need to refine estimated time of arrival calculation

RoyHB · 2009-10-30 16:14:16

The problem:

I collect a series of speed observations from a moving object. The observations are collected about every 30 minutes.
The speed of the moving objects can vary quite a bit, but when the observations do vary that tends to be indicative of a trend.
i.e. if the speeds have been 30kph/26kph/32kph and then they consistently begin to fall i.e. 27kph/25kph/26kph/24kph/23kph
that often indicates that they will continue to fall for some period.

Currently, I average all the speed observations and use the historical average to calculate an estimated time of arrival at a point. This is less than satisfactory as it simply assumes that data gathered in the past will indicate what future data will be and for this application that is not necessarily true.

I would like to enhance the algorithm to take account of the likelyhood that current (instantaneous or recent) speed may be indicative of
a trend. As background - one of the major determinants of speed achievable in the future is changing weather conditions - but it would be too complicated for me to extract the most relevant weather measures from forecasts and try to apply them to a prediction.

This seems, on the surface, like a simple problem. If I calculate the overall average of all data points, then I calculate the average of the
most recent (n) points, then adjust the overall average based on the recent average I will sometime achieve a more accurate ETA.

Before I take my mathematically uneducated approach I'd like to ask those of you with a more sophisticated appreciation of math what the "proper" way
would be to achieve my ambition of a calculated ETA that is more accurate than one based purely on historical data.

I'm hesitant to use my simple approach because I think that averaging the results of multiple averaging may be a meaningless and misleading method.

The only additional info available (in addition to measured historical speed) is the approximate maximum speed that the object can attain.

bobbym · 2009-10-31 08:14:54

Hi RoyHB;

I am not saying I can solve it but could you provide a detailed example where you use your method. I would like to see it.

RoyHB · 2009-11-04 17:38:20

A sailboat is going on a circuitous route from point A to B.
The speed of the sailboat varies quite a bit as the wind strength changes.

I know the approximate distance from any point along the route to the end of the route,

I'll ignore for now the problem that a sailboat sometimes can't proceed directly from point A to point B because it must
sail on headings dictated by the wind angle.

At any given time I can calculate the approximate distance yet to be traversed - I assume that the boat will proceed to the 'next'
point along the perfect route and from there along the 'perfect route' to the end.

So I know a distance, I know an instananeous speed and I know all the recorded speeds since the start of the journey.
If pressed I could probably build a table that would show the possible speeds the boat could attain and the estimated probability
of travelling at each of those speeds (too complicated for this application).

What I'm after is a way to construct a speed to use in calculating the estimated time of arrival that will yield a best effort guess based
on my knowledge of speeds achieved so far.

A sailboat travelling along a known path is probably as good a model as any of illustrating the problem but it could be any mode of transport.
i.e. it could apply to a car that intermittently (but unpredictably) travels slowly in heavy traffic and at a speed which is also affected by road quality,
varying speed zones and other factors. In each case, the historical speed of the journey is known but the future speed potential is not.

Whether you can solve the problem or not, just discussing it may help me to arrive at a best achievable solution.

Thanks for letting me get this off my chest :-)

RoyHB · 2009-11-04 17:40:44

A very senior meteorologist once told me that the statistically most accurate way of forecasting what the weather will be in one hour is to assume that it will be the same as it is at present. I guess that statement has influenced my desire to use the instantaneous and historical data in arriving at an estimate for this problem.

MathsIsFun · 2009-11-04 18:22:51

RoyHB wrote:

... what the weather will be in one hour is to assume that it will be the same as it is at present ...

That sounds seductively correct! But surely if it is evening you could guess a slight drop in temperature?

I think you may get improved results by modeling your boats within a computer program.

If you say there are trends of increasing or decreasing speed, then what is the typical duration of that increase or decrease? Examine your data to see if it can help you. Hopefully there is some pattern there that you can recognize and use.

bobbym · 2009-11-04 22:02:42

Hi;

Your problem resembles a download or a tape counter problem ( sort of like how we get a rocket to the moon ) that we solved a while back. For reasons that are difficult to explain the approach of extrapolating from the n most recent points is the way to go. With n to be determined empirically.

If you provide some actual data I will attempt to use our technique on your data. If not, I can only explain it graphically.

Math Is Fun Forum

#1 2009-10-30 16:14:16

need to refine estimated time of arrival calculation

#2 2009-10-31 08:14:54

Re: need to refine estimated time of arrival calculation

#3 2009-11-04 17:38:20

Re: need to refine estimated time of arrival calculation

#4 2009-11-04 17:40:44

Re: need to refine estimated time of arrival calculation

#5 2009-11-04 18:22:51

Re: need to refine estimated time of arrival calculation

#6 2009-11-04 22:02:42

Re: need to refine estimated time of arrival calculation

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