CN108919316A - A kind of single station multisystem hardware delay estimation method symmetrically assumed based on partial sphere - Google Patents

Abstract

The invention discloses a single-station multi-system hardware delay estimation method based on local spherical symmetry assumption in the field of space technology. The technical solution is to use a single-station GNSS multi-system receiver to receive observation signals including Beidou, GPS, GLONASS and other satellite constellations, and obtain the ionospheric oblique TEC on each observation path through the method of phase smoothing pseudo-range ; At the same time, calculate the geometric information on each path, including the geographic latitude, geographic longitude and elevation angle of the penetration point; at each epoch, filter out all satellite combinations that meet the geometric conditions of local spherical symmetry, and construct the observation equation ;Use the least squares method to solve the combined hardware delay of the receiver and each satellite; according to the combined hardware delay, solve the oblique TEC on the path between the satellite and the receiver, and the vertical TEC at the position of the penetration point. The beneficial effect of the present invention is that, based on the assumption of local spherical symmetry and multi-system observation technology, the combined hardware delay of the satellite and the receiver can be calculated efficiently and accurately, and the real-time high-precision ionospheric TEC can be further obtained, and the ionospheric space environment can be improved. Monitoring and short-term forecasting are of great value.

Description

A single-station multi-system hardware delay estimation method based on local spherical symmetry assumption

technical field

The invention belongs to the field of GNSS hardware delay calculation method design, in particular to a single-station multi-system hardware delay estimation method based on local spherical symmetry assumption.

Background technique

The total electron content (TEC) of the ionosphere is not only an important parameter to describe the shape and structure of the ionosphere, but also an ionosphere correction parameter often used in precision positioning and navigation services. Nowadays, GNSS receivers are mainly used to measure TEC, and the biggest error source comes from the hardware delay of GNSS receivers and satellites. Therefore, how to accurately calculate these hardware delays is the basis for ionospheric research using GNSS.

Existing literature shows that the hardware delay of the satellite and the receiver is relatively stable, and it is generally regarded as a constant within one day. The commonly used estimation methods include: (1) factory calibration: use the calibrated GNSS receiver to calibrate the hardware delay of the GNSS receiver before leaving the factory; (2) rely on the calibration of the TEC model: map the vertical TEC published in the TEC model to It is the oblique TEC on the GNSS observation path, and interpolates according to time and location. According to the difference between the two, the combined hardware delay of the receiver and the GNSS satellite is solved, especially, sometimes depending on the satellites provided by other organizations For hardware delay data, directly deduct the hardware delay part of the satellite from the observed oblique TEC, and then make a difference between the observed TEC and the model TEC to obtain the hardware delay of the receiver; The GNSS ground observation network divides the plane where the heights of the satellite penetration points around the network are located into two-dimensional grids. Assuming that the vertical TEC in the grid is equal within the limited time and space, the observation equations are used to solve the problems in each grid. Vertical TEC and GNSS receivers with satellite hardware delays. The above three methods all have certain limitations. The first method is affected by the aging of GNSS satellites and receivers and the environment, and its hardware delay will no longer be the value at the time of factory calibration; the second method relies on ionization The accuracy of the ionospheric TEC model, where the description of the ionospheric model is not accurate enough, the calculated combined hardware delay is not accurate; the third method is suitable for the accurate solution of the local TEC, but it depends on the observation network composed of many stations , the calculation amount is large, and it is not flexible and simple enough.

Aiming at the limitations of the above three methods, we propose a single-station multi-system hardware delay estimation method based on the local spherical symmetry assumption. According to the characteristics of the ground-based GNSS TEC, this method reasonably assumes that it is centered on a single station. The sphere is locally symmetrical, making full use of the observation data of BDS, GPS and GLONASS constellations, establishing equations for all observation data that meet this assumption, and using the least square method to solve the combined hardware delay of the station and each satellite. This method only needs the observation data of one station, does not need to depend on the TEC model or observation data of other stations, the calculation amount is small, and it is independent, fast and flexible. Using the combined hardware delay, the vertical space over the station can be obtained. TEC provides stable and reliable data support for ionospheric morphology research and ionospheric correction.

Contents of the invention

Aiming at the limitations of the above-mentioned existing conventional methods in solving GNSS hardware delay, the present invention proposes a single-station multi-system hardware delay estimation method based on local spherical symmetry assumption.

A method for estimating the hardware delay of a single station multi-system based on local spherical symmetry assumption, characterized in that it specifically comprises the following steps:

Step 1: Use a single-station GNSS multi-system receiver to receive observation signals including Beidou, GPS, GLONASS and other satellite constellations, and obtain the ionospheric oblique TEC on each observation path through the phase smoothing pseudo-range method;

Step 2: Calculate the geometric information on each path, including the geographic latitude, geographic longitude and elevation angle of the penetration point;

Step 3: In each epoch, select all satellite combinations that meet the geometric conditions of local spherical symmetry, and construct the observation equation;

Step 4: Use the least squares method to solve the combined hardware delay of the receiver and each satellite; and according to the combined hardware delay, obtain the oblique TEC on the path between the satellite and the receiver, and convert it into the position of the penetration point according to the mapping function Vertical TECs.

In step 1, the formula for calculating the ionospheric oblique TEC is:

Among them, the superscript i represents the GNSS satellite number, the subscript t represents the time, the subscripts 1 and 2 represent the two carriers of GNSS, and the subscript obs represents the observed value, is the oblique TEC observation value of the ionosphere on the GNSS receiver observation path from the i-th satellite to the ground at time t (the unit is TECU, 1TECU=1.0×10 ¹⁶ electrons/m ² ), c is the speed of light, f ₁ and f ₂ represent the two carrier frequencies of GNSS satellites respectively, and Respectively represent the phase observations of the No. 1 and No. 2 carrier frequencies of the i-th satellite at time t, and Then represent the corresponding pseudo-range values respectively, and N is the number of observation samples of the i-th satellite in a continuous observation arc.

Here, the oblique TEC contains hardware delay, and the relationship between it and the "real" TEC can be expressed as:

Among them, the subscript real represents the "real" value, It represents the true value of the ionospheric oblique TEC on the observation path of the GNSS receiver from the i-th satellite to the ground at the time t, is the sum of receiver hardware delay (B _R ) and satellite hardware delay (B ⁱ ), namely Their units are also TECU.

In step 2, the formulas for calculating the geographic latitude, geographic longitude and elevation angle of the penetration point over the station are as follows:

in, and are respectively the geographic latitude and geographic longitude of the i-th satellite at the height of the penetration point at the t-th moment, is the elevation angle relative to the GNSS satellite at the penetration point position, is the elevation angle of the ground relative to the GNSS satellite, ζ is the azimuth angle of the GNSS satellite relative to the station, _RE is the average radius of the earth, z is the height of the ionosphere penetration point, is the angle of the earth, θ ₀ and λ ₀ are the geographic latitude and longitude, respectively, of the ground station.

According to the elevation angle at the penetration point, the vertical TEC can be easily converted, the formula is as follows:

in, Represents the mapping function of the i-th satellite at time t, which is a function of the elevation angle of the penetration point,

In step 3, the local spherical symmetry condition is jointly determined by the elevation and azimuth angles between the two satellites. When the difference between their elevation angles is not greater than 10° and the difference in azimuth angles is not greater than 15°, the vertical TEC between them is considered Equally, this vertical TEC is the "real" TEC after removing the hardware delay. For any two satellites i and j satisfying the condition of local spherical symmetry, the observation equation between them is as follows:

Among them, i and j represent satellite numbers respectively, and Represent the mapping functions of the i-th and j-th satellites at time t, respectively.

Obviously, for a fixed combination of satellites i and j, their observation equations within a day are all about and There are a lot of redundant data in the equation of these two unknowns. In order to reduce computational redundancy, the average is taken at all times, and a simplified equation is obtained as follows:

Among them, T represents the observation sample number of this satellite combination, and denote the average values of the respective mapping functions in the i-th and j-th satellite combinations, respectively.

In step 4, based on step 3, the combination of satellites numbered i and j is recorded as the combination numbered k, and the simplified equations of each satellite combination can be combined into the following sparse matrix form:

Among them, M represents the number of combined hardware delays to be solved, K represents the number of satellite combinations, b _m represents the combined hardware delay of the m-th satellite and the receiver, and y _k represents the number i and j in combination k Combined observations from satellites: The K×M matrix F composed of elements f _ki is a sparse matrix, each row of which has only two non-zero elements, the row subscript k represents the serial number of the satellite combination, and the column subscript i represents the satellite with the number i, f _ki represents the average value of the mapping function of satellite i in combination k.

In this observation matrix FB=Y, only the vector B is an unknown quantity, which can be solved by the method of least squares.

The beneficial effect of the present invention is that based on multi-system observation conditions and local spherical symmetry assumptions, the resources of GNSS constellations such as Beidou, GPS and GLONASS are effectively used, and only one station can quickly and accurately calculate the number of stations and GNSS satellites. The combined hardware delay has the ability to solve the ionospheric vertical TEC in real time, and has important application value in the future ionospheric space environment monitoring.

Description of drawings

Fig. 1 is a graph showing the time-varying curves of the ionospheric oblique TEC observations of the Beidou-1 satellite calculated by the method provided by the present invention.

Fig. 2 is a distribution diagram of geographic longitude and latitude of ionospheric penetration points calculated by the method provided by the present invention.

Fig. 3 is a time-varying diagram of the elevation angle and azimuth angle of two satellites calculated by the method provided by the present invention.

Fig. 4 is a histogram of the combined hardware delay of the single-station receiver and the GNSS satellite within one day calculated by the method provided by the present invention.

Fig. 5 is a curve diagram of the ionospheric vertical TEC of the Beidou-1 satellite calculated by the method provided by the present invention over time.

Fig. 6 is a graph showing the time-varying curve of the single-station ionospheric vertical TEC calculated by the method provided by the present invention.

Detailed ways

The preferred embodiments will be described in detail below in conjunction with the accompanying drawings. It should be emphasized that the following description is only exemplary and not intended to limit the scope of the invention and its application.

Taking the data of a station that supports three-system GNSS observations as an example, it can simultaneously receive data such as epochs, pseudoranges, and phases of Beidou, GPS, and GLONASS satellite constellations, and perform the following steps:

Step 1: Use the differential phase observations of each GNSS satellite to smooth the differential pseudoranges to obtain the ionospheric oblique TEC:

Here, taking Beidou satellite No. 1 (i=1) as an example, its two carrier frequencies are f ₁ =1575.42MHz, f ₂ =1227.6MHz, and the speed of light c=2.99792458×10 ⁸ m/s, at t= The two phase observations at time 1 are It is a geosynchronous satellite and can be observed throughout the day, and it has a total of N=2733 observations in one day.

Among them, i=1,2,...,2733, N=2733, and Respectively represent the pseudo-range observations of the two frequencies of No. 1 satellite at time t, and Respectively represent the phase observations of the two frequencies of the No. 1 satellite at time t. According to the method of smoothing the pseudorange difference by phase difference, the ionospheric oblique TEC observation value of the No. 1 satellite at the first moment is obtained, and its value is about -34.35TECU.

Fig. 1 shows a time-varying graph of ionospheric oblique TEC observations of Beidou-1 satellite obtained by a single-station multi-system hardware delay estimation method based on local spherical symmetry assumption provided by the present invention.

Step 2: Here still take the observation information of Beidou-1 satellite at the first moment as an example, based on the station coordinates (geographic latitude θ ₀ =18.35°, geographic longitude λ ₀ =109.62°), the ground elevation angle and azimuth angle are respectively and The height of the penetration point from the ground is 450km, and the calculated geometric parameters are as follows:

(1) Earth angle

(2) Geographical latitude of penetration point

(3) Geographic longitude of penetration point

(4) Penetration point elevation angle

Fig. 2 shows the distribution map of the geographical longitude and latitude of ionospheric penetration points calculated by the method provided by the present invention.

In step 3, according to the judging condition of local spherical symmetry, the qualified satellites are combined in pairs, still taking Beidou No. 1 satellite (i=1) as an example, it and GPS No. :43:50 The first combination (k=1) that satisfies the condition of local spherical symmetry is formed at the moment, and the parameters are:

y ₁ =-19.26.

The observation equation at this moment is as follows:

C01—G25:

Throughout the day, these two satellites have a total of 86 moments satisfying the local spherical symmetry condition, and their observation equations at each moment are averaged to obtain a simplified equation as follows:

C01—G25:

Fig. 3 is a time-varying diagram of the elevation angle and azimuth angle of two satellites calculated by the method provided by the present invention. "C01" and "G25" in the figure represent Beidou No. 1 satellite and GPS No. 25 satellite respectively. They are satellite numbers expressed in the form of three-digit "SNN". The initial letter "S" indicates the satellite constellation, " C", "G" and "R" represent Beidou, GPS and GLONASS satellite constellations respectively, and the 2-3 characters represent the serial number of the satellite in the constellation. The part sandwiched by two vertical dotted lines indicates the observations satisfying the condition of local spherical symmetry.

Step 4: For the Beidou-1 satellite in step 3, there are a total of 8 satellites that can form observation equations with it, and they are G02, G14, G17, G19, G25, R06, R11 and R21 in turn, and their respective simplified equations They are as follows:

C01—G02:

C01—G14:

C01—G17:

C01—G19:

C01—G25:

C01—R06:

C01—R11:

C01—R21:

A total of 66 satellites were observed throughout the day, including 13 Beidou satellites, 30 GPS satellites and 23 GLONASS satellites. There are a total of 256 satellite combinations available. By combining all the observation equations, a system of equations containing 66 unknowns can be obtained. This is an overdetermined system of equations that can be solved directly using the method of least squares. The result of the solution is an optimal estimate of the combined hardware delay of the ground receiver and each GNSS satellite.

The combined hardware delay of the single-station receiver and the GNSS satellite within one day calculated according to the method provided by the present invention is shown in the histogram in FIG. 4 .

The oblique TEC on the path from the ground to the GNSS satellite can be obtained by directly subtracting this combined hardware delay from the observed oblique TEC. Still taking Beidou-1 satellite as an example, its oblique TEC can be expressed as the following formula:

Correspondingly, according to the transformation of the mapping function, the vertical TEC at the height of the penetration point can be obtained:

As shown in FIG. 5 , the ionospheric vertical TEC of the Beidou-1 satellite calculated according to the method provided by the present invention varies with time.

Fig. 6 is a graph showing the time-varying curve of the single-station ionospheric vertical TEC calculated by the method provided by the present invention.

The above is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed in the present invention can easily think of changes or Replacement should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.

Claims (5)

1. A single-station multi-system hardware delay estimation method based on a local spherical symmetry hypothesis is characterized by comprising the following steps:

step 1: receiving observation signals including satellite constellations such as Beidou, GPS, GLONASS and the like by using a single-station GNSS multi-system receiver, and obtaining the ionized layer inclined TEC on each observation path by a phase smoothing pseudo range method;

step 2: calculating geometric information on each path, including geographic latitude, geographic longitude and elevation of the penetration point;

and step 3: screening out all satellite combinations which accord with the geometric conditions of local spherical symmetry on each epoch, and constructing an observation equation;

and 4, step 4: solving the combined hardware delay of the receiver and each satellite by using a least square method; and obtaining the inclined TEC on the paths of the satellite and the receiver according to the combined hardware delay, and converting the inclined TEC into the vertical TEC of the penetration point position according to a mapping function.

2. The method for estimating hardware delay of single station and multiple systems based on local spherical symmetry hypothesis according to claim 1, wherein in the step 1, the calculation formula of the ionosphere tilted TEC is:

where the superscript i denotes the GNSS satellite number, the subscript t denotes the time of day, the subscripts 1 and 2 denote the two carriers of the GNSS, the subscript obs denotes the observations,ionospheric bias TEC observation values (unit TECU, 1TECU is 1.0 × 10) on GNSS receiver observation paths from the ith satellite to the ground at the time t¹⁶Electron/m²) C is the speed of light, f₁And f₂Respectively representing the two carrier frequencies of the GNSS satellites,andphase observations at time t of carrier frequencies No. 1 and No. 2 of the ith satellite respectively,andthe corresponding pseudo-range observations are respectively represented, and N is the number of observation samples of the ith satellite in a continuous observation arc.

3. The method for single-station multi-system hardware delay estimation based on the local spherical symmetry hypothesis as claimed in claim 1, wherein in step 2, the calculation formula of the geographical latitude, the geographical longitude and the elevation of the penetration point position above the station is as follows:

wherein,andrespectively the geographical latitude and the geographical longitude of the ith satellite at the point of penetration height at time t,is the elevation angle relative to the GNSS satellites at the point of penetration,then the elevation angle on the ground relative to the GNSS satellite, ζ is the azimuth angle of the GNSS satellite relative to the station, R_EIs the average radius of the earth, z is the height at which the ionosphere penetration points are located,is the angle of the earth's sphere,θ₀and λ₀Respectively, the geographical latitude and longitude of the ground station.

4. The local sphere symmetry assumption-based single-station multi-system hardware delay estimation method according to claim 1, wherein in step 3, for any two satellites i and j observed at time t and meeting the local sphere symmetry condition, the observation equation between them is as follows:

wherein i and j represent the satellite number, f_t ⁱAnd f_t ^jRespectively representing the mapping functions of the ith and jth satellites at time t,is the combined hardware delay of the receiver and the satellite, which is the receiver hardware delay (B)_R) And satellite hardware delay (B)ⁱ) To sum, i.e.

To reduce computational redundancy, the simplified equation after averaging all the moments is as follows:

where T represents the number of observation samples for this satellite combination,andrespectively representing the average values of the mapping functions in the ith and jth satellite combinations.

5. The method for single-station multi-system hardware delay estimation based on the local spherical symmetry hypothesis as claimed in claim 1, wherein in step 4, a combination formed by satellites numbered i and j is denoted as a combination numbered k, and simplified equations of the satellite combinations can be combined into a sparse matrix form as follows:

wherein M represents the number of combined hardware delays to be solved, K represents the number of satellite combinations, b_mDenotes the combined hardware delay, y, of the m-th satellite and the receiver_kRepresents the combined observations of satellites numbered i and j in combination k:from the element f_kiThe K M matrix F is a sparse matrix with only two non-zero elements in each row, the row index K indicating the serial number of the satellite combination, the column index i indicating the satellite numbered i, F_kiRepresenting the mean of the mapping function for satellite i in combination k.

In this observation matrix FB ═ Y, only the vector B is an unknown quantity, and can be solved by the least square method.