Two-way ground positioning method based on three-dimensional coordinate rotation compensation and dynamic filtering

Abstract

The application discloses a two-way ground positioning method based on three-dimensional coordinate rotation compensation and dynamic filtering, relates to the technical field of navigation positioning and space measurement and control, and comprises the following steps: collecting phase differences obtained by all ground stations during one two-way ground positioning; obtaining a spacecraft state space equation according to dynamic modeling, further obtaining a discrete form of a state updating equation according to the spacecraft state space equation, and predicting a current spacecraft predicted state according to historical information by using the state updating equation; obtaining observation values of the spacecraft, correcting the current spacecraft predicted state by using the observation values, and obtaining a current spacecraft estimated state, wherein the current spacecraft estimated state comprises a spacecraft position estimated value and a spacecraft speed estimated value; obtaining a transmission delay according to the spacecraft position estimated value, correcting a spacecraft coordinate into a geocentric geodetic coordinate system at a positioning time, and obtaining a three-dimensional position and speed of the spacecraft in the geodetic coordinate system at the positioning time after the coordinate system is corrected.

Description

Technical Field

[0001] This invention relates to the fields of navigation and positioning, and aerospace telemetry and control, specifically to a two-way ground-based positioning method based on three-dimensional coordinate rotation compensation and dynamic filtering. Background Technology

[0002] Ground-based positioning based on two-way measurement has wide applications in navigation, positioning, and aerospace telemetry and control.

[0003] When conducting two-way measurements between a ground station and a spacecraft, the spacecraft's maneuvers during the Earth's rotation and signal processing delays cause unequal uplink and downlink transmission delays. The Earth's rotation and the spacecraft's maneuvers during the signal processing delay alter the positions of the ground station and spacecraft in the inertial coordinate system, leading to inconsistencies in the uplink and downlink transmission links, and consequently, unequal uplink and downlink transmission delays. However, traditional two-way ground-based positioning observation models assume that the two-way transmission delay of radio signals between the spacecraft and the ground station is the same. This model error leads to a decrease in the accuracy of two-way ground-based positioning. Modeling and compensating for the factors causing the inconsistency in transmission delays can effectively improve two-way positioning accuracy and is of great significance in aerospace telemetry and control.

[0004] In the August 2018 issue of IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequenty Control (Vol. 65, No. 8, pp. 1475-1486), titled "An Improved Protocol for Performing Two-Way Satellite Time and Frequency Transfer Using a Satellite in an Inclined Geo-Synchronous Orbit," the inconsistent two-way transmission delay caused by the Earth's rotation was modeled and compensated for, given the coordinates of the ground station and the spacecraft. Furthermore, by measuring the elevation and azimuth angles of the spacecraft relative to the ground station, the displacement vector of the ground station caused by the Earth's rotation was projected onto the radial vector between the ground station and the spacecraft. This can compensate for the inconsistent two-way transmission delay caused by the Earth's rotation to some extent. Compared to methods that assume identical transmission delays under symmetrical two-way transmission links, this method can improve positioning accuracy. However, this compensation method still has certain drawbacks. The model assumption that the ground station's movement with the Earth's rotation is approximated as a one-dimensional uniform linear motion introduces model errors, and accurate angle measurements are required to calculate the compensation amount.

[0005] Therefore, how to eliminate the inconsistencies in two-way transmission delays caused by Earth's rotation and spacecraft maneuvers, thereby achieving more accurate positioning, is an unsolved problem. Summary of the Invention

[0006] In view of this, the present invention provides a two-way ground-based positioning method based on three-dimensional coordinate rotation compensation and dynamic filtering. It can model the factors that cause inconsistencies in two-way transmission delay, such as Earth's rotation and spacecraft maneuvers, in the observation equation according to the actual radio signal transmission path, through a three-dimensional coordinate rotation matrix. Based on the estimated spacecraft state, the spacecraft position and velocity are aligned to the ground-fixed coordinate system at the time of positioning, thereby obtaining a more accurate positioning result.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows: A two-way ground-based positioning system is used to locate the spacecraft. The two-way ground-based positioning system consists of multiple fixed ground stations with known clock differences. The two-way ground-based positioning method includes the following steps:

[0008] Collect the phase difference obtained by all ground stations during a single two-way ground-based positioning.

[0009] The spacecraft state space equation is obtained by dynamic modeling. The discrete state update equation is then obtained based on the spacecraft state space equation. The current predicted state of the spacecraft is then predicted based on historical information using the state update equation.

[0010] The observations of the spacecraft are obtained, and the current predicted state of the spacecraft is corrected using the observations to obtain the current estimated state of the spacecraft, which includes the estimated position and velocity of the spacecraft.

[0011] The transmission delay is obtained based on the spacecraft's position estimate, and the spacecraft coordinates are corrected to the geocentric coordinate system at the time of positioning. After coordinate system correction, the three-dimensional position and velocity of the spacecraft in the geocentric coordinate system at the time of positioning are obtained.

[0012] Furthermore, the phase difference obtained by all ground stations during a single bidirectional ground-based positioning is collected. Specifically, during each positioning period, ground station i transmits an uplink signal, and the signal undergoes an uplink transmission delay τ. ui It is then received by the spacecraft; the spacecraft samples the uplink signal phase and processes it with a delay of T. p Then, a downlink signal is sent to the ground base station; the signal undergoes a downlink transmission delay τ. di The signal is then received by ground station i. Simultaneously, ground station i samples and deframes the downlink signal phase to obtain the uplink phase sampled by the spacecraft, and calculates the uplink and downlink phase difference. The phase differences obtained by all ground stations during a single two-way ground-based positioning process are collected and denoted as follows: Where N is the number of ground stations.

[0013] Furthermore, the spacecraft state-space equations are obtained based on dynamic modeling. Discrete-form state update equations are then derived from these equations. Finally, the current predicted state of the spacecraft is predicted using historical information based on these state update equations. Specifically:

[0014] The spacecraft state-space equation obtained from dynamic modeling is:

[0015]

[0016] Where p m For the spacecraft's position, For p m The first derivative; v m For the speed of the spacecraft; The acceleration corresponding to the spacecraft's fuel propulsion force. This is the acceleration corresponding to the air resistance experienced by the spacecraft. This represents the acceleration corresponding to gravity on the spacecraft. The acceleration corresponding to the Coriolis force acting on the spacecraft. This refers to the acceleration corresponding to the centripetal force of the spacecraft.

[0017] The status of the spacecraft to be located is The input for the time step prediction at time k is the spacecraft state X estimated at the previous time step. m Given the input vector U(k-1) and the posterior mean square error matrix P(k-1), the output is the one-step time prediction state. and the prior estimate mean square error matrix According to (1), the discrete state update equation is as follows:

[0018]

[0019] Where A is the state transition matrix, B is the noise allocation matrix, and Q is the process noise covariance matrix;

[0020]

[0021] Where T is the dynamic filter update time, I 3×3 Let σ1 be a 3×3 identity matrix, and let σ1 be the diffusion coefficient. The current spacecraft predicted state is obtained by using the discrete state update equation described above based on historical information.

[0022] Furthermore, the observations of the spacecraft are acquired, and the predicted state of the current spacecraft is corrected using these observations to obtain the estimated state of the current spacecraft, specifically as follows:

[0023] The predicted state of the spacecraft at time k is: The observation vector at time k is Y(k) and the prior mean square error matrix. The estimated state of the spacecraft at time k is: The mean squared error matrix of the posterior estimate is P(k):

[0024]

[0025] Where K(k) is the Kalman gain, H(k) is the Jacobian matrix of the nonlinear observation equation, and ν(k) is the residual vector.

[0026] Based on the actual radio signal transmission during two-way ground-based positioning, the time difference observation model of ground station i is obtained.

[0027]

[0028] Where f PN Here, c is the bit rate, and c is the speed of light. Let p be the set of phase differences. m For the spacecraft position, C(·) represents the rotation matrix related to Earth's rotation, Δ is the clock difference between other ground stations and ground station i, and p g For the location of the ground station, v m For the speed of the spacecraft, T p For signal processing delay, a m To accelerate the spacecraft, Let η be the sum of uplink and downlink transmission delays, and let η be Gaussian noise with zero mean and variance σ.

[0029] The Doppler frequency shift observation obtained in the uplink and downlink communication links is f. d :

[0030]

[0031] Among them, f d For Doppler frequency shift observations, v g Let ω be the velocity of the ground station in the ground-fixed coordinate system at the moment it transmits the uplink signal. For a fixed ground station, the velocity is 0. i The mean and standard deviation are zero. fi Gaussian noise.

[0032] This yields an estimated spacecraft position, denoted as [value].

[0033] Furthermore, the transmission delay is obtained based on the spacecraft's position estimate, and the spacecraft coordinates are corrected to the geocentric-ground-fixed coordinate system at the time of positioning. After coordinate system correction, the three-dimensional position and velocity of the spacecraft in the geocentric-ground-fixed coordinate system at the time of positioning are obtained, specifically:

[0034] The spacecraft position was estimated using Kalman filtering. Calculate uplink transmission delay based on base station location This will then correct the position and velocity caused by the Earth's rotation during this period to

[0035]

[0036] in This is for one-sided transmission delay.

[0037] After coordinate system correction, the three-dimensional position and velocity of the spacecraft in the Earth-fixed coordinate system at the moment of positioning are determined.

[0038] Beneficial effects:

[0039] This invention utilizes a three-dimensional coordinate rotation matrix to model the factors causing inconsistent bidirectional transmission delays during bidirectional ground-based positioning, such as Earth's rotation and spacecraft maneuvers. This constructs an asymmetric bidirectional measurement model, and bidirectional ground-based positioning is achieved through Kalman dynamic filtering. Compared to conventional ground-based positioning methods that assume consistent bidirectional transmission delays, and methods that compensate for inconsistencies by projecting ground station displacement onto a radial vector, this method's observation model more closely matches the actual characteristics of radio signal transmission, thus resulting in higher positioning accuracy. Furthermore, this method does not require high-precision angle measurements to compensate for transmission delay inconsistencies. Attached Figure Description

[0040] Figure 1 The present invention provides a flowchart of a two-way foundation positioning method based on three-dimensional coordinate rotation compensation and dynamic filtering. Detailed Implementation

[0041] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0042] This invention provides a two-way ground-based positioning method based on three-dimensional coordinate rotation compensation and dynamic filtering. This method utilizes a two-way ground-based positioning system to locate a spacecraft. The two-way ground-based positioning system consists of multiple fixed ground stations with known clock biases. The two-way ground-based positioning method includes the following steps:

[0043] State-time one-step prediction steps: collect the phase difference obtained by all ground stations during a two-way ground-based positioning; obtain the spacecraft state-space equation based on dynamic modeling; further obtain the discrete state update equation based on the spacecraft state-space equation; and use the state update equation to predict the current spacecraft state based on historical information.

[0044] Measurement update steps: Obtain the observation values ​​of the spacecraft, use the observation values ​​to correct the current predicted state of the spacecraft, and obtain the current estimated state of the spacecraft, which includes the estimated position and velocity of the spacecraft;

[0045] Coordinate system correction steps: Obtain the transmission delay based on the spacecraft position estimate, and correct the spacecraft coordinates to the geocentric-ground-fixed coordinate system at the time to be positioned. After coordinate system correction, obtain the three-dimensional position and velocity of the spacecraft in the geocentric-ground-fixed coordinate system at the time to be positioned.

[0046] In two-way ground-based positioning, a dynamic filtering module is used to calculate the spacecraft's position. The flowchart of the dynamic filtering module of this invention is as follows: Figure 1 As shown, the dynamic filtering module takes as input the phase difference between the ground station and the uplink / downlink communication during a single communication cycle, and outputs the spacecraft's position and velocity. Dynamic filtering comprises three steps: one-step state-time prediction, measurement update, and coordinate system correction. First, the current spacecraft state is predicted based on historical information, completing the one-step state-time prediction step. Then, the predicted spacecraft state is corrected based on current observations, completing the measurement update step. Finally, the transmission delay is obtained from the estimated spacecraft position, and the spacecraft coordinates are corrected to the geocentric-ground-fixed coordinate system at the desired positioning time, completing the coordinate system correction step.

[0047] The specific steps of this invention are as follows:

[0048] Without loss of generality, two-way ground-based positioning is described as follows: A two-way ground-based positioning system consists of multiple fixed ground stations with known clock biases, used to locate the spacecraft. During each positioning period, ground station i transmits an uplink signal, which is delayed by an uplink transmission delay τ. ui It was then received by the spacecraft. The spacecraft sampled the uplink signal phase and processed it with a delay of T. p Then, a downlink signal is sent to the ground base station. The signal undergoes a downlink transmission delay τ. di The signal is then received by ground station i. Simultaneously, ground station i samples and deframes the downlink signal phase to obtain the uplink phase sampled by the spacecraft, and calculates the uplink and downlink phase difference. The phase differences obtained by all ground stations during a single two-way ground-based positioning process are collected and denoted as follows: Where N represents the number of ground stations. Assume the state of the spacecraft to be located is... The spacecraft's position and velocity in the Earth-centered, Earth-fixed coordinate system are p, respectively. m =[x m ,y m ,z m ] T and Spacecraft acceleration is The position of the i-th ground station in the geocentric-fixed coordinate system is p. gi =[x gi ,y gi ,z gi ] T .

[0049] The following analysis will proceed sequentially from the state-time one-step prediction, measurement update, and coordinate system correction steps in the dynamic filtering module.

[0050] 1) State-time one-step prediction step

[0051] Based on dynamic modeling, the state-space equation of the spacecraft is:

[0052]

[0053] Where p m For the spacecraft's position, For p m The first derivative; v m The speed of the spacecraft; a m Accelerate the spacecraft; The acceleration corresponding to the spacecraft's fuel propulsion force. This is the acceleration corresponding to the air resistance experienced by the spacecraft. This represents the acceleration corresponding to gravity on the spacecraft. The acceleration corresponding to the Coriolis force acting on the spacecraft. This refers to the acceleration corresponding to the centripetal force of the spacecraft.

[0054] The input for the time step prediction at time k is the spacecraft state X estimated at the previous time step. m Given the input vector U(k-1) and the posterior mean square error matrix P(k-1), the output is the one-step time prediction state. and the prior estimate mean square error matrix According to (1), the discrete state update equation is as follows:

[0055]

[0056] The state transition matrix A, noise allocation matrix B, and process noise covariance matrix Q are expressed as follows:

[0057]

[0058] Where T is the dynamic filter update time, and I... 3×3 It is a 3×3 identity matrix, and σ1 is the diffusion coefficient.

[0059] Input vector The direction of the spacecraft's fuel propulsion acceleration is the same as the spacecraft's velocity, and its magnitude is expressed as...

[0060]

[0061] Where g is the acceleration due to gravity, I spLet m be the specific impulse, and m be the mass of the spacecraft. The acceleration corresponding to air resistance is in the opposite direction to the spacecraft's velocity, and its magnitude is expressed as...

[0062]

[0063] Where c D Since the drag coefficient is related to the speed, S is defined as the cross-sectional area of ​​the spacecraft perpendicular to the speed, and ρ is the air density. The direction of the spacecraft's gravity is from the spacecraft's position to the Earth's center, and its magnitude is...

[0064]

[0065] Where Ug = 3.99 × 10 14 Nm 2 / kg. The acceleration corresponding to the Coriolis force and centripetal force acting on the spacecraft is expressed as:

[0066]

[0067] Where “×” represents the cross product operation, w E =[0,0,-ω] T ω is the angular velocity of Earth's rotation.

[0068] 2) Measurement update steps

[0069] The input to the measurement update step at time k is the predicted state. Observation vector Y(k) and prior mean square error matrix The output is the estimated state. And the posterior estimated mean square error matrix P(k). The measurement update steps are as follows:

[0070]

[0071] Where K(k) is the Kalman gain, H(k) is the Jacobian matrix of the nonlinear observation equation, and ν(k) is the residual vector; Kalman gain Kalman gain, observation vector This represents the augmented form of time difference and Doppler frequency shift measurements, where c is the speed of light. There is one above. The following are the upward Doppler translation observations. The vector-valued function form of the observation equation is Y = h(x, v). T ), observation noise vector v T =[η Τ ,ω Τ ] T The model is a zero-mean Gaussian model, where R is the observation noise vector v. T The corresponding covariance matrix. The vector-valued function h(·) is determined by the time difference observation model and the Doppler frequency shift observation model.

[0072] The residual vector is defined as

[0073]

[0074] The time difference measurement section uses ground station i as the solution reference station as an example. Based on the actual radio signal transmission during two-way ground positioning, the time difference observation model of ground station i is obtained as follows:

[0075]

[0076] Where f PN Here, c is the bit rate, and c is the speed of light. Let p be the set of phase differences. m For the spacecraft position, C(·) represents the rotation matrix related to Earth's rotation, Δ is the clock difference between other ground stations and ground station i, and p g For the location of the ground station, v m For the speed of the spacecraft, T p For signal processing delay, a m To accelerate the spacecraft, The sum of uplink and downlink transmission delays is given by η, where η is Gaussian noise with zero mean and variance σ.

[0077] C(·) represents the rotation matrix related to the Earth's rotation, which can be expressed as:

[0078]

[0079] Where I 3×3 It is a 3×3 identity matrix, and ω is the Earth's rotational angular rate of 7.29×10⁻⁶. -5 , where u× is an antisymmetric matrix of u.

[0080] In addition to time difference measurements, Doppler frequency shift observations can also be obtained in uplink and downlink communication links. The uplink Doppler frequency shift observation model is as follows:

[0081]

[0082] Among them, f d For Doppler frequency shift observations, v g Let ω be the velocity of the ground station in the ground-fixed coordinate system at the moment it transmits the uplink signal. For a fixed ground station, the velocity is 0. i The mean and standard deviation are zero. fi Gaussian noise. Based on (10) and (12), the spacecraft position estimate can be obtained through the first two steps, and the spacecraft position estimate is denoted as...

[0083] 3) Coordinate system correction steps

[0084] Because the coordinate systems of other ground stations' transmission times were rotated and aligned to the ground-fixed coordinate system of ground station i during the establishment of the observation model, an estimated spacecraft position in the ground-fixed coordinate system at the reception time needs to be obtained using Kalman filtering to determine the spacecraft's position. Calculate uplink transmission delay based on base station location This will then correct the position and velocity caused by the Earth's rotation during this period to

[0085]

[0086] in The one-sided transmission delay, obtained through time-one-step prediction and measurement update steps, can be expressed as:

[0087]

[0088] Where p gi Let p be the position of the i-th ground station in the geocentric-ground coordinate system. gi =[x gi ,y gi ,z gi ] T .

[0089] After coordinate system correction, the three-dimensional position and velocity of the spacecraft in the Earth-fixed coordinate system at the moment of positioning are determined.

[0090] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A two-way ground positioning method based on three-dimensional coordinate rotation compensation and dynamic filtering, characterized in that, This method uses a two-way ground-based positioning system to locate the spacecraft. The two-way ground-based positioning system consists of multiple fixed ground stations with known clock differences. The two-way ground-based positioning method includes the following steps: Collect the phase difference obtained by all ground stations during a single two-way ground-based positioning process; The spacecraft state space equation is obtained by dynamic modeling. The discrete state update equation is further obtained from the spacecraft state space equation. The current predicted state of the spacecraft is predicted based on historical information using the state update equation. The observations of the spacecraft are acquired, and the current predicted state of the spacecraft is corrected using the observations to obtain the current estimated state of the spacecraft, which includes the estimated position and velocity of the spacecraft. The transmission delay is obtained based on the spacecraft position estimate, and the spacecraft coordinates are corrected to the geocentric coordinate system at the time of positioning. After coordinate system correction, the three-dimensional position and velocity of the spacecraft in the geocentric coordinate system at the time of positioning are obtained.

2. The bidirectional ground-based positioning method based on three-dimensional coordinate rotation compensation and dynamic filtering as described in claim 1, characterized in that, The collection of phase differences obtained by all ground stations during a single two-way ground-based positioning process specifically involves: during each positioning period, the ground stations... i Uplink signal is transmitted, and the signal undergoes uplink transmission delay. It was then received by the spacecraft; the spacecraft sampled the uplink signal phase and processed it with a signal delay. Then, a downlink signal is sent to the ground base station; the signal undergoes downlink transmission delay. Later, the ground base station i Receive, simultaneously, base station i The downlink signal phase is sampled and deframed to obtain the uplink phase sampled by the spacecraft, and the uplink and downlink phase difference is calculated. Collect and record the phase differences obtained by all ground stations during a single two-way ground-based positioning process. ,in N This refers to the number of ground stations.

3. The bidirectional ground positioning method based on three-dimensional coordinate rotation compensation and dynamic filtering as described in claim 1 or 2, characterized in that, The process involves obtaining the spacecraft's state-space equations based on dynamic modeling, further deriving discrete-form state update equations from these equations, and then using these state update equations to predict the current spacecraft state based on historical information. Specifically: The spacecraft state-space equation obtained from dynamic modeling is: （1） in For the spacecraft's position, for The first derivative; For the speed of the spacecraft; The acceleration corresponding to the spacecraft's fuel propulsion force. This is the acceleration corresponding to the air resistance experienced by the spacecraft. This represents the acceleration corresponding to gravity on the spacecraft. The acceleration corresponding to the Coriolis force acting on the spacecraft. This refers to the acceleration corresponding to the centripetal force of the spacecraft. The status of the spacecraft to be located is , k The input for the one-step prediction at time step is the spacecraft state estimated at the previous time step. Input vector and posterior mean square error matrix The output is the predicted state at one time step. and the prior estimate mean square error matrix According to (1), the discrete-form state update equation is: （2） in State transition matrix, Assign a matrix to the noise. The process noise covariance matrix; （3） Where T is the dynamic filter update time, and I is... 3×3 It is a 3×3 identity matrix. The diffusion coefficient is denoted as . The current predicted state of the spacecraft is obtained by using the discrete state update equation described above based on historical information.

4. The bidirectional ground positioning method based on three-dimensional coordinate rotation compensation and dynamic filtering as described in claim 3, characterized in that, The process of acquiring observations of the spacecraft, using these observations to correct the current predicted state of the spacecraft, and obtaining the current estimated state of the spacecraft specifically involves: k The spacecraft's predicted state at that moment is , k The observation vector at time is and prior mean square error matrix , k The estimated state of the spacecraft at that moment is The mean square error matrix of the posterior estimate is : （8） in For Kalman gain, The Jacobian matrix of the nonlinear observation equation is... The residual vector; Based on the actual radio signal transmission during two-way ground-based positioning, the ground station was obtained. i Time difference observation model （10） in For code rate, c At the speed of light, For the set of phase differences, For the spacecraft's position, C (·) represents the rotation matrix related to the Earth's rotation. For other ground base stations and ground base stations i The clock difference, For the location of the ground station, For the speed of the spacecraft, For signal processing delay, To accelerate the spacecraft, This is the sum of uplink and downlink transmission delays. With zero mean and variance Gaussian noise; Doppler frequency shift observations were obtained in the uplink and downlink communication links. : （12） in, For Doppler frequency shift observation, Let be the velocity of the ground station in the ground-fixed coordinate system at the moment it transmits the uplink signal. For a fixed ground station, the velocity is 0. The mean and standard deviation are zero. Gaussian noise; This yields an estimated spacecraft position, denoted as [value]. .

5. The bidirectional ground positioning method based on three-dimensional coordinate rotation compensation and dynamic filtering as described in claim 4, characterized in that, The process involves obtaining the transmission delay based on the spacecraft's estimated position and correcting the spacecraft coordinates to the geocentric-ground-fixed coordinate system at the time of positioning. After coordinate system correction, the three-dimensional position and velocity of the spacecraft in the geocentric-ground-fixed coordinate system at the time of positioning are obtained. Specifically: The spacecraft position was estimated using Kalman filtering. Calculate uplink transmission delay based on base station location Therefore, the position and velocity caused by the Earth's rotation during this period are corrected as follows: （13） in This is for one-sided transmission delay; After coordinate system correction, the three-dimensional position and velocity of the spacecraft in the Earth-fixed coordinate system at the moment of positioning are determined.

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