the free encyclopedia

Please feel free to place comments on text that I wrote :

GPS :

You clearly have a great grasp of the concepts involved, and I learned a lot from reading your recent comments. Especially enjoyed your reference to nearly moon distance in connection with a one second timing error. Really dramatizes the importance of good clock information. Sorry to criticize, but for your writing to really shine, your spelling could use a few minor tweaks: you mean plane, as in plane geometry, rather than plain, and in most instances (except when communicating "it is") want to write "its" rather than "it's". All the best. Hertz1888 17:01, 9 June 2007 (UTC)
Thanks for your comments. Please do correct my mistakes, by informing me or even in line. I even looked up the word 'plain' in Wikipedia, thinking that plane was wrong (for airplane) and plain was right. English is not my first language so being so involved with the subject, the language get a wack on the head. Sorry for that.Crazy Software Productions 20:45, 9 June 2007 (UTC)
Considering that, your English is excellent. Native speakers make these mistakes, too (and worse), you know. Thanks for letting me help. I don't want to be a pain, but that first correction you made, on the GPS:Talk page, of "it's" to "its" (actually to someone else's text) was incorrect. In that instance the intended meaning was indeed "it is", therefore it should get (or keep) the apostrophe ('). By the way, I believe "plane" comes directly from the Latin word for flat, planus. Hertz1888 13:39, 10 June 2007 (UTC)
Please take a look at the page again. In my enthousiasm I had changed the it's to its. Now in my enthousiasm I took your rules and undid this, but in more places than I should have. But if "it's" stands for "it is" I think I changed some correctly, could you please look at both forms. So could you check if I have made some wrong corrections ? Crazy Software Productions 19:08, 10 June 2007 (UTC)
Good job, Crazy. Looks like you've got all those glitches fixed, and it has had a positive effect on the overall quality. I notice an occasional misspelling of other words, but it's no big deal; this is a talk page, not an actual article. Enthusiasm is a good thing. Carry on! Hertz1888 22:04, 10 June 2007 (UTC)


Contents

[edit] Editing comments

Editing your own comments for changes other than spelling is frowned upon because you can change the appearance of a discussion. Also, your editing deleted a comment I had placed. I'm sure it was a mistake but please be careful in the future. - Davandron | Talk 23:30, 6 June 2007 (UTC)

Yes my apologies for that, I had an edit conflict. I had just made some minor edits in my part (satelite should be written as satellite for example), when the conflict occured I saved my 'progress', had a look at what was changed and pasted my edits back from my 'progress', not realizing that a comment was inserted in that part. Should have been more carefull.Crazy Software Productions 20:32, 9 June 2007 (UTC)

[edit] Simplified method of operation ON 20071117

A GPS receiver calculates its position by measuring the distance between itself and three or more GPS satellites. Each satellite has an atomic clock, and continually transmits messages containing the exact time, the location of the satellite (the ephemeris), and the general system health (the almanac). The receiver, using its own clock, carefully measures the reception time of each message. This gives the distance to each satellite since the signal travels at a known speed near the speed of light. Knowing the distance to at least three satellites, and their positions, the receiver computes its position using trilateration.[1] In practice, receivers typically do not have perfectly accurate clocks, but tracking four or more satellites allows them to compute their location and the accurate time.


Goal shorter, more accurate, leaving out inaccuraties.

[edit] Simplified method of operation PROPOSAL

A GPS receiver receives location and timing informatin from satellites. From this information the GPS receiver can calculate its position and the actual time. To do this the GPS receiver times the difference of arrival times of the satellite signals. The speed of the signals is know, so the receiver can determine the distance differences to the satellites. The signals of four satellites are needed to calculate the position. As a side effect the actual time can be calculated as well.

Example (in 2D). We are in a location in Great Britain, we are D meters from Iron Bridge. (We do not know the value D).

1. Iron Bridge 52 37 38.48N 2 29 7.54W (Distance is D meters)
2. London Bridge 51 30 20.07N 0 4 31.32W (64734.33 meters further than Iron Bridge, distance=D+64734.33 meters)
3. Firth of Forth 56 0 1.23N 3 23 19.10W (70712.14 meters further than London Bridge, distance=D+135446.37 meters)


From this information we can determine our position. (Actual there are two solutions not necessary both in Britain.).

GPS is a 3D situation, where the satellites are on the move all the time. Because of the extra dimension 4 satellites are needed, the information which satellites are visible (almanac) and the information where each satellite exactly is (the ephemeris) is send all the time. Distances differences are determined by multiplying the timing differences by the speed of light.


The position is calculated from the time differences between the different satellite signals.

The usual explanation is that the position is calculated from 'known' distances to the satellites. If the clock of a GPS receiver would be very accurate this would be possible. But the distances to the satellites are not know until the actual position is calculated.

[edit] Global Positioning System

I attempted to take the last two paragraphs in the Using the C/A code section and merge them into one based on how I interpreted the description of the process. Is it within your mind's "estimated precision error"?

Also, you might want to add a discussion about GPS to the multilateration article. --  Denelson83  23:53, 12 September 2007 (UTC)

[edit] Modifications on Using the C/A code

ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL

[edit] Using the C/A code

To start off, the receiver picks which C/A codes to listen for by PRN number, based on the almanac information it has previously acquired. As it detects each satellite's signal, it identifies it by its distinct C/A code pattern, then measures the time delay for each satellite. To do this, the receiver produces an identical C/A sequence using the same seed number as the satellite. By lining up the two sequences, the receiver can measure the delay and calculate the distance to the satellite, called the pseudorange[2].

Overlapping pseudoranges, represented as curves, are modified to yield the probable position
Overlapping pseudoranges, represented as curves, are modified to yield the probable position

Next, the orbital position data, or ephemeris, from the Navigation Message is then downloaded to calculate the satellite's precise position. A more-sensitive receiver will potentially acquire the ephemeris data quicker than a less-sensitive receiver, especially in a noisy environment.[3] Knowing the position and the distance of a satellite indicates that the receiver is located somewhere on the surface of an imaginary sphere centered on that satellite and whose radius is the distance to it. Receivers can substitute altitude for one satellite, which the GPS receiver translates to a pseudorange measured from the center of the earth.

ARGUMENTS FOR CHANGING, CALCULATIONS CAN BE DONE IN ONLY THREE-DIMENSIONAL SPACE. ALTHOUGH THERE ARE FOUR PARAMETERS (X,Y,Z, D), THE FOURT PARAMETER CAN BE A DISTANCE PARAMETERS. THE TIME OF THE DAY IS NOT IMPORTANT AT ALL.

Locations are calculated not in three-dimensional space, but in four-dimensional spacetime, meaning a measure of the precise time-of-day is very important. The measured pseudoranges from four satellites have already been determined with the receiver's internal clock, and thus have an unknown amount of clock error. (The clock error or actual time does not matter in the initial pseudorange calculation, because that is based on how much time has passed between reception of each of the signals.[clarify][citation needed]) The four-dimensional point that is equidistant from the pseudoranges is calculated as a guess as to the receiver's location, and the factor used to adjust those pseudoranges to intersect at that four-dimensional point gives a guess as to the receiver's clock offset. With each guess, a geometric dilution of precision (GDOP) vector is calculated, based on the relative sky positions of the satellites used. As more satellites are picked up, pseudoranges from more combinations of four satellites can be processed to add more guesses to the location and clock offset. The receiver then determines which combinations to use and how to calculate the estimated position by determining the weighted average of these positions and clock offsets. After the final location and time are calculated, the location is expressed in a specific coordinate system, e.g. latitude/longitude, using the WGS 84 geodetic datum or a local system specific to a country. ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL ORIGINAL

CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED CHANGED

[edit] Using the C/A code

To start off, the receiver picks which C/A codes to listen for by PRN number, based on the almanac information it has previously acquired. As it detects each satellite's signal, it identifies it by its distinct C/A code pattern, then measures the time delay for each satellite. To do this, the receiver produces an identical C/A sequence using the same seed number as the satellite. By lining up the two sequences, the receiver can measure the delay and calculate the distance to the satellite, called the pseudorange[4].

Overlapping pseudoranges, represented as curves, are modified to yield the probable position
Overlapping pseudoranges, represented as curves, are modified to yield the probable position

Next, the orbital position data, or ephemeris, from the Navigation Message is then downloaded to calculate the satellite's precise position. A more-sensitive receiver will potentially acquire the ephemeris data quicker than a less-sensitive receiver, especially in a noisy environment.[3] Knowing the position and the distance of a satellite indicates that the receiver is located somewhere on the surface of an imaginary sphere centered on that satellite and whose radius is the distance to it. Receivers can substitute altitude for one satellite, which the GPS receiver translates to a pseudorange measured from the center of the earth.


For the calculation of the position a GPS receiver needs:

1. the relative distances to the satellites (pseudoranges).
2. the satellites positions.

All calculations can be done without any time components. With four satellites there are four spheres which all should intersect in one point. This is four equations, with four unknown, (x,y,z, ^d) (^d = c*^t for distance). Four lineair equations with four unknowns are easy to solve. But spheres are not lineair. In pseudo range calculations 4 lineair equations (planes instead of spheres) are used. The planes approcimate the sphere well enough for this solution to work and give a very fast and very accurate results.

With 5 or more satellites, extra points can be calculated. They should be very close, but for each point calculated, it is possible to calculate how good this point is. The reciever then determins which combinations to use and how to calculate the position from all the results.

After the final location (and time) are calculated, the location is expressed in a specific coordinate system, e.g. latitude/longitude, using the WGS 84 geodetic datum or a local system specific to a country.


[edit] The principle explaned with a 2D example.

We are in a location in Great Britain, we are D meters from Iron Bridge. (We do not know the value D).

1. Iron Bridge 52 37 38.48N 2 29 7.54W (Distance is D)
2. London Bridge 51 30 20.07N 0 4 31.32W (64734.33 meters further than Iron Bridge, distance=D+64734.33)
3. Firth of Forth 56 0 1.23N 3 23 19.10W (70712.14 meters further than London Bridge, distance=D+135446.37)


From this information we can determine our position. (Actual there are two solutions not necessary both in Britain.).

Question: Where are we, and the side question what is the value of D.
The distances are determined using Google Earth, using a GPS the distances are 64.8 km and 135.72 km.


There are several methods to find the location.

1. Plotting circels around the known positions with the correct relative sizes. The three circles should intersect in one point. Some trial and error wil be neccesary.
2. Plotting all the points which are 64734.33 meters further removed from London Bridge then from Iron Bridge. And plotting al the points which are 70212.14 meters further removed from Firth of Forth than from London Bridge. This will give you two hyperboles. They intersect at two points. The location is in one of those two points.
3. Using the Pseudo range calculation for this problem. (Solving 3 equations with 3 unknowns x,y,d, where d stands for the distance to Iron Bridge.
4. Driving around the country and trying to find the correct spot by driving in the direction where the error get's less.
5. Using a Gps and measuring distances to the relative known locations.
6. Using a map (prepared), where as a grid the relative distances to the three known points are used.

If we assume Britain to be flat, and use a 'square' grid, this will aid calculations. Using London Bridge at 0,0 and use kilometers as the grid size we get :


London Bridge 0,0
Iron Bridge -167.32,124.84
Firth of Forth -207.1,500.31

In this coordinate system we can calculate the x,y position, but because Britain is not completely flat it will only be an approximation of the actual position.

Using pseudorange calculation in this flat system we have to solve the following equations. The position to be solved is x,y and D for the distance.

Iron Bridge


(X-(-167.32))^2 + (Y-124.84)^2 = D^2
(X)^2 + (Y) ^2 = (D+64.73433)^2
(X-(-207.1))^2 + (Y-500.31)^2 = (D+135446.37)^2

These equations are not lineair, but quadratic. Because of the squareroots there will be two solutions (x,y,D) which satisfy alle three solutions. This calculation can be used in several ways. Changing the D can be done until one or both solutions are found. This still takes some calculations, but substituting the D with an estimate, makes it possible to calculate several pairs of XY. using the correct D there will only be two pairs.

This is actually calculating the solution using the circle (3D sphere) method. Often used to explain the GPS principle. Very ofte simplified by assuming the D is know.

Pseudo range calculation does not use this computation intensive method. The set of equations is made into a set of lineair equations. This will only result in the same solution if the lines (3D planes) are close enough to the actual solution that the circles (spheres) can be assumed flat for the calculation. To do this a estimate is needed, the estimate should not be to far from the end solution. (We choose York as an estimated point). (3D and on the world the last known location can be used, the side of the earth were we the satelites are visible from can be used, or even the centre of the earth can be used.)

For this location we calculate the lines which we are going to work with. The lines are perpendular on the line known point to york. (They we be used as direction vectors in het new calculations).

TO BE CONTINUED HERE.



Now with some carefull plotting in Google earth the you can find the location.

There are lot of methods to determine the actual location. For a GPS on of the best methods is pseudorange calculation.

[edit] How to find the locations :

Using intersecting circles. Draw circles (of the correct size) around the known places. Change the circles until they intersect in one place. (There are two solutions where the 3 circles intersect in precise one place. They do not occure with the same circle sizes).

Using hyperboles. Plot all the points from two known locations with the same difference in distance. (An Example should be shown for this). This gives the shape of a hyperbool. Two hyperboles give two intersection points. (The third hyperbool will go through the same two points. These points are the same as the points obtained by the circle method).

Calculating methods. For easier calculation a 'rectangular' grid wil be easier, so one can calculate with x,y points. The coordinates are given above. One of the methods is finding a for one combination the line and moving over that line or following that line close, to find the other line. This can also been done with a least square method. Depending where you start you should find a point.

A better calculating method is the pseudo range calculation. Based on a first estimate, with pseudorange calculation this iterates very fast to the endsolution. The pseudorange calculation is based on the circle methods. But because lineair equations are easier to solve, 3 (in this case For GPS 4) lineair equitions are used to solve the x,y,d (where d is the distance to the nearest known location).


Suppose you have not 3 known towns (Needed for 2D calculation) but only have 2 known towns, but some additional information for example that the location is situated on the coast. The position (two possibles) can still be determined. The coast is so irregular, that calculation is not 'really' possible, but drawing the curves on the map can still be done. For example say the distances are ???? from ..... a coastal town.


Differences with GPS. Gps uses time to measure the differences between distances. In the above example the measurement of distances is not realy discussed. Gps uses a 3D model (always, because the satellites and GPS receiver are not in one plane). The example is bases on that Britain is flat. (This is offcourse not true, but makes the model easier to explain). The known location in the above example do not move (this would make the example complex). In GPS the known locations of the satellites are moving, but for one calculation they can be considered to be at one point. The locations of teh satellites need to be calculated.

In the GPS the calculations can be done with distance in meters as the working method. But distances can be converted to travel times of light and vice versa, the distance to the first satellite (delta d) or the clock error (delta t) are equivalent. So within the calculation the distance error or the clock error can be corrected for.


[edit] Remarks :

With the example everything is in 2D, there is no time component. So all calculations fall in 2D space, although there are three unknown value's to be determined.

For a 3D world.
3 intersecting circles become 4 intersecting spheres.
2 hyperboles become 3 hyperboloides.
3 lines in the pseudorange calculation becomes 4 planes in the pseudorange calculation.
Three known bridges become 4 known locations (satellites).
Three unknown values x,y, ^d become four unknown values x,y,z ^d.
^d (distance to the closed satellite) or time to the closed satellite is interchangeble.

But there are still 2 solutions which both fit the set of given data. Because speed of light is known, distances can be converted to delaytimes. (With some correctionsof atmospheric conditions).

In the 3D world one satellite can be exchanged for a known hight (distance from the centre of the earth). In the 2 D world one of the known bridges can be exchanged for a known distance to a fixed point, the other two known bridges are still needed. The solution(s) will be the intersection of one circle (of known size) with the hyperboole which defines the distance between the two know bridges.

[edit] Why ?

[edit] why ?

First I do not mind that simplified explanations are used. Also I do not mind that incorrect concepts are used. But both if used to explain the principle.

I object to that simplified of incorrect concepts are used the explain matters they can not explain. A very specific example is the number of satellites that is needed for the calculationof the position. The simplified (and incorrect) concepts just do not explain the behavior of GPS receivers and do not explain the number of satellites needed. Because this simplified (and incorrect) explanation is used in so many places (trimble, how stuff works and even Garmin), everbody assumes it to be correct and quotes these explanations as through. While the behavior of GPS receivers, mathematics, physics and technology do not conver to this resoning.

Mathematics. If the exact time is know with enough accuracy, circles can be used as the model. In real live, the circles can be used as the model but do not determine where the GPS receiver is, these are hyperboloids. Physics. Yes the signals expand as spheres, except that the sphere size can not be determined, and therefore the distance can not be determined. Technology. Clocks drift for up to 30 seconds each month, look at expensive watches how much they drift. But even a watch that only would drift 1 sec a year would not be accurate enough. Technology at this moment does not supply is with a within clock device which is accurate enough. *)


  • ) Technologie does supply is with an extremely accurate clock when using the GPS signal to determine the time. But here the GPS system with the atomic clocks are used.


WRONGS:
The fourth satellite is needed to distinguise between two point. Incorrect even with four satellites there are still two points which satisfy the timing coditions.
The fourth satellite is needed to do time corrections. Wrong the drift of an average clock can be higher than the speed we can normally travel.
Calculations are done in 4 Dimensional space. Wrong, all calculations can be done with distances in 3 dimensional space only. There can be 4 unknown parameters, but they can be represented in three dimensional space.
Pseudorange calculation is an estimate because of a slight clock error. Slightly wrong, I do not know why it' called pseudorange calculation. Two answers could be because it's done with pseudo ranges (distances which all have the same error), or because the calculation is never exact but an approcimation to the actual point.
Implementation is done with calculating with spheres. Could be done, but is very impractical.
Implementation is done with calculating with hyperboloids. Could be done, but is very very impractical.


Pseudorange calculation is a algoritm which delivers with very little requirements on calculation resources a very accurate answer. Doing the same calculations with the sphere model, or with a hyperboloid model would use far more calculation resources. (They are not very practical to implement). Also I do not know if there is an actual solution for the spere model and the hyperboloid model, it could be that the result can only be reached by iteration and never exact.

[edit] Do we need the atomic clocks in the satellites.

Could a GPS system be designed with quartz clocks in a GPS satelite. This would very probable be possible. The principle would be simple use ground stations which would determine the clockerror for the satellite often enough and send a correction signal for this error. With enough groundstations it would be possible to determine the drift of the satellite clock and correct for this. With enough knowledge, time drift of the clock can be predicted fairly correctly and corrections can be less frequent. Even the satellites could be used to correct each other.

Because the errors would be very dependend on each other this would need a complex system to correct for the errors, on a continues base, but most problems would be solvable with software, making the system cheaper.

Would this be practical, not at the start of the GPS system, because of the limited number of satellites available, probably not enough to correct them. And by know the atomic clock only is a small part of the total cost of the satellite.

Large part of the new GPS system (Galileo) is based on the extra correction power designed in the system. Although clocks have improved as wel. Also have algoritms to correct 'smal' errors in the 'hardware' system, so that hardware with the combined software delivers a beter accuracy.

Examples of this technologie. GPS satellites can determine the distance not by using the same clock but by sending the signal from one satellite to another and then a returnsignal backwards. The time between the sending and receiving will be the time needed to travel the distance twice plus the processing time. If the processing time is known, the satellites do not need to have a clock on sync, because only the first satellite clock is used. By determining the distance between all satelites which can see each other, the satelites all become part of a know fixed grid. now the only thing which has to be done is determine where the earth is compared to this grid. Having this fixed grid of satellites sure will help the positioning system. And this fixed grid would be fairly accurate if all satellites would only carry simple quartz clocks. But what the heck, use atomic clocks in a few satellites, just to make the grid 'more fixed' to the earth. for example 3 atomic clocks, two on opposite sides of the earth and one which is does relative move from the fixed ones, so that the third satellite once in a while sees the one and the other satellite. (Maybe one, or two would be enough so sync everything, because we know the grid, but just in case). Three could als be the minimum, because then in 3D space the earth is fixed. With two it's possible to rotate. ?????

So having a grid with good timing an a relatively good emipheris. Using only a few fixed spots on earth would fix the earth as well to the grid. Maybe, 'strait' lasers can be used to determine the 'distance' or angular position to parts of the system. Only a few are needed to fix the grid to the earth. (Fixing in this context means that we know the relative position of the earth compared to the grid).

With all the corrections on the grid, I would say that this is even possible with 'standard' quartz clocks. Satellite paths do cross so then the distance is very small. Distances are at most about 50.000 km. The distance to the closed satellite will never be more than 30000 km. Without corrections and an 'inaccurate' quartzclock this would lead to positional error of hundreds of meters. With a corrected quartzclock and corrections the error could be reduced to only a few meters, not a lot worse than the actual known positions of the satellites.

[edit] A simplified and limited way to determine the position.

A lot of the GPS position system is works around the clocks. During the day there are many moments when the observers position is exactly between satellites. The distance to both satellites is the same at that moment. Using only that type of moments to determine the position, no clock is needed, no timing is needed and the position can be easely calculated. Because if the distance to both satellites is the same, we are on the (flat) plane exactly between the two satellites. The intersection of three such planes determines one single point where we are.

Even most atmospheric errors are eliminated. Because the satellites all circle abouth the same distance from the earth, two satellites having the same distance from the observer must have the same angle (above the horizon) from the observers view, so both signals travel the same distance through the atmosphere (including the ionosphere). Also there is no clock so no clockerror at the recievers side.

Offcourse this is not a practical way to use a GPS system, but it is a practical way to explain GPS.

If the reception is not exactly the same but a littlebit different, the flat plane 'warps' and becomes a hyperboloid. With small differences close to the flat plane but with greater distances the angle of the hyperboloide becomes less. The observer now is on the intersection of three independend hyperboloids. (Because of the curvature, it's possible that there are two solutions in the set).

Crazy Software Productions (talk) 14:02, 1 March 2008 (UTC)

[edit] Construction of the location in 2 D.

In two D one can use construction to determine ones position. Needed large paper. Calipers Ruler (without a scale). The three points which represent the satellites on the paper. The difference in signal differences. Markt the satellite of which the first signal is received as 1. Mark the satellite of which the second signal is received as 2. Mark the satellite of which the third signal is received as 3.

Draw a circel the size of the difference in distance between one and 2 around 2. Draw a circel the size of the difference in distance between one and 3 around 3.

Mark the middle between 1 and the circle around 2. Draw two lines A going through 1 and touching the circle around 2. Draw two lines B going from 2 through the lines where they touch the circle of 2. Draw two parallel lines C through the middle point parallel to the last two lines. Draw two parallel lines D through the middle points of the touching lines.

your position in in between the parallel lines C and D. (Two sets.)

Do the same for 1 and three.

Now your position is limited to two boxes.

From point 2 draw lines to the four points of both boxes, use the two outer most points in both cases. Reconstuct the box form that, steps to follow. 1. 2. 3.

From point 3 draw lines to the four points of both boxes in the same manner.

Repeating this process will result in the exact location.Crazy Software Productions (talk) 20:48, 3 May 2008 (UTC)