Single epoch pseudorange positioning with varying ionospheric delay

Abstract

A positioning method that takes into account frequently changing ionospheric delays. The method includes: (a) in the determination of pseudoranges associated with each signal received from various signal sources, in addition to parameters representing the position of the signal receiver and the clock drift of the signal receiver, a function representing environmental biases by one or more parameters; and (b) jointly solving the values ​​of the parameters of the function and the values ​​of the parameters representing the position of the signal receiver and the clock drift of the signal receiver. The environmental bias can be an ionospheric delay, which can be modeled by a function having parameters related to the ionospheric puncture point (IPP) of the received signal. The function can characterize the ionospheric delay as a function of the longitude and latitude variations from the signal source.

Description

Technical Field

[0001] The present invention relates to signal processing. In particular, the present invention relates to accurately processing signals transmitted from positioning satellites to determine pseudoranges (ie, the distance between a signal receiver and the transmitting satellite). Background Art

[0002] In global navigation satellite systems (GNSS) such as GPS, GLONASS, Galileo, and BeiDou, each satellite transmits a ranging signal (“navigation signal”) of a known format. Using these navigation signals, a receiver can accurately estimate its position based on measuring pseudoranges relative to a sufficiently large number (e.g., four or more) of such satellites. Accurate position estimation based on pseudorange measurements not only provides a better search range for phase measurements—which is essential for high-precision positioning (e.g., down to centimeter accuracy)—but it also significantly reduces the computational cost of achieving such high-precision positioning, in terms of time and energy. Pseudorange-based position estimation is widely used in GNSS in applications such as surveying, geophysics, and geodesy. However, estimating the position in a robust manner remains a challenging task because of the inevitable presence of various interference sources in the environment, including thermal noise in the receiver and various other interferences in the signal transmission path between the source satellite and the GPS receiver (“environmental biases”). One such interference is due to the ionosphere, which is a 85 km to 600 km thick layer of ions and free electrons in the upper part of the Earth's atmosphere. As a navigation signal travels through the ionosphere, it may experience scattering, which causes a delay in the signal ("ionospheric delay").

[0003] The position of a GPS receiver is typically estimated from snapshots of instantaneous GPS measurements using, for example, a first order approximation to the positioning equation and a generalized least squares method. The ionospheric delay can be modeled as the "RMS ionospheric range error".

[0004] In an article entitled "Ionospheric Time-Delay Algorithms for Single-Frequency GPS Users" on pages 325-331 of IEEE Transactions on Aerospace and Electronic Systems (3), J. Klobuchar discloses an empirical method for determining ionospheric errors. In the article, Klobuchar proposed having GPS satellites broadcast the parameters of his ionospheric model (the Klobuchar model) for single-frequency users. The Klobuchar model models the ionosphere as a thin layer of electron concentration at an altitude of 350 kilometers. Based on this assumption, Klobuchar calculated a "tilt delay", which is the delay experienced by the navigation signal entering the ionosphere vertically at the ionospheric pierce point (IPP) multiplied by a "tilt factor". Although the Klobuchar model aims to minimize user computational complexity and user computer storage, it ignores the varying nature of the ionospheric delay experienced by a rapidly moving receiver. For example, the ionospheric delay changes for a receiver as it moves from one location to another. Typically, Klobuchar parameters are updated at intervals greater than one day, during which the ionospheric delay becomes outdated due to inherent noise. More importantly, in high-precision positioning that combines pseudorange measurements with carrier phase measurements, excluding biases due to time-varying ionospheric noise is particularly important for accurate pseudorange position estimation. Summary of the invention

[0005] The present invention provides a positioning method that takes into account frequently changing ionospheric delays. This method is particularly suitable for navigation of fast-moving vehicles or unmanned aerial vehicles in cities or hostile areas. For example, a method of the present invention includes: (a) in the determination of pseudoranges associated with each signal received from various signal sources, in addition to parameters representing the position of the signal receiver and the clock drift of the signal receiver, a function representing environmental deviations by one or more parameters; and (b) jointly solving the values ​​of the parameters of the function and the values ​​of the parameters representing the position of the signal receiver and the clock drift of the signal receiver. In one embodiment, the environmental deviation can be an ionospheric delay, which can be modeled by a function having parameters related to the ionospheric puncture point (IPP) of the received signal. The function can characterize the ionospheric delay as a function of the longitude and latitude changes from the signal source.

[0006] According to one embodiment of the present invention, the method determines the terms characterizing the ionospheric delay by the following steps: (a) determining the position of each signal source; (b) determining the position of the receiver based on an initial estimate of the receiver position without considering environmental bias; (c) determining the position of the IPP of each signal based on the position of each signal source and the position of the receiver; (d) determining the terms in the function associated with each signal based on the position of the receiver and the position of the signal source; and (e) repeating steps (a) to (d) one or more times.

[0007] The method of the present invention uses a set of linear equations to jointly solve the parameter values ​​of the environmental bias, the position of the receiver and the position of the clock drift. The linear equations can be solved using a least squares method or any suitable regression method (e.g., a linear regression method). In one embodiment, the least squares method is a weighted least squares method based on weights related to the variance of the thermal noise.

[0008] The invention may be better understood when considered in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 The Earth-centered Earth-fixed (ECEF) coordinate system, the latitude-longitude coordinate system, and the East-Ultrasound (ENU) coordinate system are shown.

[0010] Figure 2 is an example of an illustration showing the position of a satellite 201 relative to a receiver at the origin 102 of the ENU reference frame 104 . DETAILED DESCRIPTION

[0011] In order to illustrate the embodiments of the invention described herein, the detailed description uses several coordinate systems familiar to those of ordinary skill in the art. Figure 1 The Earth-centered Earth-fixed (ECEF) coordinate system, the latitude-longitude coordinate system, and the Northeast-Ultrasound (ENU) coordinate system are shown. Figure 1 As shown, the origin of the Cartesian coordinate system (X, Y, Z) 103 is defined at the center of the sphere 101. In positioning applications, the sphere 101 represents the earth and the Cartesian coordinate system 103 is referred to as the ECEF coordinate system. On the sphere 101, the orthogonal great circles "prime meridian" (PM) and the equator, defined in the XZ and XY planes, respectively, are assigned 0° longitude and 0° latitude. Longitude is defined along great circles, each indexed by its angle λ relative to the PM plane. On the earth, by convention, for 0°≤λ≤180°, longitude is referred to as λ°E, and for 0°≤-λ≤180°, longitude is referred to as λ°W. Latitude is defined on a circle on the sphere 101 parallel to the equator, and each circle is indexed by an angle φ relative to the equatorial plane. For 0°≤φ≤90°, the latitude of the earth is referred to as φ°N, and for 0°≤φ≤90°, the latitude of the earth is referred to as φ°S.

[0012] Unless otherwise noted, this detailed description uses the ENU coordinate system when referring to positions relative to signal receivers generally located on the surface of the Earth. For example, Figure 1 The origin 102 of the ENU reference frame 104 is shown at a point on the sphere 101. The N axis is along the tangent direction of the receiver longitude and the E axis is along the tangent direction of the receiver latitude. The U axis is along the direction of the line connecting the origin of the sphere 101 to the receiver location.

[0013] Figure 2 is an example of an illustration showing the position of a satellite 201 relative to a receiver at the origin 102 of the ENU reference frame 103. Figure 2 As shown, the position of satellite 201 can be determined by the distance ρ to origin 102, the angle A in EN plane relative to the N axis, and the Z (“azimuth”) and the angle El (“elevation”) relative to the EN plane.

[0014] According to one embodiment, the method of the present invention starts with K "available" satellites whose signals are considered available to the receiver. For example, the available satellites can be identified by a pre-processing step that eliminates satellites whose signals are considered to be out of range of the receiver or otherwise excluding when the signal is measured. In one embodiment, satellites with elevation angles less than 15° are also excluded. Figure 1 , Figure 1 The signal from satellite 107 is shown arriving at the receiver via path 105. Figure 1 The point where the path 105 intersects the ionosphere is indicated in the vector 106. The vector 106 indicates the position of the IPP in the ECEF coordinate system. For each available satellite, say the i-th available satellite, i=1, ...K, the method of the present invention determines the position s of (i) the satellite in ECEF coordinates based on the receiver clock i =[x i, ,y i ,z i ] T , (ii) the nominal transmission time t of the received signal i and (iii) the reception time t of the received signal. The method further uses the variance σ i 2 For unknown receiver clock drift d t and zero-mean Gaussian thermal noise n i Modeling.

[0015] This method delays the ionosphere by g β (s i ,r) is modeled as the satellite position s i ,,Receiver position r = [x,y,z] Tand a set of unknown coefficients associated with the satellite β = [β0,β1,β2] T function.

[0016] In units of time, the i-th pseudorange tt i It is given by the observation equation:

[0017] tt i =c -1 ‖s i -r‖+g β (s i ,r)+d t +n i (1)

[0018] where c is the speed of light, is the Euclidean distance between the ith satellite and the receiver.

[0019] In one embodiment, the ionospheric delay g β (s i ,r) can be defined by a linear function such as:

[0020] g β (s i ,r)=f i ·(β0+β1(a P,i -a)+β2(o 2,i -o)) (2)

[0021] where (i)f i is the “tilt factor”, which is the satellite position s i and the receiver position r, and (ii) the coefficient β0 represents the ionospheric delay of the signal along the receiver's U axis into the atmosphere, 0a 2,i -a) is the deviation of the latitude of the IPP of the received ith satellite signal relative to the latitude of the receiver (“IPP latitude deviation”), and (o 2,i -o) is the deviation of the longitude of the IPP of the signal of the ith satellite relative to the longitude of the receiver ("IPP longitude deviation"). Thus, in this model, coefficients β1 and β2 represent the ionospheric delay correction associated with each unit of IPP latitude deviation and associated with each unit of IPP longitude deviation, respectively.

[0022] Since each tilt factor f i The latitude and longitude of each IPP depend on the unknown receiver position r, and one embodiment of the present invention computes them iteratively, applying the most recent receiver position estimate To estimate the ionospheric delay This in turn updates the receiver position estimate Receiver Position Estimation The initial value of can be obtained using conventional methods without taking into account the ionospheric delay, i.e., setting the ionospheric delay to zero. In practice, even one iteration already gives reasonable results.

[0023] The ionospheric delay vector g represents the ionospheric delay of the available satellites β It can be given by the following formula:

[0024] g βc =[g β (s1,r),g β (s2,r),…,g β (s K ,r)] T =A iono *β T (3) Among them A iono is the ionospheric delay matrix, which is a K×3 matrix, where the i-th row is given by:

[0025] A iono i =[a i1 ,a i2 ,a i3 ] (3a)

[0026] The following steps use satellite positions i , A = 1, ..., K and the receiver position estimate To calculate the matrix A iono :

[0027] (a) Determine the elevation angle el of the i-th satellite relative to the receiver in radians i and azimuth Az i , where i = 1, ... K;

[0028] (b) Determine the latitude a of the i-th satellite i and longitude o i , where A=1,…K;

[0029] (c) determine the latitude a and longitude o of the receiver;

[0030] (d) The elevation angle el i Convert to geocentric angle

[0031] (f) Determine the latitude of each satellite's IPP1 P,i ,

[0032] (g) Determine the longitude of each satellite's IPP P,i ,

[0033] (h) Determine the tilt factor f i =1+16·(0.53-el i ) 3 , i = 1,…,K; and

[0034] (i) Determine the ionospheric delay matrix A iono , A iono There are K rows, the i-th row is [a i1 ,a i2 ,a i3 ]=[f i ,f i ·(a P,i -a),f i ·(o P,i -o)], i=1,…,K.

[0035] According to one embodiment of the present invention, the unknown parameters r, d in equation (1) are t , and β are estimated jointly using a first-order Taylor expansion:

[0036]

[0037] where Δr is the error in the receiver position estimate and is given by:

[0038]

[0039] The unknown parameters to be solved can be grouped into a vector ξ=[β,Δr T ,d t ] T , and the following quantities can be defined:

[0040] (i) Vector q = [q1, q2, …, a K ] T ,in as well as

[0041] (ii) Gaussian noise vector n = [n1, n2, ..., n K ] T ,

[0042] Grouping all pseudorange equations (i.e., all equations (1), i=1,…,K) together and rearranging them yields the vector equation:

[0043] q=Xξ+n (4)

[0044] The augmented design matrix X is a K×7 matrix, which is obtained by replacing the K×3 matrix A iono Merged with the K×4 matrix whose i-th row is given by:

[0045]

[0046] Equation (4) includes 7 unknowns, so pseudorange measurements are required for at least 7 satellites. With 7 or more satellites, weighted least squares or any suitable regression method can be used to solve for the unknowns. For example, when the variance of the Gaussian noise vector n is When known, the diagonal matrix The variance can be estimated from the thermal noise measurement. In this embodiment, the solution for the unknown value is given by:

[0047] ξ=(k T Wk) -1 k T Wq (6)

[0048] Note that equation (1) does not explicitly include the delay term due to the rest of the atmosphere. The coefficient values ​​c0, c1, and c2 in the linear ionospheric model described above vary with distance. The difference in the coefficient values ​​between two locations that are sufficiently far apart includes the contribution of the delay due to the difference in weather conditions (e.g., the pressure of the water vapor fraction) between the two locations. Therefore, the determined coefficients can be associated with weather conditions and used for weather forecasting purposes.

[0049] The method of the present invention can be extended to include the ionospheric delay g β (s i ,r). In this case, the vector ζ is augmented to include additional unknown parameters corresponding to the ionospheric delay g β (s i ,r) The coefficients of the nonlinear terms added in. Then, using the method described above, the values ​​of the additional unknown parameters can be solved jointly with the other unknown parameters.

[0050] The above detailed description is provided to illustrate specific embodiments of the present invention, and is not intended to be limiting. Various modifications and variations are possible within the scope of the present invention. The present invention is set forth in the appended claims.

Claims

1. A method for determining a position of a signal receiver based on pseudorange determination of signals received from a plurality of signal sources, the method taking into account environmental biases, comprising: In the equation for determining the pseudorange associated with each signal received from the signal source, in addition to the parameters representing the position of the signal receiver and the clock drift of the signal receiver, a function representing the environmental bias by one or more parameters is included; as well as Using the equations for pseudorange determination, values ​​of parameters of the function and values ​​of parameters representing the position of the signal receiver and the clock drift of the signal receiver are jointly solved, wherein jointly solving the values ​​of the parameters includes solving a set of linear equations.

2. The method according to claim 1, wherein: The environmental deviations include interference from the Earth's ionosphere.

3. The method according to claim 2, wherein: Parameters associated with the parameters of the function include coefficients of terms characterizing an ionospheric penetration point (IPP) of the received signal.

4. The method according to claim 3, wherein: The terms characterize the changes in longitude and latitude of a signal source associated with the received signal. The method of claim 3 , further comprising multiplying each coefficient by a factor.

6. The method according to claim 5, wherein: The parameters of the function for each signal source signal are obtained by the following steps: (a) determine the location of each signal source; (b) determining the receiver's position based on an initial estimate of the receiver's position without taking into account environmental bias; (c) determining the location of the IPP of each signal based on the location of the source of each signal and the location of the receiver; (d) determining a term in the function associated with each signal based on the location of the receiver, the location of the source of the signal; as well as (e) Repeating steps (a) to (d) one or more times.

7. The method according to claim 6, wherein: The location of each signal source is expressed as latitude, longitude and altitude.

8. The method of claim 6, further comprising determining the elevation and azimuth of each signal source relative to the receiver in radians.

9. The method of claim 6, further comprising determining a tilt factor at the IPP of each signal.

10. The method according to claim 1, wherein: Solving the set of linear equations includes using a least squares method.

11. The method according to claim 10, wherein: The least squares method includes a weighted least squares method.

12. The method according to claim 11, wherein: The weighted least squares method uses weights that are related to the thermal noise.

13. The method according to claim 12, wherein: The weights include the variance of the thermal noise in each signal source.

14. The method of claim 1, further comprising using the values ​​of the parameters of the function for weather forecasting.

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