A precise orbit determination and time synchronization method based on time-sharing two-way ranging

Abstract

The present invention relates to a method for precise orbit determination and time synchronization based on time-sharing two-way ranging, comprising the following steps: using an almanac with kilometer-level error to perform two-way ranging between a spacecraft whose orbit and time synchronization are to be determined and corresponding navigation satellites according to a transmitting and receiving time slot to obtain inter-satellite pseudo-range; the navigation satellite broadcasts an ephemeris; the spacecraft receives the ephemeris through the communication function of a Ka inter-satellite link; using a polynomial with unknown coefficients to express the position, velocity and clock error of the spacecraft; reducing the inter-satellite pseudo-range of each group of two-way ranging and establishing a two-way measurement equation; and using the least square method to iterate multiple times to determine the coefficients of the position polynomial, velocity polynomial and clock error polynomial of the spacecraft.

Description

Technical Field

[0001] The present invention generally relates to the field of aerospace measurement and control technology, and in particular to a precise orbit determination and time synchronization method based on time-sharing bidirectional ranging. Background Art

[0002] At present, the traditional global positioning system (GNSS) positioning method is generally that GNSS satellites continuously broadcast wireless signals, and the GNSS receiver simultaneously measures the pseudo-range of visible satellites, and uses the pseudo-range and error of the same time scale and the calculated instantaneous position of the GNSS satellite at the time of transmission to build equations to solve its own position and clock error. This method relies on the GNSS receiver to obtain multiple satellite pseudo-ranges at the same time to establish equations.

[0003] The BeiDou system is equipped with a Ka-band intersatellite link payload. The Ka-band has a higher frequency, a smaller beam angle, and uses phased array transmission and reception. This system uses time-sharing two-way link establishment to complete communication and ranging. For a certain star or ground station, it only needs to know a simple almanac or station address with an error within 10 kilometers to complete the two-way link establishment with the other party's navigation satellite. In one transceiver time slot, there are two equal time periods: reception and transmission. If a certain star or ground station transmits first, the other party's satellite will receive first. In the next time period, it will receive itself and the other party's satellite will transmit, and vice versa. Therefore, the two pseudo-range values ​​obtained by a certain star or ground itself with an opposing satellite are completed in two different time periods in one transceiver time slot. One transceiver time slot establishes a link with one satellite, and the subsequent time slots can establish links with other satellites. The pseudo-ranges obtained by itself with different satellites are completed in different transceiver time slots.

[0004] With the development of low-orbit satellites or other long-distance spacecraft equipped with Ka inter-satellite link payloads and accessible to the navigation satellite inter-satellite network, in situations such as the Earth-Moon space where the GNSS signal is weak but the Ka signal strength can be guaranteed, using the pseudo-range values ​​measured in the Ka band to complete orbit determination and time synchronization has become the best choice. Summary of the invention

[0005] Based on the prior art, the task of the present invention is to provide a method for precise orbit determination and time synchronization based on time-sharing two-way ranging. Through this method, when the GNSS signal is very weak but the Ka signal strength is stable, the inter-satellite pseudo-range of the Ka-band time-sharing two-way ranging can be used to complete the precise satellite orbit determination and time synchronization of the spacecraft.

[0006] According to the present invention, the aforementioned task is solved by a method for precise orbit determination and time synchronization based on time-sharing bidirectional ranging, the method comprising the following steps:

[0007] Using an almanac with kilometer-level error, two-way ranging is performed between the spacecraft whose orbit and time synchronization are to be determined and the corresponding navigation satellite according to the transmission and reception time slots to obtain inter-satellite pseudorange;

[0008] The navigation satellite broadcasts ephemeris;

[0009] The spacecraft receives the ephemeris through the communication function of the Ka intersatellite link;

[0010] Expressing the position, velocity and clock error of the spacecraft using polynomials with unknown coefficients;

[0011] Calculate the inter-satellite pseudo-range of each set of two-way ranging and establish a two-way measurement equation; and

[0012] The coefficients of the spacecraft position polynomial, velocity polynomial and clock error polynomial are determined by using the least square method for multiple iterations.

[0013] In a preferred embodiment of the present invention, it is provided that the use of a polynomial with unknown coefficients to express the position, velocity and clock error of the spacecraft includes:

[0014] Let the reference time be t ref , the position of the spacecraft at time t is expressed as expression F1:

[0015]

[0016] where b i 、c i ,d i is the coefficient to be determined of the position, x, y, z represent the position of the spacecraft, and the reference time t ref is the set value;

[0017] Derivative expression F1 with respect to t yields the velocity expression F2 of the spacecraft:

[0018]

[0019] Where vx, vy, vz are the velocities of the spacecraft;

[0020] The clock error of the spacecraft is expressed as Expression F3:

[0021]

[0022] Among them, δt(t) is the clock error, a i is the coefficient of clock error to be determined, t ref is the reference time; the spacecraft may select the order of the position and clock error polynomial according to its own position and clock characteristics;

[0023] The higher the order, the higher the fitting accuracy of the polynomial, the more data accumulation is required, and the higher the calculation complexity is; and

[0024] For each set of ranging pairs, the time slot 0 t0 is known, and the position, velocity and clock error of the spacecraft at the time slot 0 can be represented by expressions F1, F2 and F3 respectively.

[0025] In another preferred embodiment of the present invention, it is provided that calculating the inter-satellite pseudo-range of each set of two-way ranging and establishing the two-way measurement equation comprises:

[0026] Calculate the propagation delay of the Ka signal;

[0027] The inter-satellite pseudo-range of the two-way ranging is calculated to the time slot 0;

[0028] Establish the bidirectional measurement equation F6 after reduction and rewrite it into equation F7;

[0029] Add and subtract the two equations in equation F7 to obtain equation F8;

[0030] Rewrite equation F8 according to the position and clock error of the navigation satellite and the position and clock error of the spacecraft to obtain equation F9;

[0031] At the approximate values ​​of the orbit coefficients to be determined and the approximate values ​​of the clock error coefficients to be determined, the right sides of the two equations in equation F9 are linearly expanded to obtain equation F10;

[0032] By discarding the higher order terms, equation F10 is rewritten in matrix form to obtain equation F11; and

[0033] For M sets of chained ranging pairs, M sets of equations F11 are combined to obtain equation F12.

[0034] In another preferred embodiment of the present invention, it is provided that calculating the propagation delay of the Ka signal includes:

[0035] The propagation delay τ1 of the Ka signal from the navigation satellite to the spacecraft is calculated according to equation F4:

[0036]

[0037] Among them, T r1 is the spacecraft measurement time, T e1 is the time when the navigation satellite sends the Ka signal, R(T r1 ) represents the spacecraft at T r1 The position at the moment, R j (T e1 ) represents the navigation satellite at T e1 The location at the moment;

[0038] The propagation delay τ2 of the Ka signal from the spacecraft to the navigation satellite is calculated according to equation F5:

[0039]

[0040] Among them, T r2 is the navigation satellite measurement time, T e2 is the time when the spacecraft sends the Ka signal, R j (T r2 ) represents the navigation satellite at T r2 The position at the moment, R(T e1 ) represents the spacecraft at T e1 The location at the moment;

[0041] The propagation delays τ1 and τ2 are calculated by iterating Equation F4 and Equation F5.

[0042] In another preferred embodiment of the present invention, it is provided that the calculation of the inter-satellite pseudo-range of the two-way ranging to the time slot 0 includes:

[0043] Calculate the return time Δt according to the following formula:

[0044]

[0045] Wherein Δt1 is the calculated time of the spacecraft, and Δt2 is the calculated time of the navigation satellite;

[0046] The spacecraft and the navigation satellite measure pseudo-range based on the clock face time, and the clock difference of the spacecraft at time t is represented by δt(t), δt j (t) represents the clock error of the navigation satellite at time t;

[0047] At the time of measurement by the spacecraft, the clock time of the spacecraft is t r At the time of measurement of the navigation satellite, the clock time of the navigation satellite is

[0048] but

[0049] Where δt(t r ) is the spacecraft at the measurement time T r1 The clock difference, is the navigation satellite at the measurement time T r2 The clock difference

[0050] At time slot 0, the clock speed of the spacecraft is a1, and the clock speed of the navigation satellite is The inter-satellite pseudorange correction Δρ is expressed as the following formula:

[0051]

[0052] Where Δρ1 is the inter-satellite pseudo-range correction of the spacecraft, Δρ2 is the inter-satellite pseudo-range correction of the navigation satellite, R(t0) is the position of the spacecraft at time slot 0, R j (t0) is the position of the navigation satellite at time slot 0;

[0053] Assume that the inter-satellite pseudo-range measured by the spacecraft to be The intersatellite pseudo-range of the spacecraft measured by the navigation satellite is: Then the pseudo-range after calculation is:

[0054]

[0055] where ρ ji The inter-satellite pseudo-range measured by the spacecraft for the navigation satellite is converted to the value of the time slot 0, ρ ij The inter-satellite pseudo-range of the spacecraft measured by the navigation satellite is converted to the value at the time slot 0.

[0056] In another preferred embodiment of the present invention, it is provided that the bidirectional measurement equation F6 after reduction is established and rewritten as equation F7 including:

[0057] The two-way measurement equation F6 is established using the calculated pseudo-range:

[0058]

[0059] δt(t0) is the clock error of the spacecraft at time slot 0, δt j (t0) is the clock error of navigation satellite j at time slot 0, c is the speed of light, are the transmit and receive channel delays of the spacecraft and navigation satellite j, respectively, relji , l relij To correct for the relativistic effect, l troji and l troij is the atmospheric tropospheric delay, is the phase center correction, ε ji and ε ij To measure noise; and

[0060] Rewrite Equation F6 as Equation F7:

[0061]

[0062] In another preferred embodiment of the present invention, it is provided that equation F8 obtained by adding and subtracting the two equations in equation F7 comprises:

[0063] Will and They are recorded as:

[0064]

[0065] Will and Substitute into equation F7, then add and subtract the two terms of equation F7 to obtain equation F8:

[0066]

[0067] In another preferred embodiment of the present invention, it is provided that rewriting equation F8 according to the position and clock error of the navigation satellite and the position and clock error of the spacecraft to obtain equation F9 includes:

[0068] The position, velocity and clock error of the navigation satellite at time slot 0 are calculated using the ephemeris:

[0069]

[0070] in is the position of the navigation satellite at the time slot 0, is the speed of the navigation satellite at time slot 0, δt j (t0) is the clock difference of the navigation satellite at the time slot 0; and

[0071] Rewrite equation F8 according to the position and clock error of the navigation satellite and the position and clock error of the spacecraft to obtain equation F9:

[0072]

[0073] The coefficient a on the right side of equation F9 i , b i , c i , d i unknown.

[0074] In another preferred embodiment of the present invention, it is provided that at the approximate values ​​of the orbit coefficients to be determined and the approximate values ​​of the clock error coefficients to be determined, the right sides of the two equations in equation F9 are linearly expanded to obtain equation F10 including:

[0075] set up

[0076] Where Aorb is the orbit coefficient to be determined, and Aclk is the clock error coefficient to be determined;

[0077] Taking the orbit coefficient to be determined and the clock error coefficient to be determined as variables, the right sides of the two equations in equation F9 are linearly expanded at the approximate values ​​of the orbit coefficient to be determined and the approximate values ​​of the clock error coefficient to be determined, respectively, to obtain equation F10:

[0078]

[0079] Aorb * is the approximate value of the coefficient to be determined for the orbit, Aclk * is the approximate value of the clock error coefficient to be determined, ρ 0 ij (Aorb * ) is the approximate value Aorb of the coefficient to be determined for the orbit * Calculate the distance between the spacecraft and the navigation satellite at time t0.

[0080] In another preferred embodiment of the present invention, it is provided that the high-order terms are discarded and equation F10 is rewritten into a matrix form to obtain equation F11 including:

[0081]

[0082] in is a 1×(3n+3) matrix;

[0083] and They are:

[0084]

[0085]

[0086]

[0087] In another preferred embodiment of the present invention, it is provided that for M sets of chained distance measuring pairs, the equation F12 obtained by combining M sets of equations F11 includes:

[0088] For M link-building and ranging pairs, M equations F11 are combined and X1 = Aorb-Aorb * and X2 = Aclk-Aclk * As variables, we get equation F12:

[0089]

[0090] Among them B orb is an M×1 matrix, H orb is an M×(3n+3) matrix, X1 is a (3n+3)×1 matrix, B clk is an M×1 matrix, H clk is an M×(p+1) matrix, and X2 is a (p+1)×1 matrix.

[0091] In a preferred embodiment of the present invention, it is provided that the coefficients of the position polynomial, velocity polynomial and clock error polynomial of the spacecraft are determined by multiple iterations of the least square method, including:

[0092] Set a reasonable initial value X1 1 , X2 1 , according to the iterative formula F12 of the least squares method, the optimal solution of the kth step is:

[0093]

[0094] but

[0095] Aor b+1 is the polynomial coefficient of the trajectory of the K+1th step, Aclk k+1 are the polynomial coefficients of the clock error at the K+1th step; and

[0096] The iteration threshold is set, and after multiple iterations, a set of polynomial coefficient solutions for position, velocity, and clock error are obtained.

[0097] The present invention has at least the following beneficial effects: when the GNSS signal is very weak but the Ka signal strength is stable, the orbit determination and time synchronization of the spacecraft can be completed by adopting the method of the present invention and utilizing the inter-satellite pseudo-range of Ka-band time-sharing two-way ranging without knowing the position, speed and clock error information of the spacecraft. The method is simple and has high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] The present invention will be further described below with reference to specific embodiments in conjunction with the accompanying drawings.

[0099] Figure 1 A schematic diagram of the bidirectional pseudorange reduction principle according to the present invention is shown;

[0100] Figure 2 A flow chart of a method for precise orbit determination and time synchronization based on time-sharing bidirectional ranging according to the present invention is shown;

[0101] Figure 3 The maximum error of the polynomial order and position according to the present invention is shown;

[0102] Figure 4 shows the error of the position expressed by a fourth-order polynomial within 5 minutes according to the present invention; and

[0103] Figure 5 The figure shows the positioning error and time synchronization error of a Beidou satellite within 5 minutes according to the present invention. DETAILED DESCRIPTION

[0104] It should be noted that the components in the figures may be shown exaggeratedly for the sake of illustration and are not necessarily true to scale. In the figures, identical or functionally identical components are provided with the same reference numerals.

[0105] In the present invention, each embodiment is only intended to illustrate the aspects of the present invention and should not be construed as limiting.

[0106] In the present invention, unless otherwise specified, the quantifiers "a", "an" and "an" do not exclude the presence of a plurality of elements.

[0107] It should also be pointed out that in the embodiments of the present invention, for the sake of clarity and simplicity, only a portion of the parts or components may be shown, but a person of ordinary skill in the art will understand that under the teachings of the present invention, required parts or components may be added as needed in specific scenarios.

[0108] It should also be pointed out that within the scope of the present invention, the terms "same", "equal", "equal to" and the like do not mean that the two values ​​are absolutely equal, but allow a certain reasonable error, that is, the terms also cover "substantially the same", "substantially equal", and "substantially equal to".

[0109] In addition, the numbering of the steps of the methods of the present invention does not limit the execution order of the method steps. Unless otherwise specified, the method steps can be executed in different orders.

[0110] The solution of the present invention is based on the following insight of the inventor: for a certain spacecraft, it is only necessary to know an almanac with an error kilometer level to complete the two-way link establishment with the corresponding navigation satellite. The two inter-satellite pseudo-ranges obtained by the spacecraft with a navigation satellite are completed in two different time periods within a transceiver time slot. The inter-satellite pseudo-ranges obtained by the spacecraft with different navigation satellites are completed in different transceiver time slots. If these inter-satellite pseudo-ranges of time-sharing two-way ranging are to be used for orbit determination and time synchronization, the position, velocity and clock error of the spacecraft must be known, and the inter-satellite pseudo-ranges measured in different time periods must be converted to the same moment, and then the position, velocity and clock error of the spacecraft must be corrected according to the calculation results of the two-way measurement equation. However, when the precise position, velocity and clock error of the spacecraft are unknown, it is impossible to accurately convert the inter-satellite pseudo-ranges obtained in different transceiver time slots, and it is also impossible to use these inter-satellite pseudo-ranges of time-sharing two-way ranging to determine the position, velocity and clock error of the spacecraft. In order to achieve precise orbit determination and time synchronization of a spacecraft by using inter-satellite pseudo-range of time-sharing two-way ranging when the position, velocity and clock error information of the spacecraft are unknown, the inventors have proposed a precise orbit determination and time synchronization method based on time-sharing two-way ranging. The present invention will be further described below in conjunction with specific embodiments and with reference to the accompanying drawings.

[0111] Embodiment 1

[0112] Figure 1 The figure shows the principle diagram of two-way pseudorange reduction according to the present invention.

[0113] The two intersatellite pseudoranges obtained by the spacecraft from the navigation satellite j are completed in two different time periods within a transmit and receive time slot. The two intersatellite pseudoranges need to be converted to the same time to obtain the converted pseudoranges before calculation. Figure 1 As shown, T r1 is the spacecraft measurement time, T r2 is the measurement time of navigation satellite j, and T r1 The inter-satellite pseudo-range and T of the navigation satellite j measured by the spacecraft at time r2 The inter-satellite pseudo-ranges of the navigation satellite j measuring the spacecraft obtained at time slot 0 are all calculated to the time slot 0.

[0114] The first step is to calculate the propagation delay, τ1 is the propagation delay of the Ka signal from navigation satellite j to the spacecraft, and τ2 is the propagation delay of the Ka signal from the spacecraft to navigation satellite j. The second step is to calculate the return time, which is the difference between the measurement time and the time slot 0. The third step is to calculate the pseudorange return correction, using the return time of the spacecraft and navigation satellite j, the clock speed of the spacecraft and navigation satellite at time slot 0, the propagation delay τ1, the propagation delay τ2, the position of the spacecraft and navigation satellite j at time slot 0, and the spacecraft at T r1 The position at time T, navigation satellite j e1 The position at time T, navigation satellite j r2 The position of the spacecraft at time T e2 The fourth step is to use the inter-satellite pseudo-range measured by the spacecraft to measure the navigation satellite j, the inter-satellite pseudo-range measured by the navigation satellite j to measure the spacecraft, and the pseudo-range correction to calculate the pseudo-range after calculation.

[0115] Embodiment 2

[0116] Figure 2 A flow chart of a method for precise orbit determination and time synchronization based on time-sharing bidirectional ranging according to the present invention is shown.

[0117] A method for precise orbit determination and time synchronization based on time-sharing two-way ranging is specifically carried out in the following steps:

[0118] Step 1: Using the almanac with kilometer error level, two-way ranging is performed between the spacecraft whose orbit and time synchronization are to be determined and the corresponding navigation satellite according to the transmit and receive time slots to obtain the inter-satellite pseudo-range.

[0119] Step 2: The navigation satellite broadcasts the ephemeris, and the spacecraft whose orbit and time synchronization are to be determined receives the corresponding navigation satellite ephemeris through the communication function of the Ka inter-satellite link.

[0120] Step 3, using a polynomial with unknown coefficients to represent the position, velocity and clock error of the spacecraft whose orbit and time synchronization are to be determined, is specifically performed in the following steps:

[0121] Step 3.1, let the reference time be t ref , the position of the spacecraft whose orbit and time synchronization are to be determined at time t is expressed as expression F1:

[0122]

[0123] where b i 、c i d i is the coefficient to be determined of the position, x, y, z represent the position of the spacecraft, and the reference time t ref is a set value; and

[0124] The spacecraft can select the order of the position polynomial based on its own position. The higher the order of the polynomial, the higher the fitting accuracy of the polynomial, the more data accumulation is required, and the higher the calculation complexity is.

[0125] Step 3.2, take the derivative of expression F1 with respect to t, and obtain the velocity expression F2 of the spacecraft whose orbit and time synchronization are to be determined:

[0126]

[0127] Where vx, vy, and vz are the velocities of the spacecraft;

[0128] Step 3.3, express the spacecraft clock error as expression F3:

[0129]

[0130] Among them, δt(t) is the clock error, a i is the coefficient of clock error to be determined, t ref is the reference time;

[0131] The spacecraft can select the order of the clock error polynomial according to its own clock characteristics. The higher the order, the higher the fitting accuracy of the clock error polynomial, the more data accumulation is required, and the higher the calculation complexity; and

[0132] For each set of ranging pairs, the time slot 0 t0 is known, and the expressions F1, F2 and F3 can be used to represent the position, velocity and clock error of the spacecraft at the time slot 0 respectively.

[0133] Step 4, calculate the inter-satellite pseudo-range of each set of two-way ranging and establish a two-way measurement equation, specifically according to the following steps:

[0134] Step 4.1, calculate the propagation delay of the Ka signal:

[0135] The propagation delay τ1 of the Ka signal from the navigation satellite to the spacecraft j is calculated according to equation F4:

[0136]

[0137] Among them, T r1 is the spacecraft measurement time, T e1 is the time when navigation satellite j sends Ka signal, R(T r1 ) represents the spacecraft at T r1 The position at the moment, R j (T e1 ) represents the navigation satellite j at T e1 The location at the moment;

[0138] The propagation delay τ2 of the Ka signal from the spacecraft to the navigation satellite j is calculated according to equation F5:

[0139]

[0140] Among them, T r2 is the measurement time of navigation satellite j, T e2 The moment when the spacecraft sends the Ka signal, R j (T r2 ) represents the navigation satellite j at time T r2 Position, R(T e2 ) represents the spacecraft at time T e2 location;

[0141] Calculate the propagation delays τ1 and τ2 by iterating equations F4 and F5;

[0142] Step 4.2, calculate the inter-satellite pseudo-range of the two-way ranging to the time slot 0, specifically according to the following steps:

[0143] Step 4.2.1, calculate the return time Δt according to the following formula:

[0144]

[0145] Where Δt1 is the spacecraft’s return time, and Δt2 is the navigation satellite j’s return time;

[0146] Step 4.2.2, calculate the inter-satellite pseudo-range correction:

[0147] The intersatellite pseudorange is measured by the spacecraft and the navigation satellite based on the clock time. δt(t) represents the clock error of the spacecraft at time t. j (t) represents the clock error of the navigation satellite at time t;

[0148] At the time of measurement by the spacecraft, the clock time of the spacecraft is t r At the time of measurement by navigation satellite j, the clock time of the navigation satellite is

[0149] but

[0150] Where δt(t r ) is the spacecraft at the measurement time T r1 The clock difference, is the navigation satellite j at the measurement time T r2 The clock difference

[0151] At time slot 0, the clock speed of the spacecraft is a1, and the clock speed of navigation satellite j is The inter-satellite pseudorange correction Δρ is expressed as the following formula:

[0152]

[0153] Where Δρ1 is the inter-satellite pseudo-range correction of the spacecraft, Δρ2 is the inter-satellite pseudo-range correction of navigation satellite j, R(t0) is the position of the spacecraft at time slot 0, and R j (t0) is the position of navigation satellite j at time slot 0;

[0154] Step 4.2.3, calculate the converted pseudorange based on the inter-satellite pseudorange correction and the inter-satellite pseudorange:

[0155] Assume that the inter-satellite pseudo-range measured by the spacecraft for navigation satellite j is The intersatellite pseudo-range of the navigation satellite j measuring the spacecraft is Then the pseudo-range after calculation is:

[0156]

[0157] where ρ ji is the inter-satellite pseudo-range measured by the spacecraft to the value of time slot 0, ρ ij The inter-satellite pseudo-range of the spacecraft measured by navigation satellite j is converted to the value at time slot 0;

[0158] Step 4.3, establish the bidirectional measurement equation F6 after reduction, and rewrite it into equation F7:

[0159] The two-way measurement equation F6 is established using the calculated pseudo-range:

[0160]

[0161] δt(t0) is the clock error of the spacecraft at time slot 0, δt j (t0) is the clock error of navigation satellite j at time slot 0, c is the speed of light, are the transmit and receive channel delays of the spacecraft and navigation satellite j, respectively, relji , l relij To correct for the relativistic effect, l troji and l troijis the atmospheric tropospheric delay, is the phase center correction, ε ji and ε ij To measure noise;

[0162] Rewrite Equation F6 as Equation F7:

[0163]

[0164] Step 4.4, add and subtract the two equations in equation F7 to obtain equation F8:

[0165] Will and They are recorded as:

[0166]

[0167] Will and Substitute into equation F7, then add and subtract the two terms of equation F7 to obtain equation F8:

[0168]

[0169] Step 4.5, use the ephemeris to calculate the position, velocity and clock error of navigation satellite j at time slot 0:

[0170]

[0171] in is the position of navigation satellite j at time slot 0, is the speed of navigation satellite j at time slot 0, δt j (t0) is the clock error of navigation satellite j at time slot 0;

[0172] Step 4.6, rewrite equation F8 according to the position and clock error of navigation satellite j and the position and clock error of the spacecraft to obtain equation F9:

[0173]

[0174] The coefficient a on the right side of equation F9 i , b i , c i , d i unknown;

[0175] Step 4.7, at the approximate values ​​of the orbit coefficients to be determined and the approximate values ​​of the clock error coefficients to be determined, linearize and expand the right sides of the two equations in equation F9 to obtain equation F10:

[0176] set up

[0177] Where Aorb is the orbit coefficient to be determined, and Aclk is the clock error coefficient to be determined;

[0178] Taking the orbit coefficient to be determined and the clock coefficient to be determined as variables, the right sides of the two equations in equation F9 are linearly expanded at the approximate values ​​of the orbit coefficient to be determined and the approximate values ​​of the clock coefficient to be determined, respectively, to obtain equation F10:

[0179]

[0180] Aorb * is the approximate value of the orbital coefficient to be determined, Aclk * is the approximate value of the clock error coefficient to be determined, ρ 0 ij (Aorb * ) is the approximate value of the orbital coefficient to be determined Aorb * The calculated distance between the spacecraft and navigation satellite j at time t0;

[0181] Step 4.8, discard the higher-order terms and rewrite equation F10 into matrix form to obtain equation F11:

[0182]

[0183] in is a 1×(3n+3) matrix;

[0184] and They are:

[0185]

[0186]

[0187]

[0188] Step 4.9, for M sets of chained distance measurement pairs, combine M sets of equations F11 to obtain equation F12 including:

[0189] For M link-building and ranging pairs, M equations F11 are combined and X1 = Aorb-Aorb * and X2 = Aclk-Aclk * As variables, we get equation F12:

[0190]

[0191] Among them B orb is an M×1 matrix, H orb is an M×(3n+3) matrix, X1 is a (3n+3)×1 matrix, B clk is an M×1 matrix, Hclk is an M×(p+1) matrix, and X2 is a (p+1)×1 matrix.

[0192] Step 5, use the least squares method to iterate multiple times to determine the coefficients of the spacecraft position polynomial, velocity polynomial, and clock error polynomial:

[0193] Set a reasonable initial value X1 1 , X2 1 , according to the iterative formula F12 of the least squares method, the optimal solution of the kth step is:

[0194]

[0195] but

[0196] Aorb k+1 is the polynomial coefficient of the trajectory of the K+1th step, Aclk k+1 are the polynomial coefficients of the clock error at the K+1th step; and

[0197] The iteration threshold is set, and after multiple iterations, a set of polynomial coefficient solutions for orbits and clock errors is obtained.

[0198] Embodiment 3

[0199] Figure 3 shows the maximum error of the polynomial order and position according to the present invention, and Figure 4 The error of the position expressed by a fourth-order polynomial within 5 minutes according to the present invention is shown.

[0200] A navigation MEO satellite in a Beidou satellite system is randomly selected as the spacecraft for which the orbit and clock error are to be determined. It completes ranging and communication with other navigation satellites within the specified time according to the time slot table. To achieve a certain accuracy, the fitting polynomials of position, velocity and clock error must meet a certain order. For navigation MEO satellites, in the case of long periods of time, the position polynomial generally reaches 8-10 orders. The longer the data period, the more data is accumulated, the higher the calculation complexity, and the longer the time required for calculation. In the scenario set by the present invention, an implicit requirement is to achieve positioning and time synchronization as quickly as possible, so the data period cannot be too long. Therefore, the order of the polynomial can be greatly reduced, and when calculating, the dimension M×(3n+3) of the coefficient matrix will also be reduced.

[0201] In this embodiment, the data period is set to 5 minutes. When the data period is set to 5 minutes, the position polynomial order can be 3rd, 4th, or 5th order, and the clock error polynomial is generally set to 2nd order. Figure 3As shown in the figure, when the data period is 5 minutes, the higher the order, the higher the fitting accuracy of the position polynomial, and the smaller the error of the position expressed by the polynomial. When the polynomial order is 3rd order, the error of x is 0.0475 meters, the error of y is 0.0013 meters, and the error of z is 0.0273 meters; when the polynomial order is 4th order, the error of x is 5.9330e -06 Meters, the error of y is 1.6153e -04 meters, the error of z is 4.1530e -05 When the polynomial order is 5, the error of x is 7.1450e -07 Meters, the error of y is 5.5134e -07 meters, the error of z is 5.2899e -07 Meter. Figure 4 As shown in Figure 1, the position error expressed by the fourth-order polynomial changes within 300 seconds (5 minutes), where the position errors xerr, yerr and zerr are the smallest at 300 seconds. Figure 3 and Figure 4 As shown, within 5 minutes, if the polynomial order is 4 or above, the fitting error of the polynomial can be reduced to less than millimeter.

[0202] If the second embodiment There is a solution, which requires that the rank of the coefficient matrix is ​​greater than or equal to (3n+3). When the rank n=4, the number of link building and ranging logarithms should satisfy:

[0203] M≥3n+3=15;

[0204] When the order n = 5, the number of link building and ranging logarithms should satisfy:

[0205] M≥3n+3=18.

[0206] In actual spacecraft operation, the design of the time slot table is set according to the antenna visibility, which may not meet the above requirements. Therefore, a fourth-order polynomial is selected to express the position of the spacecraft. At this time, the link establishment and ranging correspondence meet the requirement of at least 15.

[0207] Embodiment 4

[0208] In this embodiment, for a specific model of satellite, a 5-minute data period is selected as the data period, the order of the position polynomial is selected as 4th order, the order of the clock error polynomial is selected as 2nd order, and steps 1-2 and steps 4.1-4.5 in step 4 are consistent with steps 1-2 and steps 4.1-4.5 in step 4 in embodiment 1.

[0209] Step 3, using a polynomial with unknown coefficients to represent the position, velocity and clock error of the spacecraft whose orbit and time synchronization are to be determined, is specifically performed in the following steps:

[0210] Step 3.1, express the position of the spacecraft whose orbit and time synchronization are to be determined as expression F1:

[0211]

[0212] where b i 、c i d i is the position coefficient to be determined, x, y, z represent the position of the spacecraft, n = 4, tt ref For a 5-minute period, t ref is the reference time;

[0213] Step 3.2, take the derivative of expression F1 with respect to t, and obtain the velocity expression F2 of the spacecraft whose orbit and time synchronization are to be determined:

[0214]

[0215] Where vx, vy, vz are the velocities of the spacecraft, n = 4, tt ref The time period is 5 minutes;

[0216] Step 3.3, express the spacecraft clock error as expression F3:

[0217]

[0218] Among them, δt(t) is the clock error, a i is the coefficient of clock error to be determined, p = 2, t ref is the reference time, tt ref The time period is 5 minutes;

[0219] For each set of ranging pairs, the time slot 0 t0 is known, and the expressions F1, F2 and F3 can be used to represent the position, velocity and clock error of the spacecraft at the time slot 0 respectively.

[0220] Step 4.6, rewrite equation F8 according to the position and clock error of the navigation satellite and the position and clock error of the spacecraft to obtain equation F9:

[0221]

[0222] The coefficient a on the right side of equation F9 i , b i , c i , d i Unknown, t0-t ref =5 minutes, n=4,

[0223] p=2.

[0224] Step 4.7, at the approximate values ​​of the orbit coefficients to be determined and the approximate values ​​of the clock error coefficients to be determined, linearize and expand the right sides of the two equations in equation F9 to obtain equation F10:

[0225] set up

[0226] Where Aorb is the orbit coefficient to be determined, and Aclk is the clock error coefficient to be determined;

[0227] Taking the orbit coefficients to be determined and the clock coefficients to be determined as variables, the right sides of the two equations in equation F9 are linearly expanded at the approximate values ​​of the orbit coefficients to be determined and the approximate values ​​of the clock coefficients to be determined, respectively, to obtain equation F10:

[0228]

[0229] Aorb * is the approximate value of the orbital coefficient to be determined, Aclk * is the approximate value of the clock error coefficient to be determined, ρ 0 ij (Aorb * ) is the approximate value of the orbital coefficient to be determined Aorb * The calculated distance between the spacecraft and the navigation satellite at time t0, tt ref The time period is 5 minutes, n=4, p=2.

[0230] Step 4.8, discard the higher-order terms and rewrite equation F10 into matrix form to obtain equation F11:

[0231]

[0232] in is a 1×15 matrix, tt ref The time period is 5 minutes;

[0233] and They are:

[0234]

[0235]

[0236]

[0237] where tt ref The period is 5 minutes.

[0238] Step 4.9, for M sets of chained distance measurement pairs, combine M sets of equations F11 to obtain equation F12 including:

[0239] For M link-building and ranging pairs, M equations F11 are combined and X1 = Aorb-Aorb * and X2 = Aclk-Aclk * As variables, we get equation F12:

[0240]

[0241] Among them B orb is an M×1 matrix, H orb is an M×15 matrix, X1 is a 15×1 matrix, B clk is an M×1 matrix, H clk is an M×3 matrix, and X2 is a 3×1 matrix.

[0242] Step 5, use the least squares method to iterate multiple times to determine the coefficients of the spacecraft position polynomial, velocity polynomial, and clock error polynomial:

[0243] Set the initial value of the iteration:

[0244]

[0245] According to the iterative formula F12 of the least squares method, the optimal solution of the kth step is:

[0246]

[0247] but

[0248] Aorb k+1 is the polynomial coefficient of the trajectory of the K+1th step, Aclk k+1 are the polynomial coefficients of the clock error at the K+1th step; and

[0249] The iteration threshold is set, and after multiple iterations, a set of polynomial coefficient solutions for position, velocity, and clock error are obtained.

[0250] Embodiment 5

[0251] Figure 5 The figure shows the positioning error and time synchronization error of a Beidou satellite within 5 minutes according to the present invention.

[0252] According to the method of the present invention, the two-way ranging value obtained by a navigation MEO satellite in a Beidou satellite system within a certain 5-minute period is used for calculation to obtain a set of polynomial coefficient solutions for orbit and clock error, and finally the position and clock error polynomial of a navigation MEO satellite are obtained and then the error curve is obtained by subtracting the standard orbit. Figure 5As shown, the xerr curve, yerr curve and zerr curve represent the position error of a navigation MEO satellite, and the clkerr curve represents the clock error of a navigation MEO satellite. The values ​​of clkerr and xerr are in the range of 0 to -0.1 meters, and the values ​​of yerr and zerr are in the range of 0 to 0.12 meters. It can be seen that no matter the position or the clock error, the error within 5 minutes is within the range of 0.12 meters. The above data show that the positioning method based on time-sharing two-way ranging according to the present invention can better complete the orbit determination and time synchronization of the satellite.

[0253] The present invention has at least the following beneficial effects: when the GNSS signal is very weak but the Ka signal strength is stable, the orbit determination and time synchronization of the spacecraft can be completed by adopting the method of the present invention and utilizing the inter-satellite pseudo-range of Ka-band time-sharing two-way ranging without knowing the position, speed and clock error information of the spacecraft. The method is simple and has high accuracy.

[0254] Although some embodiments of the present invention have been described in this application document, it will be appreciated by those skilled in the art that these embodiments are merely shown as examples. Those skilled in the art may conceive of numerous variations, alternatives, and improvements under the teachings of the present invention without departing from the scope of the present invention. The appended claims are intended to define the scope of the present invention and thereby cover methods and structures within the scope of these claims themselves and their equivalents.

Claims

1. A method for precise orbit determination and time synchronization based on time-sharing bidirectional ranging, the method comprising the following steps: Using an almanac with kilometer-level error, two-way ranging is performed between the spacecraft whose orbit and time synchronization are to be determined and the corresponding navigation satellite according to the transmission and reception time slots to obtain inter-satellite pseudorange; The navigation satellite broadcasts ephemeris; The spacecraft receives the ephemeris through the communication function of the Ka intersatellite link; Expressing the position, velocity and clock error of the spacecraft using polynomials with unknown coefficients; Calculate the inter-satellite pseudo-range of each set of two-way ranging and establish the two-way measurement equation; as well as Using a least square method for multiple iterations to determine coefficients of a position polynomial, a velocity polynomial, and a clock error polynomial for the spacecraft; The polynomials with unknown coefficients used to express the position, velocity and clock error of the spacecraft include: Let the reference time be t ref , the position of the spacecraft at time t is expressed as expression F1: where b i 、c i d i is the coefficient to be determined of the position, x, y, z represent the position of the spacecraft, and the reference time t ref is the set value; Derivative expression F1 with respect to t yields the velocity expression F2 of the spacecraft: Where vx, vy, vz are the velocities of the spacecraft; The clock error of the spacecraft is expressed as Expression F3: Among them, δt(t) is the clock error, a i is the coefficient of clock error to be determined, t ref is the reference time; The spacecraft may select the order of the position and clock error polynomial according to its own position and clock characteristics; The higher the order, the higher the fitting accuracy of the polynomial, the more data accumulation is required, and the higher the calculation complexity is; and For each set of ranging pairs, the time slot 0 t0 is known, and the position, velocity and clock error of the spacecraft at the time slot 0 can be represented by expressions F1, F2 and F3 respectively.

2. The method according to claim 1, wherein calculating the inter-satellite pseudo-range of each set of two-way ranging and establishing the two-way measurement equation comprises: Calculate the propagation delay of the Ka signal; The inter-satellite pseudo-range of the two-way ranging is calculated to the time slot 0; Establish the bidirectional measurement equation F6 after reduction and rewrite it into equation F7; Add and subtract the two equations in equation F7 to obtain equation F8; Rewrite equation F8 according to the position and clock error of the navigation satellite and the position and clock error of the spacecraft to obtain equation F9; At the approximate values ​​of the orbit coefficients to be determined and the approximate values ​​of the clock error coefficients to be determined, the right sides of the two equations in equation F9 are linearly expanded to obtain equation F10; Discarding the higher-order terms, rewriting equation F10 into matrix form yields equation F11; as well as For M sets of chained ranging pairs, M sets of equations F11 are combined to obtain equation F12.

3. The method according to claim 2, wherein calculating the propagation delay of the Ka signal comprises: The propagation delay τ1 of the Ka signal from the navigation satellite to the spacecraft is calculated according to equation F4: Among them, T r1 is the spacecraft measurement time, T e1 is the time when the navigation satellite sends the Ka signal, R(T r1 ) represents the spacecraft at T r1 The position at the moment, R j (T e1 ) represents the navigation satellite at T e1 The location at the moment; The propagation delay τ2 of the Ka signal from the spacecraft to the navigation satellite is calculated according to equation F5: Among them, T r2 is the navigation satellite measurement time, T e2 is the time when the spacecraft sends the Ka signal, R j (T r2 ) represents the navigation satellite at T r2 The position at the moment, R(T e1 ) represents the spacecraft at T e1 The location at the moment; The propagation delays τ1 and τ2 are calculated by iterating Equation F4 and Equation F5.

4. The method according to claim 2, wherein the step of converting the inter-satellite pseudo-range of the two-way ranging to the time slot 0 comprises: Calculate the return time Δt according to the following formula: Wherein Δt1 is the calculated time of the spacecraft, and Δt2 is the calculated time of the navigation satellite; The spacecraft and the navigation satellite measure pseudo-range based on the clock face time, and the clock difference of the spacecraft at time t is represented by δt(t), δt j (t) represents the clock error of the navigation satellite at time t; At the time of measurement by the spacecraft, the clock time of the spacecraft is t r At the time of measurement of the navigation satellite, the clock time of the navigation satellite is but Where δt(t r ) is the spacecraft at the measurement time T r1 The clock difference, is the navigation satellite at the measurement time T r2 The clock difference At time slot 0, the clock speed of the spacecraft is a1, and the clock speed of the navigation satellite is The inter-satellite pseudorange correction Δρ is expressed as the following formula: Where Δρ1 is the inter-satellite pseudo-range correction of the spacecraft, Δρ2 is the inter-satellite pseudo-range correction of the navigation satellite, R(t0) is the position of the spacecraft at time slot 0, R j (t0) is the position of the navigation satellite at time slot 0; Assume that the inter-satellite pseudo-range measured by the spacecraft to be The intersatellite pseudo-range of the spacecraft measured by the navigation satellite is: Then the pseudo-range after calculation is: where ρ ji The inter-satellite pseudo-range measured by the spacecraft for the navigation satellite is converted to the value of the time slot 0, ρ ij The inter-satellite pseudo-range of the spacecraft measured by the navigation satellite is converted to the value at the time slot 0.

5. The method according to claim 2, wherein establishing the reduced bidirectional measurement equation F6 and rewriting it into equation F7 comprises: The two-way measurement equation F6 is established using the calculated pseudo-range: δt(t0) is the clock error of the spacecraft at time slot 0, δt j (t0) is the clock error of the navigation satellite at time slot 0, c is the speed of light, are the transmit and receive channel delays of the spacecraft and the navigation satellite, respectively, l relji , l relij To correct for the relativistic effect, l troji and l troij is the atmospheric tropospheric delay, is the phase center correction, ε ji and ε ij To measure noise; and Rewrite Equation F6 as Equation F7:

6. The method of claim 2, wherein adding and subtracting two equations in equation F7 to obtain equation F8 comprises: Will and They are recorded as: Will and Substitute into equation F7, then add and subtract the two terms of equation F7 to obtain equation F8:

7. The method according to claim 2, wherein rewriting equation F8 to obtain equation F9 according to the position and clock error of the navigation satellite and the position and clock error of the spacecraft comprises: The position, velocity and clock error of the navigation satellite at time slot 0 are calculated using the ephemeris: in is the position of the navigation satellite at the time slot 0, is the speed of the navigation satellite at time slot 0, δt j (t0) is the clock difference of the navigation satellite at the time slot 0; as well as Rewrite equation F8 according to the position and clock error of the navigation satellite and the position and clock error of the spacecraft to obtain equation F9: The coefficient a on the right side of equation F9 i , b i , c i , d i unknown.

8. The method according to claim 2, wherein at the approximate values ​​of the orbit coefficients to be determined and the approximate values ​​of the clock error coefficients to be determined, the right sides of the two equations in equation F9 are linearly expanded to obtain equation F10, which comprises: set up Where Aorb is the orbit coefficient to be determined, and Aclk is the clock error coefficient to be determined; Taking the orbit coefficient to be determined and the clock error coefficient to be determined as variables, the right sides of the two equations in equation F9 are linearly expanded at the approximate values ​​of the orbit coefficient to be determined and the approximate values ​​of the clock error coefficient to be determined, respectively, to obtain equation F10: Where Aorb* is the approximate value of the orbit coefficient to be determined, Aclk* is the approximate value of the clock error coefficient to be determined, and ρ 0 ij (Aorb * ) is the approximate value Aorb of the coefficient to be determined for the orbit * Calculate the distance between the spacecraft and the navigation satellite at time t0.

9. The method of claim 2, wherein discarding high-order terms and rewriting equation F10 into a matrix form to obtain equation F11 comprises: in is a 1×(3n+3) matrix; and They are:

10. The method according to claim 2, wherein for M sets of chained ranging pairs, combining M sets of equations F11 to obtain equation F12 comprises: For M link-building and ranging pairs, M equations F11 are combined and X1 = Aorb-Aorb * and X2 = Aclk-Aclk * As variables, we get equation F12: Among them B orb is an M×1 matrix, H orb is an M×(3n+3) matrix, X1 is a (3n+3)×1 matrix, B clk is an M×1 matrix, H clk is an M×(p+1) matrix, and X2 is a (p+1)×1 matrix.

11. The method according to claim 1 or 10, wherein using the least square method for multiple iterations to determine the coefficients of the position polynomial, velocity polynomial and clock error polynomial of the spacecraft comprises: Set a reasonable initial value X1 1 , X2 1 , according to the principle of least squares method, formula F12 is iterated, and the optimal solution of the kth step is: but Aorb k+1 is the polynomial coefficient of the trajectory of the K+1th step, Aclk k+1 are the polynomial coefficients of the clock error at the K+1th step; and The iteration threshold is set, and after multiple iterations, a set of polynomial coefficient solutions for position, velocity, and clock error are obtained.

Images