RU2333507C2 - Method for ionosphere range error detection within two-frequency measurements - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: invention refers to methods of ionosphere range error elimination in radio-navigational receivers. Proposed method implies that linear combination of range measurements is created to eliminate regular errors and detect ionosphere errors, followed by local modelling of vertical ionosphere range errors within consumer area in the form of Taylor limited sequence of several variables with the degrees not exceeding two, creation of combined equations associating stated linear combinations with local error modelling indices, solution of the said redundant combined linear equations with least squares method whereat exact Doppler increments on two coherent frequencies f₁ and f₂ are applied instead of rough code pseudorange measurements.

EFFECT: elimination of ionosphere measurement errors.

Description

The invention relates to the field of improving the accuracy of satellite navigation, in particular, to methods for eliminating ionospheric measurement errors in radio navigation receivers.

In any receiver of consumer navigation equipment (NAP), pseudorange (PD) to each visible satellite and pseudo Doppler integrals (PDI) are measured. PDIs are PD increments at integration intervals Δt of carrier phase incursions. The errors in the measurement of PD include systematic ones caused by the non-identity of the satellite reference oscillators and NAPs and the delay in the propagation of signals in the troposphere. These errors are independent of the carrier frequency, while the ionospheric delay in the first approximation, which is sufficient for two-frequency measurements, is inversely proportional to the square of this frequency [1, p. 84]. However, there is no mathematical dependence of the ionospheric delay in ranges from PDI to the prior art.

A known method and device for determining the parameters of the local ionosphere model for calculating ionospheric errors from two-frequency code measurements in GPS receivers is US patent No. 5428358 dated 06/27/1995 [2], which consists in forming a linear combination of these measurements to eliminate systematic errors and highlight ionospheric errors at the first frequency; building a local model of vertical ionospheric range error in the vicinity of the consumer’s location in the form of a limited Taylor series of several variables with degrees not exceeding two; the formation of a system of equations linking the above linear combinations with the coefficients of the local error model; solving the above redundant system of linear equations using the least squares method; graphic display of the generated map of vertical ionospheric error. This method allows to determine the ionospheric error of ranges by two-frequency pseudo-range-finding measurements, and the device that implements the method includes a two-frequency NAP receiver with meters of radio navigation parameters and a processor. Let's take it as a prototype.

However, this method has disadvantages, such as a high level of measurement noise and errors caused by multipath propagation of satellite signals due to reflections from local objects surrounding the NAP receiving antenna in the code measurements of the PD for the delay of the ranging code. This requires an increase in time to smooth them. In turn, an increase in this time leads to the need to take into account the temporal variability of the parameters of the ionosphere model: both vertical delay and spatial gradients by including additional unknowns among the estimated parameters. But an increase in the number of estimated unknowns worsens the conditionality of the task and leads to a deterioration in the random components of all estimates. In addition, the inter-frequency delays in the radio path of both the satellite transmitter and the NAP receiver have a level of units of meters, are manifested in measurements as their sum and cannot be separated during processing. Therefore, the delays in the NAP in accordance with the prototype must be calibrated in advance, and satellite delays are additionally included in the number of unknown model parameters. In accordance with the foregoing, the local model of the ionosphere according to the prototype method contains (6 + 4 + m) unknown parameters: 6 parameters of the spatial local model of the ionosphere “frozen” at a fixed point in time, 4 parameters of temporal variability during the accumulation of measurements and m - inter-frequency delays for m satellites. An increase in the number of satellites, the measurements of which are included in the processing to refine the parameters of the ionosphere model, does not give a beneficial effect, since each additional satellite introduces its inter-frequency delay into the number of unknowns to be estimated. Some compromise adopted in the prototype for processing information of 5 satellites is the measurement accumulation time of 90 ÷ 120 minutes.

All this limits the achievable accuracy and application of the prototype method and device in NAP to the field of expensive receivers, mainly stationary terrestrial ones. In this case, the actually achievable error in determining the ionospheric error in the range is more than 100 times higher than the potential error for two-frequency measurements.

The basis of the invention is the task of creating such a method in which the accuracy of the local model of vertical ionospheric error increases, the accumulation time of measurements decreases, the requirements for processor performance decrease, and ionospheric measurement errors are eliminated.

The problem is solved in that instead of coarse code measurements of pseudorange they use their exact Doppler increments at two coherent frequencies f ₁ and f ₂ .

Doppler measurements are only increments of ranges on the interval Δt, which does not allow us to relate them directly to the absolute values of ionospheric errors, but they have approximately 1500 times lower level of measuring noise and approximately 200 times lower level of multipath errors compared to AP measurements. In addition, the PDI does not contain (by definition) errors caused by inter-frequency delays in radio paths.

To connect the Doppler measurements with the ionospheric range error, use the factorization of this error in the form [1, p. 85]

where δD _V1j ^ion is the vertical delay at a frequency f ₁ at the subionospheric point, that is, the projection of the puncture point of a thin spherical ionospheric layer onto the Earth’s surface by a beam connecting the NAP to the jth satellite (j = 1, 2 ... m);

m is the number of visible navigation satellites;

ψ _j is the elevation angle of the j-th satellite above the NAP horizon.

Ф (ψ) is the slope factor, which is calculated according to the well-known formula for a thin spherical ionospheric layer, for example:

where R _e is the radius of the Earth (R _e ≈6400 km);

Н _ion - the height of a thin spherical ionospheric layer above the Earth’s surface (Н _ion ≈400 km).

Both factors in (2) are functions of time. The vertical delay depends on the illumination of the ionosphere (time of day), solar activity and changes in the geographical coordinates of the subionospheric point caused by the orbital motion of the j-th satellite. The value of the inclined beam function depends on the current satellite height ψ _j above the consumer’s horizon.

Differentiating both parts of the above expression (2) with respect to time, we obtain

where δV _1j ^ion is the ionospheric error of the radial velocity at a frequency f ₁ for the jth satellite.

In addition, unlike PD, used to determine the parameters of the local ionosphere model in the prototype method, to eliminate systematic measurement errors of pseudo-Doppler integrals and highlight the ionospheric error of radial velocity, for example, the following linear combination is used at the first frequency:

where λ ₁ and λ ₂ are the wavelengths of the radio signals emitted by the satellites at frequencies f ₁ and f _2, respectively;

_{PDI 1ji} and _{PDI 2ji} are pseudo- _Doppler integrals measured at these frequencies (carrier phase incursions) expressed in phase cycles (dimensionless quantities);

Δt is the PDI accumulation time, with index j correlating the variables with the satellite number, and index i with the time t _i .

In connection with the use of substantially more accurate measurements, they limit the time of their accumulation to the interval at which the state of the ionosphere remains practically unchanged. According to the results of experimental testing of the proposed method, this interval is several tens of seconds.

Thus, the obtained ionospheric errors of radial velocities δV _1ji ^ion are averaged over time at intervals of several tens of seconds, where the state of the ionosphere is considered unchanged - “frozen”, for example, according to the well-known arithmetic mean formula:

Based on the foregoing, the local ionosphere model is simplified by eliminating the terms of the Taylor expansion associated with time (4 unknown coefficients), as well as m unknown inter-frequency delays for m satellites, since the PDIs at different frequencies do not contain them. The latter circumstance allows us to use the measurements of all visible satellites to increase the accuracy of constructing a local model of the “frozen” ionosphere at intervals of several tens of seconds.

The time dependences of the estimates of the vertical delay of the remaining 6 Taylor expansion coefficients in the two-dimensional Taylor series (with discarding the terms of degree higher than the second) are used for additional (polynomial) smoothing of the time series of these estimates at large time intervals, thereby monitoring the state of the ionosphere.

In addition, for vertical ionospheric range errors, a simplified model is written in the form of a two-dimensional expansion in a Taylor series in the vicinity of the NA, according to the degrees of latitudinal and longitudinal deviations of the pion ionosphere points from the corresponding coordinates of the current position of the NA, limited by members not higher than the second degree:

where δD _V1 ^ion (x, y) is the spatial distribution function of the vertical ionospheric range error;

and _k are the model parameters, k = 0, 1 ... 5;

x and y are the values associated with the differences in longitudes and latitudes of the subionosphere point and NAP:

where φ ₀ , λ ₀ - geographical latitude and longitude of the NAP;

φ, λ — geographical latitude and longitude of the pionosphere point;

A is the azimuth of the subionospheric point;

α is the angle between the radius vectors of the NAP and the subionospheric point. This angle is calculated by the formula [2]

Substituting expression (7) into formula (4), performing time differentiation and equating the left-hand sides of equalities (4) and (5) for each j-th satellite, we obtain a system m (by the number of processed satellites) of equations for 6 unknowns a _k .

A linear combination of measured PDI (5), expressed in terms of the model parameters a _k , is written in the form

The partial derivatives h _jk with respect to the parameters of the model a _k have the form

формируют численным дифференцированием (3):Derivative

form by numerical differentiation (3):

where Ф (ψ (t ₁ )) and Ф (ψ (t ₂ )) are the values of the function calculated at time instants t ₁ and t _2, respectively.

и

вычисляют численным дифференцированием так же, как и

.Derivatives

and

computed by numerical differentiation in the same way as

.

To associate Doppler measurements with ionospheric range errors, the expression for the aforementioned error in the form of a spatial model is also differentiated by time and equations are obtained that relate time-smoothed linear combinations of Doppler measurements for j-satellites with vertical ionospheric range errors at j-pion ionospheric points, and the system of these m equations for 6 unknown parameters and _{k are} written in matrix form:

- вектор линейных комбинаций измерений в моменты времени t_i;Where

is the vector of linear combinations of measurements at time t _i ;

- вектор неизвестных параметров;

- vector of unknown parameters;

H is the matrix of partial derivatives;

i = 1, 2 ... n, where n is the number of measurements, and δV _1ji ^{ion is} calculated by the formula (5) for different times t _i .

The excess (overdetermined) system of equations (14) ((n · m)> 6) is solved in a known least-squares way:

Taking into account (6), the dimension of the matrix H decreases tenfold and becomes equal to k × m, where m is the number of processed satellites, k is the number of unknown model parameters (k = 6).

In the prototype method, H has a dimension, for example, of at least 15 × 1200 (it is believed that the ionosphere does not change in the 30 second interval).

In view of the foregoing, the matrix H is formed from the partial derivatives h _jk (12) calculated on the middle of the smoothing interval [t ₁ ; t _n ]:

Having determined the parameters of the local model of vertical ionospheric range error in the vicinity of the NAP location from the solution of system of equations (15), the obtained values of a _{k are} smoothed out by time polynomials at intervals of several tens of minutes. The smoothed model parameters are substituted into (7) and the value of the vertical ionospheric range error δD _V1j ^{ion is} _obtained . Multiplying the δD _V1j ^ion by the slope factor of the jth satellite, we obtain its oblique ionospheric range error.

A device that implements the method includes a two-frequency NAP receiver with meters of radio navigation parameters and a processor that solves both the navigation problem and the implementation of the aforementioned method for determining the ionospheric range error from two-frequency measurements, and pseudo-Doppler integrals obtained as code (standard) are used as radio navigation parameters a method of tracking carrier frequencies f ₁ and f ₂ , and codeless (semi-codeless) tracking frequency f ₂ .

Information sources

1. Dennis Odijk, Fast precise GPS positioning in the presence of ionospheric delays. Delft, 2002.262 pages.

2. United States Patent No. 5428358 Apparatus and method for ionospheric mapping. June 27, 1995

3. Schaer S. (1999), Mapping and Predicting the Earth's Ionosphere Using the Global Positioning System, Ph.D. Thesis, Astronomical Institute, University of Berne, 205 pages.

Claims (1)

A method for eliminating ionospheric errors in measuring ranges to visible satellites in radio navigation receivers of consumer equipment, which consists in measuring parameters of received satellite signals in radio navigation receivers of consumers, measuring ranges to visible satellites, and eliminating systematic measurement error from ranging by generating linear combinations these measurements at two known frequencies of received signals form a local model of vertical onospheric range error in the form of a vertical delay of the signal in the ionosphere and its latitude and longitude gradients in the vicinity of the consumer equipment, characterized in that Doppler range increments at two coherent frequencies are used as the measured parameters of the received satellite signals in the formation of a local model of vertical ionospheric range error in the form of increments of pseudorange over the integration intervals of the phase incursions of the carrier phase of the corresponding satellite signal, with By eliminating errors caused by interfrequency delays in the radio paths of the radio navigation receivers of consumer equipment for visible navigation satellites and limiting the accumulation time of measurements by the interval at which the state of the atmosphere remains practically unchanged, the parameters of the local model of vertical ionospheric range error for time moments of averaged measurements are smoothed, multiplied by the angle factor tilt of the corresponding satellite and when assessing the generated model of the ionospheric range error, I get inclined ionospheric error range to the corresponding satellite.