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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Horizontal Sextant angles plot.
From: Richard B. Langley
Date: 2012 Apr 6, 15:05 -0300
From: Richard B. Langley
Date: 2012 Apr 6, 15:05 -0300
When I walk around inside my house with my Garmin etrex 20 handheld receiver, it displays my speed and heading giving reasonable values of 1 to 2 km/hr and the more or less correct cardinal or intercardinal direction. Given the position uncertainty of say 5 to 10 metres due to multipath and noise, you couldn't get such low speeds and heading with any accuracy/precision by simply differencing positions computed say 1 second apart. You can easily convince yourself of this by doing a simple propagation of error calculation. Let's consider that we are moving in a particular direction, say along the x-axis of some coordinate system at a constant speed. If we compute the speed as the difference between two positions divided by the transit time, the error in the computed speed based on the error in the positions is given by speed-sigma = 1/delta-t * sqrt ((x2-sigma)^2 + (x1-sigma)^s) This expression assumes the position errors are independent or uncorrelated. That assumption becomes more and more valid the bigger delta-t is. But let's ignore the correlation for this back-of-the-envelope calculation. If we assume x1-sigma = x2-sigma = 10 metres and delta-t is 1 second, we get (approximately) speed-sigma = 14 metres/second or 51 kilometres/hour! That's huge. Even if we assume the position errors to be 5 metres, we still get high speed-sigma values of 7 metres/second or 25 kilometres/hour. Sure, we could get smaller sigmas by increasing delta-t but then we're not getting near instantaneous speed values but rather longer-term averages. I won't go through the analysis, but speed computed from a Doppler frequency shift measurement is far more accurate/precise. All GPS receivers determine the Doppler frequency shifts of the received signals as a by-product of tracking the signals and those values are easily used to determine the receiver's velocity vector. -- Richard Quoting Lu Abel: > Richard: > > I'm wondering if we're talking about two different levels of > capability -- consumer GPS vs GPS systems for the military or other > high-precision, high-cost applications. � You're absolutely right, > one can detect velocity by Doppler shift. � But I wonder if this > capability is built into consumer-level (eg, Garmin) receivers. � > Everything I've read about consumer-level receivers says they simply > determine latitude, longitude and, in some cases, altitude, and > everything else is derived by comparing position. � > > Lu > > > >> ________________________________ >> From: Richard B. Langley >> To: NavList@fer3.com >> Sent: Friday, April 6, 2012 4:47 AM >> Subject: [NavList] Re: Horizontal Sextant angles plot. >> >> GPS receivers determine their velocity vector from Doppler shift >> measurements not a succession of positions. Quoting from my article >> "The Magnetic Compass and GPS": >> >> "A GPS receiver can provide accurate information about its position >> and velocity, and from the velocity vector it can determine the >> direction in which it is moving - called the course or track. The >> accuracy with which a receiver can compute this direction depends >> on its speed (the velocity magnitude) but is usually better than >> one degree for speeds greater than about 10 kilometers per hour. >> The course is not necessarily the same as the heading or direction >> in which the GPS receiver, or the platform on which it is mounted, >> is pointing. A single-antenna GPS receiver cannot determine >> heading. However, a compass can provide this information and as >> mentioned earlier, some GPS receivers incorporate an electronic >> compass, usually a two-axis sensor. Some receivers have three-axis >> sensors that give relatively accurate bearings even if they are >> slightly tilted." >> >> The article can be found here: >> >> http://www.gpsworld.com/gps/the-magnetic-compass-and-gps-828 >> >> -- Richard Langley >> >> Quoting Alexandre E Eremenko : >> >>> >>> Lu, >>> >>>> The problem with "GPS as compass" is that GPSs can only determine >>>> position. >>>> Everything else that a GPS might show (especially direction of >>>> movement) is derived from a succession of positions. >>> >>> This was exactly what I thought when I was shown this "GPS compass". >>> One was supposed to turn the GPS device (like a compass) in certain >>> direction and it told you the asimuth of this direction... >>> with the error of sevral 10's of degrees:-) >>> >>> (I did not even need a compass to see this, an analog watch and >>> the Sun was enough). >>> >>> I imagine some people who believe in technology, carry only GPS >>> with them, and use this info without even looking at the Sun:-) >>> >>> Alex. >>> >>> >>> >>> >> >> >> >> ----------------------------------------------------------------------------- >> | Richard B. Langley� � � � � � � � � � � � � � E-mail: >> lang@unb.ca� � � � | >> | Geodetic Research Laboratory� � � � � � � � � Web: >> http://www.unb.ca/GGE/ | >> | Dept. of Geodesy and Geomatics Engineering� � Phone:� � +1 506 >> 453-5142� | >> | University of New Brunswick� � � � � � � � � Fax:� � � +1 506 >> 453-4943� | >> | Fredericton, N.B., Canada� E3B 5A3� � � � � � � � � � � � � � � � >> � � � � | >> |� � � � Fredericton?� Where's that?� See: >> http://www.fredericton.ca/� � � | >> ----------------------------------------------------------------------------- >> >> >> >> >> >> >> ----------------------------------------------------------------------------- | Richard B. Langley E-mail: lang@unb.ca | | Geodetic Research Laboratory Web: http://www.unb.ca/GGE/ | | Dept. of Geodesy and Geomatics Engineering Phone: +1 506 453-5142 | | University of New Brunswick Fax: +1 506 453-4943 | | Fredericton, N.B., Canada E3B 5A3 | | Fredericton? Where's that? See: http://www.fredericton.ca/ | ----------------------------------------------------------------------------- ----------------------------------------------------------------------------- | Richard B. Langley E-mail: lang@unb.ca | | Geodetic Research Laboratory Web: http://www.unb.ca/GGE/ | | Dept. of Geodesy and Geomatics Engineering Phone: +1 506 453-5142 | | University of New Brunswick Fax: +1 506 453-4943 | | Fredericton, N.B., Canada E3B 5A3 | | Fredericton? Where's that? See: http://www.fredericton.ca/ | -----------------------------------------------------------------------------