RU2453868C1 - Improved assessment of position for receiving device of global navigation satellite system - Google Patents

Abstract

FIELD: radio engineering.

SUBSTANCE: invention relates to the field of satellite navigation systems, and namely to methods and systems to increase accuracy of assessing the position of a receiving device, and may be used in a global navigation satellite system (GNSS). The method to assess the position of a satellite receiving device (2) includes calculation of a matrix of weight coefficients and calculation of the estimated position of the satellite receiving device on the basis of the matrix of weight coefficients, at the same time calculation of the matrix of weight coefficients includes calculation of values indicating reductions of quality suffered by satellite signals, and noise in multiradiate distribution, and calculation of the matrix of weight coefficients on the basis of calculated values, besides, the specified values are related to parameters of distribution functions associated with various classes of quality reduction for each class of height of satellites, which have released the signals.

EFFECT: invention provides for the possibility to increase accuracy of assessment of the position of a receiving device using a simplified method of calculation for records of a matrix of weight coefficients.

12 cl, 7 dwg

Description

FIELD OF THE INVENTION

The present invention relates generally to satellite navigation systems, and more particularly, to improving position estimation for a receiver based on a global navigation satellite system (GNSS).

State of the art

FIG. 1 schematically shows a global navigation satellite system (GNSS) 1 comprising a plurality of satellites 4 emitting signals directed to a plurality of receivers 2 and local elements 3 (only one of which is shown in FIG. 1) communicating with each other in a known manner, therefore not described in detail. Each receiving device 2, in General, is included in the corresponding user terminal, configured to implement high-level applications based on the data provided by the receiving device 2. From a technical point of view, each receiving device 2 can be considered as a radio frequency (RF) input stage of the corresponding user terminal , namely, the network part of the user terminal, in contrast to the application part containing the user interface and the above high-level Appendicies.

Each satellite 4 transmits signals modulated by the pseudo-random sequence (PN sequence) characteristics of satellite 4. In addition, the signals emitted by each satellite 4 contain a navigation message, which in turn contains, in addition to data suitable for increasing accuracy in the calculation the position of the receiver, the ephemeris of the satellite, namely the mathematical functions that describe the satellite’s orbit in a very accurate way. Therefore, based on the information carried by the signals, each receiving device 2 calculates its distance from satellite 4. In particular, the receiving device 2 calculates the propagation time of the signal from satellite 4 to the receiving device 2, namely, the time difference between the emission time, which is time, at which satellite 4 emits a signal, and a reception time, which is the time at which receiver 2 receives the same signal. Subsequently, a rough estimate of the satellite-receiver distance is obtained by multiplying the propagation time by the speed of light; such a rough estimate of the satellite-receiver distance is known as pseudorange. The pseudoranges associated with the various satellites (generally at least four satellites, as shown in FIG. 2) are then used to calculate an estimate of the position of the receiver, as will be explained in more detail below.

In some cases, after determining the pseudorange, instead of calculating an estimate of its position, the receiving device 2 sends pseudorange to the local element 3, which is responsible for calculating the estimated position of the receiving device and sending the estimate back to the receiving device 2. In specific GNSS, commonly known as auxiliary global navigation satellite systems (A-GNSS), satellite ephemeris are provided to the receiver 2 and local elements 3, so that the receiver 2 should not extract them from the navigation tional messages. Based on the pseudorange and received ephemeris, the receiving device 2 calculates an estimate of its position. In specific A-GNSSs, commonly known as A-GNSS “using a subscriber device,” receiving device 2 only calculates pseudorange estimates and sends them to local element 3, which is responsible for all remaining operations (ambiguity resolution in fractional pseudorange measurements, position calculation, and etc.).

In more detail, the position of the receiving device represented by the position vector is calculated by N pseudo-ranges associated with N respective satellites whose signals are received by the receiving device 2. However, it should be noted that the pseudorange is the distance between the position of the corresponding satellite 4 during transmission and the position of the receiving device 2 during reception. Since the satellite clock and the clock are not perfectly synchronized, it is not possible to calculate the exact distance between satellite 4 and receiver 2.

Neglecting propagation errors, multipath interference, and receiver errors, the basic definition of pseudorange p ^J relative to the jth satellite is as follows:

(1)

(one)

(2)

(2)

Where:

- X ^j , Y ^j , Z ^j are the coordinates of the position of the j-th satellite;

- X, Y, Z are the coordinates of the position of the receiving device;

- c is the speed of light;

- δ ^j and δ are respectively the offset of the j-satellite satellite clock generator and the offset of the receiver clock generator; and

- R ^j is the geometric distance between the j-th satellite and the receiving device 2, and it is a function of time and also of the pseudorange p ^J (moreover, R ^{j is} calculated during transmission).

Coordinates X, Y, Z of the position of the receiving device form the above position vector of the receiving device, hereinafter indicated by [X, Y, Z]. The same applies to the coordinates X ^j , Y ^j , Z ^{j of the} position of the j-th satellite, the position vector of which is further indicated by [X ^j , Y ^j , Z ^j ].

Starting from equation (1), the position vector [X, Y, Z] of the receiver, which is an unknown quantity, can be calculated based on the calculated pseudorange R ³ , the vector [X ^j , Y ^j , Z ^j ] of the satellite position and the offset of the clock generator satellite δ ^J. In particular, the satellite position vector [X ^j , Y ^j , Z ^j ] is calculated based on the transmission time, which is the difference between the reception time and the propagation time and the received ephemeris, while the offset of the satellite clock generator δ ^{J is} calculated using the correction parameters included in the navigation message.

The relationship between the calculated pseudo-ranges, also known as observable values, and the position of the receiver is not linear, as shown by equation (1), therefore, known methods are used to obtain a linearized equation. According to the aforementioned known methods, the approximate position of the receiver is assumed, thereby the approximate position vector [X ₀ , Y ₀ , Z ₀ ] of the receiver is selected. This assumption implies that the position of the receiving device can be considered as the sum of the approximate position of the receiving device and the regulation coefficient. From a vector point of view, the position vector [X, Y, Z] of the receiver is the sum of the vector [X ₀ , Y ₀ , Z ₀ ] of the approximate position of the receiver and the control vector [ΔX, ΔY, ΔZ]. Due to this assumption, the unknown quantities to be calculated are the components ΔX, ΔY and ΔZ of the control vector [ΔX, ΔY, ΔZ], as well as the offset of the satellite clock generator δ.

In order to calculate the unknown values ΔX, ΔY, ΔZ and δ, equation (1) is expanded into a Taylor series truncated after the linear terms and centered around the approximate position vector [X ₀ , Y ₀ , Z ₀ ] of the receiver, thereby obtaining:

(3)

(3)

(4)

(four)

In equation (3), all unknown quantities (ΔX, ΔY, ΔZ, and δ) are on the right side of the equation, while the left side is known. Due to the presence of four unknown quantities, in order to calculate the position of the receiver, it is necessary to have at least four equations, i.e. it is necessary to receive signals from at least four satellites in order to calculate the corresponding pseudorange. In general, the number N of satellites whose signals are received by the receiving device varies from four to twelve depending on the geometry of the satellite constellation and the position of the receiving device, leading to a system of equations that has more equations than unknown quantities, i.e. obviously overridden. In fact, the observed values are affected by errors and noise, therefore, the system is inconsistent. This obvious inconsistency is solved by introducing the noise vector e , leading to the following system of linearized pseudorange equations:

(5)

(5)

Where:

- X is the vector [ΔX ΔY ΔZ δ] containing the coordinates of the control vector [ΔX, ΔY, ΔZ] associated with the approximate position vector of the receiver [X ₀ , Y ₀ , Z ₀ ], which represents the center of the Taylor series, and clock offset of the receiver δ;

- это матрица, имеющая четыре столбца и N строк, причем каждая строка ассоциирована с соответствующим спутником, сигнал которого принимается приемным устройством;-

is a matrix having four columns and N rows, with each row associated with a corresponding satellite, the signal of which is received by the receiving device;

- y is an N-dimensional vector containing N pseudo-ranges, each of which is derived from the corresponding geometric distance p ^J between the corresponding satellite and the receiving device, thereby depending on the approximate position of the receiving device; and

- the noise vector e is an N-dimensional vector containing errors of the components of the vector y .

It can be demonstrated that each row of the matrix can be expressed as follows:

(6)

(6)

зависит от высоты El_i и азимута Az_i соответствующего i-го спутника, а именно от положений приемного устройства и спутника, причем положение спутника является известной величиной либо из эфемерид, либо из данных, содержащихся в навигационных сообщениях.According to equation (6), each row of the matrix

depends on the height El _i and the azimuth Az _{i of the} corresponding i-th satellite, namely on the positions of the receiving device and the satellite, and the position of the satellite is a known value either from the ephemeris or from the data contained in the navigation messages.

вектора X. Фактически посредством случайного выбора приблизительного положения приемного устройства, а именно вектора приблизительного положения приемного устройства [X₀, Y₀, Z₀], можно вычислять соответствующую аппроксимацию

вектора y, а также аппроксимацию

матрицы

. Далее, начиная с системы уравнений (5) и пренебрегая вектором e, система уравнений

*

=

может разрешаться, и первая оценка

вектора X=[ΔX ΔY ΔZ δ] тем самым вычисляться, причем это вычисление заключает в себе вычисление вектора [X₁, Y₁, Z₁] оцененного положения приемного устройства.The well-known GNSS system of equations (5) is used to iteratively calculate the estimates

vector X. In fact, by randomly selecting the approximate position of the receiving device, namely, the vector of the approximate position of the receiving device [X ₀ , Y ₀ , Z ₀ ], the corresponding approximation can be calculated

vector y , as well as the approximation

matrices

. Further, starting with the system of equations (5) and neglecting the vector e , the system of equations

*

=

may be resolved and the first assessment

vector X = [ΔX ΔY ΔZ δ] is thereby calculated, and this calculation includes the calculation of the vector [X ₁ , Y ₁ , Z ₁ ] estimated position of the receiving device.

In fact, the vector [X ₁ , Y ₁ , Z ₁ ] of the estimated position of the receiver is defined by the sum of the vector [X ₀ , Y ₀ , Z ₀ ] of the approximate position of the receiver and the control vector [ΔX ΔY ΔZ] formed by the first three components of the calculated vector X .

вектора X. На основе нового приблизительного положения приемного устройства новый приблизительный вектор

вектора y и новая аппроксимация

матрицы

вычисляются, чтобы вычислять новую оценку

вектора X и, следовательно, новую оценку положения приемного устройства, посредством решения снова системы уравнений

*

=

. Описанная последовательность операций затем итеративно выполняется до тех пор, пока разность между последовательными оценками

вектора X становится не меньше заранее определенного порогового значения.Subsequently, the estimated position vector [X ₁ , Y ₁ , Z ₁ ] of the receiving device is used as the new approximate position of the receiving device for the subsequent iteration in calculating the estimate

vector X. Based on the new approximate position of the receiver, the new approximate vector

vectors y and a new approximation

matrices

computed to calculate a new grade

vector X and, therefore, a new estimate of the position of the receiving device, by solving again the system of equations

*

=

. The described sequence of operations is then iteratively performed until the difference between successive estimates

vector X becomes no less than a predetermined threshold value.

*

=

разрешается с помощью метода наименьших квадратов, который использует обобщенную инверсию аппроксимации

матрицы

и приводит к уравнению:In more detail, the system of equations

*

=

resolved using the least squares method, which uses a generalized approximation inversion

matrices

and leads to the equation:

(7)

(7)

^T - это транспонированная матрица от матрицы

, а апекс -1 указывает обратную матрицу, на которую она ссылается.Where

^T is the transposed matrix from the matrix

, and apex -1 indicates the inverse matrix to which it refers.

From the above, it can be taken into account that the position vector [X, Y, Z] of the receiver depends on the calculated pseudorange p ^J contained in the vector y and in the corresponding approximate vectors y . Since the pseudoranges associated with different satellites are affected by errors to different degrees, each pseudorange is calculated with a different degree of accuracy, which affects the calculation of the position of the receiver.

In order to improve the accuracy of the calculated position of the receiving device, it has recently been proposed to initialize the weight matrix when calculating the position of the receiving device. For example, US 2003/0036849 A1 discloses a restriction based on a tracking model for a GPS position in which a diagonal matrix of pseudorange observation weighting coefficients is expanded with diagonal entries that are records of reciprocal of pseudorange deviations.

The purpose and essence of the invention

The applicant drew attention to the fact that, from an architectural point of view, the solution proposed in the above patent application requires that the initialization of differential stations correct pseudorange and support the estimation of phase uncertainty.

The applicant also drew attention to the fact that, from a computational point of view, the solution proposed in the above patent application involves a calculation with a large amount of calculations of individual entries of the weight matrix based on the geographical information of the territory in which the receiving device is located, and this geographical information retrieved through high-altitude and photographic surveys.

Therefore, it is an object of the present invention to provide a simplified calculation method for recording matrixes of weights, moreover, this method enables improved estimation of the position of the receiver.

These and other objectives are achieved in accordance with the present invention, which relates to a method, system and software product, as defined in the attached claims.

Brief Description of the Drawings

The present invention is further described with reference to a non-limiting example and to the accompanying drawings, in which:

Figure 1 illustrates an auxiliary global navigation satellite system (A-GNSS);

Figure 2 illustrates a GNSS receiver and four satellites of the GNSS satellite constellation;

Figure 3 shows a histogram according to the present invention;

Figure 4 shows the probability density functions of Rice, Rayleigh, and Lou;

Figure 5 qualitatively shows the distribution of impairments in the height class according to the present invention and the corresponding distribution functions by the selection method, an array of indices and intervals of impairment according to the present invention;

6 shows a lookup table according to the present invention;

7 shows a comparison in terms of topocentric errors between the present invention and known technologies.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is obtained as a result of the following observation. GNSS receivers work well when there are line of sight (LOS) signals that are signals emitted by the satellite and propagating directly to the receiver without reflection and / or diffraction from external elements such as buildings. In a real environment, GNSS receivers are rarely based on LOS signals; more often they should consider copies (replicas) of signals emitted by the satellite, formed through the interaction of signals with a real medium. Each copy is subjected to a certain number of reflections and / or attenuations, thereby reaching the receiver with its own amplitude. In addition, each replica of the signal reaches the receiving device after propagation along a particular path, therefore, with its own delay relative to the time of emission of the signal, thereby interfering positively or negatively with other copies on the side of the receiving device. This phenomenon is known as multipath interference and causes signal degradation in received signals, in addition to the inherent attenuation during propagation, thereby reducing the performance of the receiving device.

From a practical point of view, receivers must manage efficiently the replicas having various delays in order to extract the information associated with the signals emitted by the satellites. In addition, in general, receivers receive signals from various satellites, and the multipath phenomenon affects all communication established between receivers and satellites. However, the signals emitted by various satellites are affected to varying degrees by multipath interference, and as a result, communications with satellites have varying degrees of reliability.

The idea underlying the present invention is to calculate the degradation experienced by the received satellite signals and due to multipath interference, and then calculate the weight matrix based on the calculated degradation.

The calculation method for recording the matrix W of the weights according to the present invention is described in detail below, moreover, this calculation can be performed either by the receiving device 2 or by a local element 3 responsible for calculating the estimated position of the receiving device.

The following system of equations corresponds to the system of equations (7) with initialization of the proposed matrix W of weight coefficients:

(8)

(8)

Deterioration of the received satellite signals due to their propagation in a real environment with the influence of multipath propagation, such as a city street or, to summarize, the so-called city canyons, and not in an ideal practically multipath-free environment, such as the environment in which the receiving device receives only LOS signals are determined using known methods. For example, the signal degradation of a received satellite signal can be calculated by subtracting or the residual attenuation (expressed in dB) experienced by the satellite signal in a practically non-multipath environment from the residual attenuation (expressed in dB) experienced by the satellite signal in a multipath effect propagation, or power (expressed in dB) of the received satellite signal, measured by the receiving device in an environment with the influence of multipath propagation, from the power and (expressed in dB) of the received satellite signal, measured by the receiving device in an environment practically free of multipath propagation. Additionally, since the signal power is generally measured in terms of a power-carrier-to-noise (CNR) ratio, which is the C / N ratio between the average modulated carrier power when receiving C and the average noise power when receiving N after filters receiver, the degradation can easily be calculated as the difference between the CNR of the signal (expressed in dB) measured in a real environment and the CNR of the signal (expressed in dB) measured in an ideal environment.

After the deterioration is calculated, statistical data processing is performed as described in detail below to determine values indicating the quality of the received signals.

In particular, the following data are available for each satellite, hereinafter referred to as satellite data: pseudorange of the satellite, deterioration of the signals emitted by the satellite, and the azimuth and altitude of the satellite. A histogram of the type shown in FIG. 3 is therefore calculated based on satellite data. In more detail, the signals received by the receiver are first classified into the number M of different altitude classes based on the height of the satellite that emits the signals.

For each height class, signals belonging to the height class in question are then further classified into the number A of different classes of degradation, which are common to all height classes, based on the corresponding calculated degradations. Widths of height and impairment classes can be arbitrarily selected. In the histogram shown in FIG. 3, the degradation classes are indicated on the abscissa axis, and the number of elements of each degradation class, namely, the number of signals with degradation signals falling into each degradation class, is indicated on the ordinate as a percentage of all received signals. In the example shown in FIG. 3, the height classes are five (M = 5) in number and, accordingly, are associated with the following ranges of the degree of height: 0-10, 10-20, 20-40, 60-90.

For each altitude class, the distribution along the abscissa axis of the corresponding numbers of signals with impairments of signals falling into the corresponding impairment classes is globally selected using many different distribution functions, in this example using the three well-known distribution functions of Rice, Rayleigh, and Lou shown in FIG. 4, and each of which is set, inter alia, by appropriate parameters, such as mean value and variance. Those of skill in the art can immediately understand that other distributions can be used, but the following description refers to the distributions of Rice, Rayleigh, and Lou.

The choice of these three distribution functions is due to the following. When a signal emitted by a satellite is interfered with by multipath propagation, attenuation of received signals can be modeled using the Rice distribution:

where v is the amplitude of the received LOS signal, K is the power ratio between the LOS signal and the signal generated by multipath interference, and I ₀ is the Bessel function of order 0.

Instead, when the signal emitted by the satellite cannot reach the receiver directly and, therefore, the receiver only receives signals generated by multipath interference, attenuation of the received signals follows the Rayleigh distribution, which is a specific case of the Rice distribution:

where v, K and I ₀ have the same meaning as in the Rice distribution.

In conclusion, when the signal emitted by the satellite is received directly by the receiving device, subject to attenuation due to materials such as leaves, the signal is called “shaded”, the attenuation of the received signal can be modeled using the distribution of Lu:

where v, K, and I ₀ have the same meaning as in the Rice distribution, while m is the mean value of the attenuation, and σ is the standard deviation.

It should be noted that the Lu distribution contains two components: one corresponds to the attenuated LOS signal according to the log-normal distribution and one corresponds to multipath interference according to the Rayleigh distribution.

Then, for each degradation class in each height class, one of the three corresponding distribution functions by the selection method, which is most suitable, namely, is closer to the number of signals, is associated with signal degradations falling into the corresponding degradation class. As shown in FIG. 5, this processing leads to the formation of an array of indices for each height class, in which each index is associated with a corresponding degradation class and serves as a sign of the best fit distribution function for such a degradation class.

Then, in each array of indices, subsequent groups of indices are identified, while each group contains only the same indices, and successive groups of indices contain different indices. Each group of identical indices thus identifies a corresponding group of successive degradation classes that are selected using the same best-fit distribution function, with each group of degradation classes referred to hereinafter as the degradation interval.

At the end of this process, for each height class and each degradation interval, the corresponding best-fit distribution function is identified, which has, among other things, its own variance.

Then, the search table is compiled based on the identified index groups, the search table having the number of rows equal to the number M of height classes and the number of columns equal to the number L of degradation intervals. In particular, each row is associated with a corresponding height class, each column is associated with a corresponding degradation interval, and each search entry is associated with a best fit distribution function parameter associated with a corresponding height class and degradation interval. Conveniently, each search entry is related, preferably practically equal (with the exception of minor adjustments) to the reciprocal of the variance of the corresponding distribution function by the best selection method. 6 shows a search table corresponding to the example shown in FIG. 3, namely with five rows and eight columns. You can take into account that in the lookup table degradation intervals (columns) are common to all height classes (rows). However, in general, different height classes may be associated with different degradation intervals, thereby leading to a lookup table in which columns are not common to all rows, and each row is associated with its own columns, which may be the same or different from columns associated with other rows, either by number, or by deterioration intervals associated with them, or both.

In conclusion, the aforementioned weighting matrix W is calculated based on the generated lookup table, wherein the weighting matrix W is a square matrix with the number of rows and columns equal to the number N of satellites “visible” to the receiving device. Preferably, the weighting matrix W is diagonal, with each diagonal entry being set equal to a search table entry corresponding to the height of the satellite associated with the diagonal entry, and the signal degradation of the received signal or a group of signals emitted by such a satellite. Other off-diagonal entries can be either equal to zero, as a result of which the weight matrix W is purely diagonal, or negligible compared to diagonal entries, as a result of which the weight matrix W is pseudo- or quasi-diagonal.

From a practical point of view, the weighting matrix W assigns to each of the above satellite data and, in particular, each pseudorange, a corresponding weighting coefficient related to the satellite height and signal degradation of the respective received signals in order to assign large weighting factors to the satellite data contained in the received signals, which are affected to a lesser extent by the phenomenon of multipath propagation and, therefore, which are less degraded and have a lower ation dispersion, and assign lower weights to others.

Extensive computer simulations have proven that the application of the present invention makes it possible to significantly increase the accuracy of estimating the position of the receiving device as compared to satellite receivers on the market that either do not perform weighting at all or implement other approaches with weighting, as generalized from the point of view of topocentric coordinate errors position in the table shown in Fig.7.

In conclusion, it is obvious that many modifications and variations can be made in the present invention, all of which fall within the scope of the invention defined in the attached claims.

In particular, the histogram can be calculated based on the deterioration of the signals received in the corresponding time interval by several receiving devices located in environments with the influence of multipath propagation, the time interval being equal, as an example, to the orbital period of the satellite constellation, thereby increasing the accuracy of calculating the dispersion and, as a result, evaluating the position of the receiving device.

In addition, the search table can be calculated statically or dynamically, namely, updated periodically, through periodic surveys and stored in the database. This second solution can advantageously be used in auxiliary GNSS, which includes auxiliary servers in local elements where such a database can be located.

Additionally, weights are sent to the receiver according to the position of the receiver, preferably when a receiver requests support. In this case, the support request contains a rough estimate of the position of the receiving device to enable the auxiliary server to scan the database and retrieve the appropriate weights that are sent back to the receiving device. Conversely, the extracted weights can be directly used by the support server in order to calculate the position of the receiver.

Claims (12)

1. A method for evaluating the position of a satellite receiver, comprising the steps of:
- calculating values indicating a decrease in quality experienced by satellite signals and due to interference in multipath propagation; and
- calculate the matrix of weights based on the calculated values; and
- calculate the estimated position of the satellite receiving device based on the matrix of weights;
characterized in that the calculation of the matrix of weights includes the steps in which:
- classify the received signals into altitude classes based on the height of the satellites that emitted the signals;
- for each height class, signals belonging to the height class are classified into quality degradation classes based on corresponding quality reductions, each quality degradation class has a corresponding number of elements determined by the number of quality reduction signals falling into the quality degradation class;
- for each height class, different distribution functions are identified that globally correspond to the distributions of the corresponding quantities of quality-decreasing signals falling into the corresponding quality-decreasing classes;
- for each height class, each quality reduction class is associated with one of the corresponding distribution functions, which satisfies a given criterion regarding the number of reduced quality signals falling into the corresponding quality reduction class; and
- calculate the matrix of weighting coefficients based on the values associated with the parameters of the distribution functions associated with the quality reduction classes. 2. The method according to claim 1, further comprising a step in which:
- for each height class, groups of successive quality reduction classes associated with the same distribution function are identified. 3. The method according to claim 1 or 2, in which the matrix of weighting coefficients includes diagonal entries, each of which is associated with a corresponding satellite, and in which the calculation of the matrix of weighting coefficients based on the values associated with the parameters of the distribution functions associated with the reduction classes quality, includes a stage in which:
- calculate each diagonal entry of the matrix of weighting coefficients based on the value associated with the distribution function parameter associated with the quality reduction class containing the quality reduction of signals from the corresponding satellite, and with the height class containing the height of the corresponding satellite. 4. The method according to claim 1 or 2, in which the parameter of the distribution function is the dispersion of the distribution function, and the value associated with the parameter is the inverse of the variance. 5. The method according to claim 1, in which various distribution functions include the distribution functions of Rice, Rayleigh and Lu. 6. The method according to claim 1 or 2, in which the matrix of weighting coefficients includes recording weighting coefficients, each of which is associated with a corresponding satellite, and in which the calculation of a value indicating a decrease in quality experienced by satellite signals from the corresponding satellite and due to interference with multipath propagation, includes stages in which:
- measure a value indicating the attenuation experienced by the satellite signal in an environment practically free of multipath propagation;
- measure a value indicating the attenuation of the satellite signal in the environment with the influence of multipath propagation; and
- calculate a value indicating a decrease in quality, based on the measured values. 7. The method according to claim 1 or 2, in which values indicating a decrease in quality due to interference during multipath propagation are calculated based on satellite signals emitted in a given period of time. 8. The method according to claim 1 or 2, in which the calculation of the estimated position of the satellite receiving device on the basis of the matrix of weights includes a stage in which:
- iteratively calculate the following system of equations:

Where

is a vector indicating the estimated position of the satellite receiver;

is a matrix of weights;

is a matrix with the number of rows equal to the number N of satellites, the signals emitted by them are received by the satellite receiver, and each row is associated with the corresponding satellite and has the form [cosEl _i cos Az ₁ cosEl _i cos Az _i sinEl _i 1], where El _i and Az _i are respectively the altitude and azimuth of the corresponding satellite;

is a transposed matrix

and

is a vector with N records, each of which is associated with a corresponding satellite, and the signals emitted by it are received by the satellite receiver, and each record is equal to the difference between the corresponding calculated pseudorange of the satellite and the calculated geometric distance between the satellite receiver and the corresponding satellite. 9. A satellite navigation system including a satellite constellation, a local terrestrial element, configured to communicate with satellites, and a satellite receiver, configured to communicate with satellites and a local terrestrial element; comprising a system for evaluating the position of a satellite receiving device, configured to implement the method according to any preceding paragraph. 10. The system of claim 9, wherein the system for evaluating the position of the satellite receiver is contained in the satellite receiver. 11. The system according to claim 9, in which the system for evaluating the position of the satellite receiving device is contained in a ground-based local element. 12. A storage device for a positioning system for a satellite receiving device contained in a satellite navigation system storing processor-executable instructions to cause a processor in the positioning system for a satellite receiving device to execute the method according to any one of claims 1 to 8.

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