CN115356754A - Combined navigation positioning method based on GNSS and low-orbit satellite - Google Patents

Combined navigation positioning method based on GNSS and low-orbit satellite Download PDF

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CN115356754A
CN115356754A CN202210906836.2A CN202210906836A CN115356754A CN 115356754 A CN115356754 A CN 115356754A CN 202210906836 A CN202210906836 A CN 202210906836A CN 115356754 A CN115356754 A CN 115356754A
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low
orbit
orbit satellite
satellite
vector
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周文涛
刘峰
刘璞
高亚豪
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Beijing Automation Control Equipment Institute BACEI
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Beijing Automation Control Equipment Institute BACEI
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/35—Constructional details or hardware or software details of the signal processing chain
    • G01S19/37—Hardware or software details of the signal processing chain
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/20—Integrity monitoring, fault detection or fault isolation of space segment
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/40—Correcting position, velocity or attitude
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G01S19/48—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
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  • Computer Security & Cryptography (AREA)
  • Position Fixing By Use Of Radio Waves (AREA)

Abstract

The invention provides a combined navigation and positioning method based on a GNSS and a low-earth orbit satellite, which comprises the following steps: acquiring a TLE file of the low-orbit satellite, and calculating an original orbit parameter of the low-orbit satellite according to the TLE file; measuring a Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver by using the low-orbit satellite receiver; under the condition that GNSS positioning information is available, utilizing the GNSS positioning information to perform navigation positioning, utilizing TLE files, doppler frequency shift measurement values and the GNSS positioning information to perform real-time correction on orbital errors of low-orbit satellites through Kalman filtering to obtain corrected orbital parameters, and utilizing a neural network to perform orbital parameter prediction to obtain predicted orbital parameters; and under the condition that the GNSS positioning information is unavailable, performing navigation positioning by using the predicted orbit parameters and the Doppler frequency shift measurement values. By applying the technical scheme of the invention, the technical problems that the navigation precision of the low-orbit satellite is poor and the GNSS signal is unstable to influence the navigation positioning effect in the prior art are solved.

Description

Combined navigation positioning method based on GNSS and low-orbit satellite
Technical Field
The invention relates to the technical field of opportunistic signal navigation, in particular to a combined navigation positioning method based on GNSS and low-orbit satellites.
Background
At present, the satellite navigation has wide application field, relates to the aspects of national production and life, and is also an important component of various accurate guided weapons. The traditional navigation satellites are distributed on middle and high orbits, signals are weak when reaching the ground, signal interruption is easy to cause under the condition of shielding, and the signal formats are public and are easy to suffer from interference and deception. In contrast, low earth orbit satellites have a lower orbital altitude, a higher power for signals to reach the ground, and a fast change in the geometric position of the satellite, so that countries compete to transmit low earth orbit satellites. However, the main communication of the low-earth orbit satellite is used for communication, the navigation message is not broadcast in real time like GNSS (global navigation satellite system), and the communication content and format of the non-cooperative satellite are encrypted, so the method for obtaining the orbit information of the low-earth orbit satellite mostly depends on two lines of root files (TLE files) issued by north american aviation commanders, and although the TLE files are updated every day, the satellite orbit calculated according to the TLE files has a very large error, even in kilometer levels, which has a very large influence on the positioning result.
Disclosure of Invention
In order to solve one of the problems in the prior art, the invention provides a combined navigation and positioning method based on a GNSS and a low-earth orbit satellite.
According to an aspect of the present invention, there is provided a combined navigation and positioning method based on GNSS and low earth orbit satellites, the combined navigation and positioning method comprising:
acquiring a TLE file of the low-orbit satellite, and calculating to obtain an original orbit parameter of the low-orbit satellite according to the TLE file;
measuring by using a low-orbit satellite receiver to obtain a Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver;
under the condition that GNSS positioning information is available, utilizing the GNSS positioning information to perform navigation positioning, utilizing TLE files, doppler frequency shift measurement values and the GNSS positioning information to perform real-time correction on the orbit error of the low-orbit satellite through Kalman filtering to obtain corrected orbit parameters, and utilizing a neural network to perform orbit parameter prediction based on the original orbit parameters and the corrected orbit parameters to obtain predicted orbit parameters;
and under the condition that the GNSS positioning information is unavailable, performing navigation positioning by using the predicted orbit parameters and the Doppler frequency shift measurement values.
Further, the GNSS positioning information includes a local position vector and a local velocity vector, and the real-time correction of the orbital error of the low earth orbit satellite through the kalman filter by using the TLE file, the doppler shift measurement value, and the GNSS positioning information to obtain the corrected orbit parameter includes:
establishing a motion equation of the low-orbit satellite;
establishing a state equation taking a position vector and a velocity vector of the low-orbit satellite as state quantities according to the motion equation;
establishing a measurement equation according to the TLE file, the local position vector, the local velocity vector and the Doppler frequency shift measurement value;
and correcting the orbit error of the low-orbit satellite in real time through Kalman filtering based on the state equation and the measurement equation to obtain a corrected orbit parameter.
Further, establishing a measurement equation according to the TLE file, the local location vector, the local velocity vector, and the doppler shift measurement value includes:
predicting to obtain a Doppler frequency shift predicted value between the low-orbit satellite and the low-orbit satellite receiver according to the TLE file, the local position vector and the local velocity vector;
and establishing a measurement equation according to the Doppler frequency shift measurement value and the Doppler frequency shift predicted value.
Further, the obtaining of the predicted value of the doppler frequency shift between the low orbit satellite and the low orbit satellite receiver according to the TLE file, the local position vector and the local velocity vector prediction comprises:
predicting to obtain a predicted position vector and a predicted speed vector of the low-orbit satellite according to the TLE file;
calculating to obtain a relative position vector from the low-orbit satellite to a low-orbit satellite receiver according to the predicted position vector and the local position vector;
calculating to obtain a relative velocity vector from the low-orbit satellite to the low-orbit satellite receiver according to the predicted velocity vector and the local velocity vector;
and calculating to obtain a Doppler frequency shift predicted value according to the relative position vector and the relative velocity vector.
Further, establishing a measurement equation according to the measured doppler shift value and the predicted doppler shift value includes:
calculating a Doppler frequency shift difference value between the Doppler frequency shift predicted value and the Doppler frequency shift measurement value;
and establishing a measurement equation taking the Doppler shift difference as a measurement quantity.
Further, a predicted doppler shift value is calculated from the relative position vector and the relative velocity vector by the following formula:
Figure BDA0003772794150000031
in the above formula, f r (k) Showing the predicted value of the Doppler shift at the kth sample point, f 0 (k) Represents the emission frequency of the low-orbit satellite at the k sampling point, c represents the propagation speed of the electromagnetic wave in the space, n (k) represents the measurement error of the emission frequency of the low-orbit satellite at the k sampling point, rho (k) represents the relative position vector of the low-orbit satellite at the k sampling point to the low-orbit satellite receiver,
Figure BDA0003772794150000032
representing the relative velocity vector, ρ, of the sample point k from the low earth orbit satellite to the low earth orbit satellite receiver x (k)、ρ y (k) And ρ z (k) Representing components of the relative position vector p (k) in three directions,
Figure BDA0003772794150000041
and
Figure BDA0003772794150000042
representing relative velocity vectors
Figure BDA0003772794150000043
Components in three directions.
Further, the real-time correction of the orbit error of the low-orbit satellite through the Kalman filtering based on the state equation and the measurement equation comprises:
obtaining a position error and a speed error of the low-orbit satellite through Kalman filtering based on a state equation and a measurement equation;
correcting the predicted position vector and the predicted speed vector in real time according to the position error and the speed error to obtain a corrected position vector and a corrected speed vector of the low-orbit satellite;
and converting according to the corrected position vector and the corrected speed vector to obtain the orbit parameters of the low-orbit satellite after the orbit error is corrected.
Further, the equation of motion for a low earth orbit satellite is:
Figure BDA0003772794150000044
in the above formula, x, y and z respectively represent the components of the position vector of the low-orbit satellite in the inertial rectangular coordinate system in three directions,
Figure BDA0003772794150000045
and
Figure BDA0003772794150000046
respectively representing the components of the acceleration of the low-orbit satellite in the X, Y and Z directions in an inertial rectangular coordinate system, mu represents the Kepler constant of the earth, and R e Denotes the equatorial radius of the earth, J 2 Which represents a spherical-shaped mechanical factor of the earth,
Figure BDA0003772794150000047
and the distance of the origin of the inertial rectangular coordinate system of the low-earth orbit satellite is represented.
Further, the state equation is:
Figure BDA0003772794150000048
in the above equation, X (k + 1) represents the state quantity of the (k + 1) th sampling point, X (k) represents the state quantity of the (k) th sampling point, X (t) represents the state quantity at time t, and t represents the state quantity at time t k Indicating the time instant of the kth sample point,
Figure BDA0003772794150000051
r (k) represents the position vector of the low-earth satellite in the k sampling point in the inertial rectangular coordinate system,
Figure BDA0003772794150000052
representing the velocity vector of the low-earth-orbit satellite in the k-th sampling point in an inertial rectangular coordinate system, r (k) = [ x [) k y k z k ]，
Figure BDA0003772794150000053
x k 、y k And z k Respectively represents the components of the position vector of the low-earth satellite in the k-th sampling point in the inertial rectangular coordinate system in three directions,
Figure BDA0003772794150000054
and
Figure BDA0003772794150000055
respectively representing the components of the velocity vector of the low-earth satellite in the k-th sampling point in the inertial rectangular coordinate system in three directions, wherein T represents the sampling interval, I represents an identity matrix, F represents a nonlinear transformation matrix of the state quantity X, and omega (k) represents a system noise matrix.
Further, the measurement equation is:
Figure BDA0003772794150000056
in the above equation, Z (k) represents the amount of measurement at the kth sample point, Δ f k Which represents the difference in the doppler shift frequency,
Figure BDA0003772794150000057
indicating the distance of the low orbit satellite from the low orbit satellite receiver.
The combined navigation positioning method based on the GNSS and the low orbit satellite is applied, the GNSS positioning information is utilized to carry out navigation positioning when the GNSS positioning information is available, meanwhile, TLE files, doppler frequency shift measurement values and the GNSS positioning information of the low orbit satellite are utilized to carry out real-time correction on orbit errors of the low orbit satellite through Kalman filtering, corrected orbit parameters are obtained, orbit parameter prediction is carried out through a neural network algorithm based on original orbit parameters and the corrected orbit parameters, predicted orbit parameters of the low orbit satellite are obtained, and the predicted orbit parameters and the Doppler frequency shift measurement values are called to carry out navigation positioning when the GNSS positioning information is unavailable, namely, the low orbit satellite is switched to be used for navigation positioning.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
FIG. 1 is a flow chart illustrating a combined GNSS and low-earth satellite-based navigation positioning method according to an embodiment of the present invention;
fig. 2 is a schematic diagram illustrating a combined GNSS and low-earth satellite-based navigation positioning method according to an embodiment of the present invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be obtained by a person skilled in the art without inventive step based on the embodiments of the present invention, are within the scope of protection of the present invention.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The relative arrangement of the components and steps, the numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless specifically stated otherwise. Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any particular value should be construed as exemplary only and not as limiting. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.
As shown in fig. 1, according to an embodiment of the present invention, there is provided a combined GNSS and low-earth satellite-based navigation positioning method, including:
s1, acquiring a TLE file of a low-orbit satellite, and calculating to obtain an original orbit parameter of the low-orbit satellite according to the TLE file;
s2, measuring by using a low-orbit satellite receiver to obtain a Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver;
s3, under the condition that GNSS positioning information is available, utilizing the GNSS positioning information to perform navigation positioning, utilizing TLE files, doppler frequency shift measurement values and the GNSS positioning information to perform real-time correction on the orbit error of the low-orbit satellite through Kalman filtering to obtain corrected orbit parameters, and utilizing a neural network to perform orbit parameter prediction based on the original orbit parameters and the corrected orbit parameters to obtain predicted orbit parameters;
and S4, under the condition that the GNSS positioning information is unavailable, performing navigation positioning by using the predicted orbit parameters and the Doppler frequency shift measurement values.
In the embodiment of the present invention, the coordinate system is an inertial rectangular coordinate system, such as WGS84 inertial coordinate system. The GNSS positioning information is acquired through a GNSS receiver, the GNSS receiver sequentially captures satellite navigation signals, original telegraph text is analyzed through the steps of capturing, tracking, frame synchronization, bit synchronization and the like, and a positioning result is obtained through least square. The GNSS receiver and the low-earth satellite receiver belong to a combined navigation positioning system.
Referring to the schematic diagram of the combined navigation and positioning principle of fig. 2, the combined navigation system includes a GNSS receiver and a low-earth-orbit satellite receiver, and when GNSS positioning information is available, the combined navigation and positioning system operates in a GNSS positioning mode, and meanwhile, a prediction model of low-earth-orbit satellite orbit parameters is obtained through training by using corrected orbit parameters corrected in real time and original orbit parameters calculated according to TLE files as a training set of a neural network, and the orbit parameters are predicted by using the prediction model to obtain predicted orbit parameters, thereby obtaining an orbit database composed of predicted orbit parameters (time series) of low-earth-orbit satellites.
The neural network algorithm is selected according to actual conditions, as a specific embodiment of the invention, the LSTM prediction algorithm is adopted for training, the input of the neural network is track six parameters, the track six parameters comprise an original track six parameter resolved according to a TLE file and a corrected track six parameter, and the original track six parameter is used as prior information. The training process is as follows: firstly, initializing a network, setting a deviation value, obtaining an output value through forward operation, then determining a target function, calculating the error between an actual value and an estimated value, constructing an error function, and finally updating the weight and the bias of the network according to a gradient descent principle. The process of training the neural network algorithm is well known to those skilled in the art of neural networks and will not be described herein.
By applying the configuration mode, the combined navigation and positioning method based on the GNSS and the low-orbit satellite is provided, the method carries out navigation and positioning by utilizing the GNSS positioning information when the GNSS positioning information is available, meanwhile, the TLE file, the Doppler frequency shift measurement value and the GNSS positioning information of the low-orbit satellite are utilized to carry out real-time correction on the orbit error of the low-orbit satellite through Kalman filtering to obtain corrected orbit parameters, then, the orbit parameter prediction is carried out through a neural network algorithm based on the original orbit parameters and the corrected orbit parameters to obtain the predicted orbit parameters of the low-orbit satellite, and the predicted orbit parameters and the Doppler frequency shift measurement value are called to carry out navigation and positioning when the GNSS positioning information is unavailable, namely, the low-orbit satellite is switched to be in navigation and positioning. Compared with the prior art, the technical scheme of the invention can solve the technical problems that the navigation precision of the low-orbit satellite is poor and the GNSS signal is unstable to influence the navigation positioning effect in the prior art.
Further, in the embodiment of the present invention, the GNSS positioning information includes a local position vector and a local velocity vector, and the performing real-time correction on the orbit error of the low earth orbit satellite through kalman filtering by using the TLE file, the doppler shift measurement value, and the GNSS positioning information to obtain the corrected orbit parameter includes:
establishing a motion equation of the low-orbit satellite;
establishing a state equation taking a position vector and a velocity vector of the low-orbit satellite as state quantities according to the motion equation;
establishing a measurement equation according to the TLE file, the local position vector, the local velocity vector and the Doppler frequency shift measurement value;
and correcting the orbit error of the low-orbit satellite in real time through Kalman filtering based on the state equation and the measurement equation to obtain a corrected orbit parameter.
In the embodiment of the present invention, a kalman filtering manner is selected according to an actual situation, for example, as shown in fig. 2, extended kalman filtering may be adopted, a filtering initial value of a state quantity is set as a satellite position vector and a velocity vector obtained by resolving a TLE file, the state vector, that is, the position vector and the velocity vector of the low-orbit satellite, is resolved in real time according to an established state equation and a measurement equation, and kalman filtering is updated only when a low-orbit satellite signal (instantaneous doppler frequency shift of a visible satellite) can be received. Meanwhile, the state quantity of the invention does not contain the clock error and the clock drift of the low-orbit satellite receiver, the time is based on the GNSS, and the calculation quantity can be reduced so as to facilitate the engineering realization.
In the embodiment of the present invention, the expression of the state quantity X is:
Figure BDA0003772794150000101
wherein r = [ x y z =]And
Figure BDA0003772794150000102
respectively, the position vector and the velocity vector of the low-orbit satellite in the WGS84 inertial coordinate system.
The differential equation of state for a low earth orbit satellite is:
Figure BDA0003772794150000103
where F denotes a nonlinear transformation matrix of the state quantity X.
According to the law of universal gravitation, the equation of motion of a low-orbit satellite is as follows:
Figure BDA0003772794150000104
further, the equation of motion for a low earth orbit satellite is to consider J 2 The equation for the perturbation term, i.e., the equation of motion for a low earth orbit satellite, is:
Figure BDA0003772794150000111
in the above formula, x, y and z respectively represent the components of the position vector of the low-orbit satellite in the inertial rectangular coordinate system in three directions,
Figure BDA0003772794150000112
and
Figure BDA0003772794150000113
respectively representing the components of the acceleration of the low-orbit satellite in the X, Y and Z directions in an inertial rectangular coordinate system, mu represents the Kepler constant of the earth, and R e Representing the equatorial radius of the earth, J 2 Which represents a spherical-shaped mechanical factor of the earth,
Figure BDA0003772794150000114
and the distance of the origin of the inertial rectangular coordinate system of the low-orbit satellite is represented.
The state prediction equation is:
Figure BDA0003772794150000115
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003772794150000116
t denotes the sampling interval, T k Indicating the sample point time.
Discretizing the state transition matrix can obtain:
Figure BDA0003772794150000117
the state equation obtained after linearization and discretization is as follows:
X(k+1)＝Φ(k+1/k)·X(k)+ω(k)，
that is, in the embodiment of the present invention, the state equation is:
Figure BDA0003772794150000118
in the above equation, X (k + 1) represents the state quantity of the (k + 1) th sampling point, X (k) represents the state quantity of the (k) th sampling point, X (t) represents the state quantity at the time t, t k Indicating the time instant of the kth sample point,
Figure BDA0003772794150000119
r (k) represents the position vector of the low-orbit satellite in the k sampling point in the inertial rectangular coordinate system,
Figure BDA00037727941500001110
representing the velocity vector of the low-earth-orbit satellite in the k-th sampling point in an inertial rectangular coordinate system, r (k) = [ x [) k y k z k ]，
Figure BDA0003772794150000121
x k 、y k And z k Respectively represents the components of the position vector of the low-orbit satellite in the k-th sampling point in the inertial rectangular coordinate system in three directions,
Figure BDA0003772794150000122
and
Figure BDA0003772794150000123
respectively representing the components of the velocity vector of the low-earth satellite in the k-th sampling point in the inertial rectangular coordinate system in three directions, T representing the sampling interval, I representing an identity matrix, F representing a nonlinear transformation matrix of the state quantity X, omega (k) representing a system noise matrix, and the corresponding covariance matrix being Q (k) = E [ omega (k) < omega (k) & gt) T (k)]。
In addition, in the invention, because relative motion exists between the GNSS receiver and the low-orbit satellite and between the low-orbit satellite receiver and the low-orbit satellite, doppler frequency shift exists between the GNSS receiver and the low-orbit satellite and between the low-orbit satellite receiver and the low-orbit satellite. Based on this, in the embodiment of the present invention, establishing a measurement equation according to the TLE file, the local location vector, the local velocity vector, and the doppler shift measurement value includes:
predicting according to the TLE file, the local position vector and the local velocity vector to obtain a Doppler frequency shift predicted value between the low-orbit satellite and the low-orbit satellite receiver;
and establishing a measurement equation according to the Doppler frequency shift measurement value and the Doppler frequency shift predicted value.
Based on the foregoing embodiment, in the embodiment of the present invention, obtaining the predicted doppler shift value between the low-earth orbit satellite and the low-earth orbit satellite receiver according to the TLE file, the local position vector, and the local velocity vector prediction includes:
predicting to obtain a predicted position vector and a predicted speed vector of the low-orbit satellite according to the TLE file;
calculating to obtain a relative position vector from the low-orbit satellite to a low-orbit satellite receiver according to the predicted position vector and the local position vector;
calculating to obtain a relative velocity vector from the low-orbit satellite to the low-orbit satellite receiver according to the predicted velocity vector and the local velocity vector;
and calculating to obtain a Doppler frequency shift predicted value according to the relative position vector and the relative velocity vector.
Further, as an embodiment of the present invention, the doppler shift prediction value is calculated according to the relative position vector and the relative velocity vector by the following formula:
Figure BDA0003772794150000131
in the above formula, f r (k) Predicted value of Doppler shift, f, representing the kth sample point 0 (k) Representing the transmitting frequency of the low-orbit satellite at the k-th sampling point, c representing the propagation speed of electromagnetic waves in space, n (k) representing the measurement error of the transmitting frequency of the low-orbit satellite at the k-th sampling point, rho (k) representing the relative position vector from the low-orbit satellite at the k-th sampling point to the low-orbit satellite receiver,
Figure BDA0003772794150000132
representing the relative velocity vector, ρ, of the sample point k from the low earth orbit satellite to the low earth orbit satellite receiver x (k)、ρ y (k) And ρ z (k) Representing the components of the relative position vector p (k) in three directions,
Figure BDA0003772794150000133
and
Figure BDA0003772794150000134
representing relative velocity vectors
Figure BDA0003772794150000135
Component in three directions, where n (k) is generally white noise, the mean is set to zero, and the variance is σ 2 K =0,1, \8230, N represents the number of sampling points, i.e. observation points.
In addition, in the embodiment of the present invention, establishing a measurement equation according to the measured doppler shift value and the predicted doppler shift value includes:
calculating a Doppler frequency shift difference value between the Doppler frequency shift predicted value and the Doppler frequency shift measured value;
and establishing a measurement equation taking the Doppler frequency shift difference as a measurement quantity.
As a specific embodiment of the present invention,the expression for measuring Z (k) is Z (k) = Δ f k ＝f r (k)-f c (k) Wherein, Δ f k Representing the difference in Doppler shift between the predicted Doppler shift value and the measured Doppler shift value, i.e. the predicted Doppler shift value minus the measured Doppler shift value, f c (k) Indicating a doppler shift measurement. Based on this embodiment, the quantity measurement Z (k) is represented as a nonlinear function of the state quantity X as:
Z(k)＝H(X(k))+n(k)，
where H (X (k)) represents a nonlinear transformation matrix for measuring the quantity of state, and n (k) corresponds to a covariance matrix R (k) = E [ n (k) n = E [) T (k)]＝σ 2 。
Further, the measured Jacobian matrix is:
Figure BDA0003772794150000141
the partial differentiation is as follows:
Figure BDA0003772794150000142
Figure BDA0003772794150000143
wherein
Figure BDA0003772794150000144
Indicating the distance of the low orbit satellite from the low orbit satellite receiver.
The measurement equation obtained after linearization and discretization is as follows:
Z(k)＝H(k+1/k)·X(k)+n(k)，
that is, in the embodiment of the present invention, the measurement equation is:
Figure BDA0003772794150000145
in the above equation, Z (k) represents the amount of measurement at the kth sample point, Δ f k Which represents the difference in the doppler shift frequency,
Figure BDA0003772794150000146
indicating the distance of the low orbit satellite from the low orbit satellite receiver.
Further, the constructed discretized and linearized state equation and measurement equation are substituted into Kalman filtering man-hour for calculation, so that the orbit error of the low-orbit satellite is corrected. In the embodiment of the invention, the real-time correction of the orbit error of the low-orbit satellite through Kalman filtering based on the state equation and the measurement equation comprises the following steps:
obtaining a position error and a speed error of the low-orbit satellite through Kalman filtering based on a state equation and a measurement equation;
correcting the predicted position vector and the predicted speed vector in real time according to the position error and the speed error to obtain a corrected position vector and a corrected speed vector of the low-orbit satellite;
and converting according to the corrected position vector and the corrected speed vector to obtain the orbit parameters of the low-orbit satellite after the orbit error is corrected.
Wherein, the filtering estimation step is as follows:
state one-step prediction mean square error matrix:
P(k+1/k)＝Φ(k+1/k)·P(k)·Φ T (k+1/k)+Q，
and parameters in the Q array are reasonably selected according to actual conditions.
K(k+1)＝P(k+1/k)·H(k+1/k)·(H(k+1/k)·P(k)·H T (k+1/k)+R(k+1))，
And (3) state estimation:
Figure BDA0003772794150000151
state estimation mean square error matrix:
P(k+1)＝(I-K(k+1)·H(k+1))·P(k+1/k)，
the filtering estimation process is well known to those skilled in the art, and is not described herein again, the position error and the velocity error of the low-orbit satellite can be obtained through filtering estimation, the corrected position vector and the corrected velocity vector of the low-orbit satellite can be obtained by correcting the predicted position vector and the predicted velocity vector according to the position error and the velocity error, and the corrected position vector and the corrected velocity vector are converted into orbit parameters to obtain orbit parameters after the orbit error is corrected. In the embodiment of the invention, the track parameters mainly comprise six parameters of a track inclination angle, a rising intersection declination, an perigee angular distance, a track semimajor axis, a latitude argument and a true perigee angle, and the specific process of track parameter conversion is as follows:
area integral formula of satellite
Figure BDA0003772794150000161
Wherein h is an integral constant vector, and the expression of h = (h) in an inertial rectangular coordinate system x ,h y ,h z ) Then, then
Figure BDA0003772794150000162
Where h represents the length of the integral constant vector h, h x 、h y And h z Respectively representing the components of the integral constant vector h in three directions.
In the orbit coordinate system with h as z 'axis and r direction as x' axis, h = (0, h), and then the conversion relation between the inertia rectangular coordinate system and the orbit rectangular coordinate system can be obtained:
Figure BDA0003772794150000163
in the above formula, i represents the track inclination angle, and Ω represents the ascent intersection right ascension, which can be obtained by the following formula:
Figure BDA0003772794150000164
Figure BDA0003772794150000165
further, by
Figure BDA0003772794150000166
The following can be obtained:
Figure BDA0003772794150000167
in the above equation, e represents the orbital eccentricity, and its coordinate in the inertial rectangular coordinate system is e = (e) x ,e y ,e z ) Then, then
Figure BDA0003772794150000168
Wherein e is x 、e y And e z Respectively represents the projection of the track eccentricity in three directions of the coordinate axis.
Next, the perigee angular distance w can be calculated by the formula:
Figure BDA0003772794150000169
the calculation formula of the semi-major axis a of the track obtained by the formula of the conical section is as follows:
Figure BDA0003772794150000171
and then calculating the latitude argument u according to the following formula, wherein the latitude argument u is defined as the angular distance from the rising point to the low-orbit satellite position relative to the geocenter in the orbit plane:
Figure BDA0003772794150000172
the true anomaly f is calculated by the formula:
f＝u-w，
in addition, the relationship between the off-proximal angle and the true proximal angle is
Figure BDA0003772794150000173
And calculating a mean anomaly angle M by using a Kepler equation, wherein the mean anomaly angle refers to an angle of the low-orbit satellite running at the average angular speed from the anomaly point in the orbit plane, and the calculation formula is M = E-esinE, wherein E represents a deviation anomaly angle.
In summary, the invention provides a combined navigation and positioning method based on a GNSS and a low orbit satellite, the method uses the GNSS positioning information to perform navigation and positioning when the GNSS positioning information is available, uses a TLE file, a doppler shift measurement value and the GNSS positioning information of the low orbit satellite to perform real-time correction on an orbit error of the low orbit satellite through kalman filtering, so as to obtain a corrected orbit parameter, performs orbit parameter prediction through a neural network algorithm based on an original orbit parameter and the corrected orbit parameter, so as to obtain a predicted orbit parameter of the low orbit satellite, and calls the predicted orbit parameter and the doppler shift measurement value to perform navigation and positioning when the GNSS positioning information is unavailable, that is, switches to the low orbit satellite navigation and positioning. Compared with the prior art, the technical scheme of the invention can solve the technical problems that the navigation precision of the low-earth orbit satellite is poor and the GNSS signal is unstable to influence the navigation positioning effect in the prior art.
For ease of description, spatially relative terms such as "over 8230," "upper surface," "above," and the like may be used herein to describe the spatial positional relationship of one device or feature to other devices or features as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if a device in the figures is turned over, devices described as "above" or "on" other devices or configurations would then be oriented "below" or "under" the other devices or configurations. Thus, the exemplary terms "at 8230; \8230; 'above" may include both orientations "at 8230; \8230;' above 8230; 'at 8230;' below 8230;" above ". The device may be otherwise variously oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
It should be noted that the terms "first", "second", and the like are used to define the components, and are only used for convenience of distinguishing the corresponding components, and unless otherwise stated, the terms have no special meaning, and therefore, the scope of the present invention should not be construed as being limited.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. A combined navigation positioning method based on GNSS and low orbit satellite is characterized in that the combined navigation positioning method comprises:
acquiring a TLE file of the low-orbit satellite, and calculating to obtain an original orbit parameter of the low-orbit satellite according to the TLE file;
measuring a Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver by using a low-orbit satellite receiver;
under the condition that GNSS positioning information is available, utilizing the GNSS positioning information to perform navigation positioning, utilizing the TLE file, the Doppler frequency shift measurement value and the GNSS positioning information to perform real-time correction on the orbit error of the low orbit satellite through Kalman filtering to obtain corrected orbit parameters, and utilizing a neural network to perform orbit parameter prediction based on the original orbit parameters and the corrected orbit parameters to obtain predicted orbit parameters;
and under the condition that the GNSS positioning information is unavailable, performing navigation positioning by using the predicted orbit parameters and the Doppler frequency shift measurement values.
2. The integrated navigation positioning method according to claim 1, wherein the GNSS positioning information includes a local position vector and a local velocity vector, and the performing the real-time correction on the orbit error of the low earth orbit satellite through the kalman filter by using the TLE file, the doppler shift measurement value, and the GNSS positioning information to obtain the corrected orbit parameter includes:
establishing a motion equation of the low-orbit satellite;
establishing a state equation taking the position vector and the velocity vector of the low-orbit satellite as state quantities according to the motion equation;
establishing a measurement equation according to the TLE file, the local position vector, the local velocity vector and the Doppler frequency shift measurement value;
and correcting the orbit error of the low orbit satellite in real time through Kalman filtering based on the state equation and the measurement equation to obtain a corrected orbit parameter.
3. The integrated navigational positioning method of claim 2, wherein establishing a measurement equation based on the TLE file, the local position vector, the local velocity vector, and the doppler shift measurement comprises:
predicting to obtain a Doppler frequency shift predicted value between the low-orbit satellite and the low-orbit satellite receiver according to the TLE file, the local position vector and the local velocity vector;
and establishing a measurement equation according to the Doppler frequency shift measurement value and the Doppler frequency shift predicted value.
4. The integrated navigational positioning method of claim 3, wherein predicting a predicted value of a Doppler shift between the low orbiting satellite and the low orbiting satellite receiver from the TLE file, the local position vector, and the local velocity vector comprises:
predicting to obtain a predicted position vector and a predicted speed vector of the low-orbit satellite according to the TLE file;
calculating to obtain a relative position vector from the low-orbit satellite to the low-orbit satellite receiver according to the predicted position vector and the local position vector;
calculating to obtain a relative velocity vector from the low-orbit satellite to the low-orbit satellite receiver according to the predicted velocity vector and the local velocity vector;
and calculating to obtain the Doppler frequency shift predicted value according to the relative position vector and the relative velocity vector.
5. The integrated navigational positioning method of claim 4, wherein establishing a measurement equation based on the measured Doppler shift value and the predicted Doppler shift value comprises:
calculating a Doppler shift difference value between the Doppler shift predicted value and the Doppler shift measured value;
and establishing a measurement equation taking the Doppler frequency shift difference as a measurement quantity.
6. The integrated navigational positioning method of claim 5, wherein the predicted Doppler shift value is calculated from the relative position vector and the relative velocity vector by the following formula:
Figure FDA0003772794140000031
in the above formula, f r (k) Predicted value of Doppler shift, f, representing the kth sample point 0 (k) Representing the transmitting frequency of the low-orbit satellite at the k-th sampling point, c representing the propagation speed of electromagnetic waves in space, n (k) representing the measurement error of the transmitting frequency of the low-orbit satellite at the k-th sampling point, rho (k) representing the relative position vector from the low-orbit satellite at the k-th sampling point to the low-orbit satellite receiver,
Figure FDA0003772794140000032
representing the relative velocity vector, ρ, of the low-orbiting satellite to the low-orbiting satellite receiver at the kth sample point x (k)、ρ y (k) And ρ z (k) Representing components of the relative position vector p (k) in three directions,
Figure FDA0003772794140000033
and
Figure FDA0003772794140000034
representing said relative velocity vector
Figure FDA0003772794140000035
Components in three directions.
7. The integrated navigational positioning method of claim 6, wherein the real-time correction of the orbital error of the low earth orbit satellite through Kalman filtering based on the state equation and the measurement equation comprises:
obtaining a position error and a speed error of the low-orbit satellite through Kalman filtering based on the state equation and the measurement equation;
correcting the predicted position vector and the predicted speed vector in real time according to the position error and the speed error to obtain a corrected position vector and a corrected speed vector of the low-orbit satellite;
and converting according to the corrected position vector and the corrected speed vector to obtain the orbit parameters of the low-orbit satellite after the orbit error is corrected.
8. The integrated navigational positioning method of claim 7, wherein the equation of motion of the low earth orbit satellite is:
Figure FDA0003772794140000041
in the above formula, x, y and z respectively represent the components of the low-orbit satellite in the three directions of the position vector in the inertial rectangular coordinate system,
Figure FDA0003772794140000042
and
Figure FDA0003772794140000043
respectively representing the components of the acceleration of the low-orbit satellite in the X, Y and Z directions in an inertial rectangular coordinate system, mu represents the Kepler constant of the earth, and R e Representing the equatorial radius of the earth, J 2 The spherical-shaped mechanical factor is expressed,
Figure FDA0003772794140000044
and the distance of the origin of the inertial rectangular coordinate system of the low-orbit satellite is represented.
9. The integrated navigational positioning method of claim 8, wherein the state equation is:
Figure FDA0003772794140000045
in the above equation, X (k + 1) represents the state quantity of the (k + 1) th sampling point, X (k) represents the state quantity of the (k) th sampling point, X (t) represents the state quantity at time t, and t represents the state quantity at time t k Indicating the time instant of the kth sample point,
Figure FDA0003772794140000046
r (k) represents the position vector of the low-orbit satellite in the k sampling point in the inertial rectangular coordinate system,
Figure FDA0003772794140000047
representing the velocity vector of the low-earth satellite in the k sampling point in an inertial rectangular coordinate system, r (k) = [ x [) k y k z k ]，
Figure FDA0003772794140000048
x k 、y k And z k Respectively representing the position of the low-orbit satellite at the kth sampling point in an inertial rectangular coordinate systemThe components of the vector in the three directions,
Figure FDA0003772794140000049
and
Figure FDA00037727941400000410
respectively representing components of velocity vectors of the low-orbit satellite in the k-th sampling point in an inertial rectangular coordinate system in three directions, wherein T represents a sampling interval, I represents an identity matrix, F represents a nonlinear transformation matrix of a state quantity X, and omega (k) represents a system noise matrix.
10. The integrated navigational positioning method of claim 9, wherein the measurement equation is:
Figure FDA0003772794140000051
in the above equation, Z (k) represents the amount of measurement at the kth sample point, Δ f k Is representative of the difference in the doppler shifts,
Figure FDA0003772794140000052
representing the distance of the low-earth satellite to the low-earth satellite receiver.
CN202210906836.2A 2022-07-29 2022-07-29 Combined navigation positioning method based on GNSS and low-orbit satellite Pending CN115356754A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115877411A (en) * 2022-12-29 2023-03-31 中国民航大学 Civil aviation anti-deception navigation positioning method utilizing communication satellite Doppler signals
CN116774264A (en) * 2023-06-25 2023-09-19 西安电子科技大学 Moving target positioning method based on low orbit satellite opportunistic signal Doppler

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115877411A (en) * 2022-12-29 2023-03-31 中国民航大学 Civil aviation anti-deception navigation positioning method utilizing communication satellite Doppler signals
CN116774264A (en) * 2023-06-25 2023-09-19 西安电子科技大学 Moving target positioning method based on low orbit satellite opportunistic signal Doppler
CN116774264B (en) * 2023-06-25 2024-01-23 西安电子科技大学 Moving target positioning method based on low orbit satellite opportunistic signal Doppler

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