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It is noted that necessity of further increase of accuracy of GPS positioning systems requires de-velopment of more perfect methods to compensate information losses occurred due to residual ionospheric delay by using optimization procedures. According to the conditions of formulated optimization task, the signal/noise ratio in measurements of zenith wet delay depends on the second order ionospheric errors, geographic latitude and day of year. At the same time if we assume that the number of measurements at the fixed geographic site is proportional to geographic latitude and if we accept existence of only two antiphase scenarios for variation of residual ionospheric delay on latitude normed by their specific constant, there should be optimum functional dependence of precipitated water on latitude upon which the quantity of measuring information reaches the maximum. The mathematical grounding of solution of formulated optimization task is given.

As it is noted in the work [

The tropospheric delay reaches 2.5 m in zenith direction, or 25 m upon 5˚ elevation angle and hardly can be compensated. In its turn, the tropospheric delay contains hydrostatic component (by percentage reaching 90%) and wet delay. The hydrostatic delay can be determined by measuring the atmospheric pressure at the antenn location zone. The wet delay cannot be determined by only using the ground measurements. As it is noted in the work [

But in order to carry out the true analyses of error generated by such delays, one should know the amount of the wet delay in zenith direction. According to the work [

1. Model of MOPS;

2. Hopfield’s model;

3. Mendes’s model.

In all abovementioned models the root mean square error decreases by the increase of the geographic latittude, because the tropics are featured by the higher level humidity, therefore, by big amount of wet delay.

As it was noted above, at present time the ionospheric delay of GPS signals can be removed on the whole. According to the work [

where

At the same time, the necessity of further increase of accuracy of GPS positioning systems requires more compensation of effect of ionospheric delay. The residual ionospheric delay, named also as an ionospheric delay of the second order, is generated as a result of interaction of ionosphere and the Earth’s magnetic field, and depends on the total amount of electrones in declined direction, parameters of the magnetic field, the angle between the magnetic field and direction of signal’s propagation.

As it is noted in the work [

As it was noted above, the main non-removable delay GPS signal is the wet delay.

According to the work [

where

In model researches, the dimensionless coefficient

where

According to the work [

where

Obviously, concerning the chosen day

Taking into account the Formulas (3), (5), the ratio of signal/noise

where

where

As it can be seen from Formula (7),

Now we consider the following optimization task. Assume that the measurements of

Integrating the Formula (9) along all the values of

Let us introduce the searched function

which can be determined alternatively as

or

where

We assume that functions

where

Taking into account the Formulas (10), (11) and (14) we can compose the following functional of unconditional variation optimization

where

In order to determine the optimum function

Taking into the Formula (16) we get

From the Formula (17) we can find

Taking into consideration the Formulas (14) and (18) we find

From the Formula (19) we get

Using the Formula (20) we can get the value of the Lagrange multiplier

Taking into consideration the Formulas (17) and (21) we get

From the Formula (22) we find

Therefore, upon function (23) the functional (15) reaches its extremum value.

In order to determine the type of extremum, we should calculate the following second derivative

It is not difficult to check out that Formula (24) gains the negative value, i.e., upon condition (23) the target functional (15) reaches its maximum. Hence, upon the functional dependence (12) the informativeness of held measurements can reach its maximum. But its well-known that the increase of

where

Taking into account (17) and (15) we get

Using the above described method we can determine that the functional (26) will reach its maximum upon condition

In this case in order to determine the type of extremum we should compute the following second derivative

From Formula (28) we get

Because Formula (28) reaches the negative value, the maximum informativeness could be reached upon condition (12), but the number of measurements in series can be determined in line with Formula (25).

Hence, informativeness of measurements carried out on geographical latitudes to determine the zenith wet delay can reach its maximum upon meeting of two conditions:

1. The total amount of precipitated water

2. The number of measurements in series should decrease by the increase of latitude.

A. Sh.Mehdiyev,R. A.Eminov,N. Y.Ismayilov,H. H.Asadov, (2015) Research of Impact of Geografical Latitute and Residual Ionospheric Noises on Informativeness of Measuring of Zenith Wet Delay of GPS Signals. Positioning,06,44-48. doi: 10.4236/pos.2015.63005