WEBVTT
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welcome friends today i am going to discuss
on quality assessment of gps surveying as
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you know that during gps surveying we do collect
gps observables which is being processed to
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get the position of points and base line now
the position what we have derived out of gps
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observable or and the baselines that we have
got from the gps observable whether that is
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meeting our specification or not that means
whether these parameters has achieved the
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standards that we are looking for the particular
project or not that has to be assessed and
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that assessment is called the quality assessment
now in order to asset that quality we need
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to know first what are the different standards
that we follow for gps surveying then on the
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basis of the standard then we have to compute
some measures which will be tested on the
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basis of standards to find out the quality
or standard of the gps surveying so in this
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class we will be talking on first we will
talk on the standards of gps surveying and
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followed by the quality measures that we will
compute to identify the standard of our surveying
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or quality of our surveying
now the standard of gps surveying is being
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defined by the root mean square error for
position and it is the parts per million for
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the baseline so gps standard for gps surveying
we will define for position and baseline length
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and the position is defined by the root mean
square error and length by parts per million
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now these standards may vary from organization
to organization from country to country there
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is such no such unified standard available
all about the world but generally we considered
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the standard defined by fgcs federal geodetic
control
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subcommittee this is the organization that
is available in us so there standard we are
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considering in gps surveying as a standard
now the fgcs has defined the position standard
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in terms of root mean square as it is written
that is they have defined the horizontal and
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vertical actually the position may be planimetric
for planimetric position go for horizontal
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standards and may be independently vertical
or we may sometimes go together has the three
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d position
now fgcs has taken ninety five percent confidence
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level now what is this actually if we know
this is the position true position then the
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observed position should be ninety five percent
within the standards that has been defined
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suppose we have defined that now for fgcs
is for the planimetric they have defined an
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error circle or ellipse error circle let us
say when the component in x and y are same
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so now suppose this is the true position of
any point now and if suppose one meter is
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the error permissible error radius of the
error circle is one meter so if we draw a
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circle of one meter around the true position
p then the observed position in ninety five
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percent cases should be within this circle
then we will say that this set of observation
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follows the standards which we are looking
for now in case of vertical we do define one
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a line uncertainty line so plus minus this
so with with this the three d for three d
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we define a cylinder suppose this is the point
so around this point this is the error ellipse
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and this is the height uncertainty
so we will get a cylinder like this that means
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if our true position is this then we will
our a set of observation of which ninety five
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percent lies within this cylinder then we
will say that that set of observation has
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met this standard has required by our proset
there is an example for our proset horizontal
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accuracy we are looking for suppose one meter
planimetric accuracy and vertical accuracy
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suppose also we are looking for one meter
so in this cases we will a cylinder having
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this radius one meter and your one meter above
and one meter below this line so we will have
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a cylinder having height of two meter and
radius of one meter
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now if we have a set of measurement which
we if see that all of them are within this
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at least ninety five percent of them are within
this cylinder then that set of observation
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are making this criteria if less than ninety
five percents are not within this or if less
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than ninety five percent is within this then
we will say that this set of observation is
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not followed our standard so we will be need
to take better set of observation so that
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that condition made by this two our standard
so that is about the positioning standard
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so and as per this fgcs consideration so fgcs
positioning standards
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so which is considered to be at ninety five
percent confidence level and for planimetric
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position the position
we considered at the datum surface datum surface
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position
and for height may be orthometric height that
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means height above or it may be ellipsoid
height so height above and height it is height
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above datum surfaces under this consideration
the fgcs has defined four categories of millimetre
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standard centimetre standard decimetre standard
and meter standard so out of these again they
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have decided to have three under millimetre
one millimetre two millimetre five millimetre
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like that you can see here that centimetre
one two and five centimetre decimetre again
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one two and five centimetre and meter one
meter two meter five meter and ten meter
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so so centimetre again one two five centimetre
decimetre again one two five but in meter
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it is one two five and ten meter so this is
the way how they have given the standard this
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is what for the point position next for baseline
for baseline the
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standard has been defined standard has been
defined parts per million now how it is being
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we got it is the error permissible divided
by the length of baseline so this is the value
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which we have to get and we have to see this
value is what is amount and that should be
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compared with this standard again fgcs has
defined seven standards and they have termed
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this as order like a order then a order b
order c one c two one c two two then c three
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so now each of this having the parts per million
as given in the table that zero point zero
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one parts per million or we can say one is
to similarly if we say this is the
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parts per million as a fraction that is one
is to like this we can get all about detailed
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here in this table now what is this actually
let me explain that means if the baseline
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is order a a then we will be we will allow
an error of one millimetre in measuring a
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distance of one zero zero zero zero zero at
the millimetre so in measuring a distance
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of this millimetre we will allow a error of
one millimetre
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now this is means hundred kilometre so if
we measure a baseline of having length hundred
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kilometre and if we end up with a solution
which provides at error of one millimetre
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that means our measurement length can be plus
minus one millimetre so the measured distance
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between the two stations if the actual distance
between the two stations a and b hundred kilometre
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the distance between a and b is hundred kilometre
that is the true distance and if we measure
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the distance between a and b and we get the
distance measured hundred kilometre plus minus
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one millimetre d is equal to this that means
d ab d measured a b should be
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so if we get these things the measured distance
is equal to or more than this or equal to
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or less than this then we will say that d
our measurement is of the order of a
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so or the baseline we got is a order similarly
for other orders so there we can see one is
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to ten thousand c three which provides an
error of hundred parts per million that means
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if we measure a distance of ten meter we may
allow an error of one millimetre in measuring
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a distance of ten meter we are allowing an
error in measurement of one millimetre that
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is what is called c three now with this background
of the with the standard of gps surveying
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now we want to find out what is the quality
of our gps surveying
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so in order to do that we need to know three
parameters one is called precision another
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is called accuracy now if we have the true
value of the position or the length of the
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baseline then we can go for accuracy measurement
but if we do not have the actual value of
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the position or the length of the baseline
then we should go for precision now in case
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of position the precision will do test by
using the t test and that will depend upon
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number of observation if it is less than thirty
or more than thirty depending upon that we
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should follow these relation that t zero point
zero two five is called root of n square root
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of sigma x square plus sigma y square t this
is minus and n is less than thirty the meaning
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is that now sigma x and sigma y are the standard
deviation of the measurements suppose we have
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taken n measurements which is less than thirty
so of all these measurement we will get the
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mean and standard deviation so sigma x and
mean in y direction sigma y so these sigma
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x and these sigma y is this and is called
square of and is called root mean square error
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so this is root mean square error of the observed
data and that should be that should lie within
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this so if this is if the observation satisfy
these condition then we will go for test of
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this with standard standards
now we will see what is the value of this
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is called plus what is this value of this
now if it is suppose we have this thing as
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five centimetre then as per our previous definition
that it will be under the category of five
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centimetre so we can say that this is the
our accuracy or this is the standard of this
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so depending upon this value we will be telling
in that but before that we have to satisfy
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this similar to this if the number of observation
is more than thirty then we have to use this
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formula now for this is for two dimensional
case now if we see if we want to find out
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the three d position so instead of these we
have to take the root mean square error of
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x y and z
so this is the root mean square error of x
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y z position of the observed location and
we have to see this test saying what we done
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so in this way first we have to see that we
should test first the precision further it
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satisfy the fundamental criteria then we can
categories to the category of a standard now
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in case of baseline the we do find out the
value sigma x square sigma y square sigma
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z square now as you know that one will go
for gps surveying for a baseline so we will
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get del x del y del z that is if it is the
reference this is the rover with respect to
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rover about this baseline we will get along
with that we will get (Ref er Time: 22:00)
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so these are the standard deviation of the
parameter del x del y del z with respect to
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baseline with respect to baseline
so in case of baseline in case of baseline
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we have to take the ration of this and square
root of del x del y del z so this will provide
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a some value one is to something some value
that means and that we have to convert it
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in terms of parts per million and this we
have to check with this standard that is there
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with this and depending upon this value we
can say which order baseline is this one so
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this is on the basis of precision measurement
of the baseline as i told you that accuracy
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measures we will be taking and we will now
the true values of the position of the points
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suppose a point is having x t y t z t is the
known point now and the observed value for
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that is x bar y bar z bar then we will have
x t minus x bar square y t minus y bar square
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z t minus z bar square square root it is the
root mean square error of the point
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now we have to see what is the value of this
with the now for this is the three d position
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the and for two d position it will be this
is for only x direction this is for y direction
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this is for z direction so if we call it root
mean square error x this is this part x t
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minus x bar whole square similarly root mean
square error y t minus y bar square like this
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now then we define condition in some cases
we may assumed we may allow in our work root
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mean square in x should be equal to root mean
square in y direction then it is the circular
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error in that case the amount of error root
mean square error will be equal to one point
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four one four two root mean square error in
x direction or in y direction
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so ultimately it is the radius of the circle
which is defining the error circle that means
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now these value now we have to see what is
this value depending upon these value suppose
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it is two centimetre then from our chart we
can say two centimetre means this is the our
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standard of our measurement so in this way
we do we can compute the we can see what is
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the standard of our gps surveying now if it
is this value this is root mean square of
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z suppose this is three centimetre then we
can say that three d standard is three centimetre
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if the this value is two centimetre then we
can say planimetric standard is two centimetre
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in this way by comparing this table and computing
in this way we can say what is the standard
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of this gps surveying for baseline suppose
we know the this is the component of the baseline
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and true component along x direction true
component along y direction true component
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along z direction and suppose del x del y
del z are the observed component now from
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this we will be getting l estimated which
will be equal to del x square plus del y square
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plus del z square and this is the true l length
true which is del x t del y t
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now this l true minus l estimated is the error
in observant length and this error divided
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by l true provides us the value one is to
how much and that is to be compared with the
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standard table to know what is the standard
measurement of the baseline measurement so
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in this way how we can get the standard of
our survey work and if we find that the standard
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that we have found after measurement is meeting
the specification of our gps surveying proset
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objective has been achieved otherwise if the
proset objective has not been achieved that
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means if the standard that we have found is
less than what we are looking for our proset
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then we have to repeat whole our surveying
work and we have to improve our measurement
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to achieve this standard which project equipments
so in these way actually baseline can be analysed
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in two different ways one is called fixed
baseline analysis another is called repeat
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baseline analysis in fixed baseline analysis
only one a single baseline we will take only
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once and we will do this analysis in repeat
baseline analysis we will take observation
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of the same baseline repeatedly for two three
times and then we will go for this part of
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estimation and we will see whether our baseline
standard is meeting the proset objective or
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not with this i want to conclude but before
conclusion i want to summarize that the gps
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surveying parameters should be assessed in
order to find whether our gps surveying meet
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the objective of the proset demand or not
to test the quality of gps surveying parameter
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that is basically the position and the baseline
we need to first know the basic standard that
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is available in general that is varies from
place to place or organization to organization
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however the fgcs standards may be taken as
the general standard in order to and the fgcs
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has considered the ninety five percent confident
level as the basis for it's standard and for
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point position it is the root mean square
error and for the baseline it is the parts
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per million which has been taken as the standard
to define the standards and to test the quality
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of the gps surveying we need to measure the
precision or accuracy depending upon the availability
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of the true value or not and that has to be
compared with the standards that is being
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defined and from that comparison we will be
able to judge whether the gps surveying has
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meet the quality that is looking for the particular
proset
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we will be meeting in the next class which
will be on procedure for gps surveying first
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part
thank you very much