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The factual data on error of positioning in VRS GPS networks have been analyzed, where the mobile receiver is provided with VRS. The method of highly informative zone is suggested for removal of initial vagueness in selection of reference stations for purposes of development of VRS on the basis of minimum GPS network, composed of three reference stations. The recommendations on use of suggested method are given.

It is well-known that at present time a networked RTK (NRTK) system, characterized with high accuracy makes it possible to carry out positioning upon distances between stations, equal to 70 - 100 km [

• Data from network of reference stations are transferred to processing center;

• Data of network is used for calculation of models of ionosphere, troposphere and orbital errors;

• The ambiguity of estimate of phase of carrier is fixed taking into account the base distances of network;

• The factual errors of base distances are determined with cm accuracy on the basis of measurements of fixed phase of the carrier;

• To forecast the total error of positioning of the user’s mobile receiver the linear combination of errors’ models are used;

• VRS is to be developed in close vicinity of mobile receiver.

Till now the question on well-grounded choice of place of VRS in RTK network and also the question on choosing of RS for positioning of user’s MR are not solved in proper manner. Instead such heuristic criteria as “RS, which are closest to mobile receiver” and “closest placement of VRS to mobile receiver” are used. In this paper, we shall consider the possibility on substitution of heuristic criteria with information ones.

According to work [

As it is noted in the work [

Then, the initial information, received from this RS is

to be corrected as a geometric position data taking into account the networks correction, which accords with approximate position of MP. At present time there are such competing technologies, as NRTK with VRS, NRTK with pseudo-reference station (PRS), method of parameters of correction on field, and also the concept of “master-apprentice” (MAC), and individualized correction of the same type (i-Max) [

According to work [

According to the work [

1) Removal of ambiguities occurred due to double differencing of phase of carrier’s frequency;

2) Calculation of models of errors, which depends on distances;

3) Development of ionosphere model, based on a linear ionosphere combination;

4) Development of geometrical model, containing the troposphere and orbital errors and based on linear combination of them.

In this case the processing of data can be carried out in central processor or can be distributed between the central processor and users. As it is noted in work [

1) VRS should be located maximally close to MR of user;

2) For positioning of MR it is necessary to choose those RS which are located most closely to MR.

It is obvious that development of techniques and scientific technology require substitution of heuristic approaches by well-grounded scientific ones. Next we shall describe the proposed method for selection of place for development of VRS.

According to work [

According to our opinion, the interpolation method for determining of MR-s position error in principle removes the possibility of carrying out of high-accuracy positioning due to existence of its inherent error component— error of interpolation.

In view of abovementioned we suggest the information —interpolation method for determining the error of VRS positioning, the matter of which is following:

1) VRS should be located over MR, i.e. the places of their positioning coincide.

2) The interpolation of error is to be carried out and the interpolated assessment of the VRS (MR) position’s error is to be geometrically determined.

3) The maximum informative zone in the area of location of VRS (MR) is to be determined, where the maximum amount of information can be received upon realization of some order of transfer of information from RS relating its position upon given limiting conditions;

4) For each position of VRS (MR), by purposes of interpolating such a triplet of RS should be chosen, the maximum informative zone of which determines the points of placement of VRS (MR).

The mathematical grounding of suggested method is as follows. Assume that there are six RS and the MR with unknown coordinates (

As a first step we choose stations RS1, RS3 and RS5. Taking into account the noisiness of the channel’s signals due to effect of highly variable ionosphere error the techniques of multiple sending of data of own positions is used for transfer the information from RS to MR.

Thus, using the continual form of writing, the amount of information, received by VRS may be estimated as

where T—time of transfer of information from RS to

VRS;—maximum value of;—signal/noise ratio in transferred signal;—distance between RS and VRS;.

As a first approximation we have

where—signal/noise ratio at reference stations;

.

Then with we introduce the function of relation between the distance l and duration—:

Taking into consideration Formulas (1) - (3) we get

The limitation condition relating the total value of distances from MR to RS is formulated as follows

where;.

It should be noted, that in case of monotonous type of function 3, the condition (5) may be interpreted as limitation for total duration of information reception.

In view of Equations (4) and (5) we can compose following equation of non-conditional variation optimization:

where—Lagrange multiplier.

It is well-known, that the optimum function should meet the Euler’s condition

In view of Equations (6) and (7) we get

From formula (8) we derive

Taking into consideration the formulas (5) and (9) we get.

and

Taking into consideration the formulas (8) and (11) we have

Taking into account the negative value of we have. In this case the Equation (12) can be written as

Thus, upon known values of, assuming existence of linear scale of values of T, we can calculate l using formula (13).

Then, using the composed set of values where elements of this set increase linearly on index ithe elements of the set should be calculated.

Using the calculated values of, the geometrical construction of highly informative zone, which may or may not contain the MR, should be carried out.

Thus, the new notion, maximum informative zone, suggested in this work, makes it possible to remove the initial vagueness concerning selection of minimum network of RS for determining of error of mobile receiver’s position using the interpolation method.

It should be noted that in this case the two critical conceptions for determining of error of MR-s position (using criteria of maximum interpolation accuracy and maximum amount of information) don’t follow up the classic concept of multicriterial optimization, because the competition of criteria is absent here and requirement to meet one of them could mean fulfillment of other one.