Communication and navigation integrated method for low-orbit satellite constellation

Abstract

The invention discloses a communication and navigation integrated method for a low-orbit satellite constellation, and relates to the technical field of intersection of wireless communication and satellite navigation. Based on a low earth orbit satellite constellation architecture, each low earth orbit satellite node realizes real-time information interaction and integrated networking through inter-satellite links, and communication-navigation dual-function signals are cooperatively designed and jointly transmitted. For a communication service scene, a communication user realizes high-speed information transmission service by demodulating a communication signal. For a navigation application scene, a navigation user realizes high-precision positioning, time service and speed measurement by using the received multi-satellite collaborative navigation signal. The method is oriented to low-orbit satellite constellations, and an effective communication and navigation integrated scheme is provided for a 6G non-ground network.

Description

Technical Field

[0001] The present invention relates to the field of wireless communications, and in particular to a communication and navigation integration method for a low-orbit satellite constellation. Background Art

[0002] In recent years, with the rapid development of low-orbit satellite communication and navigation technology, the global demand for the coordination of high-precision navigation (positioning, speed measurement and timing) and high-speed communication has become increasingly urgent. In traditional satellite systems, the communication and navigation functions are designed with a separate architecture, which leads to problems such as repeated occupation of spectrum resources, redundant deployment of hardware equipment, and limited efficiency of satellite-to-ground links. For example, communication satellites need to independently occupy specific frequency bands to achieve high-speed data transmission, while navigation satellites rely on onboard atomic clocks and dedicated ranging signals to complete positioning and timing. The separation between the two in signal system, resource scheduling and service mode not only increases the cost of system construction, but also faces common technical bottlenecks such as multipath interference and power consumption surge in complex electromagnetic environments.

[0003] In response to the above problems, the academic community has proposed the concept of integrated communication and navigation design, which realizes functional integration and service efficiency doubling by sharing time-frequency-space multi-dimensional resources. At present, the existing integrated communication and navigation technology mainly relies on ground base stations or single satellite systems. However, due to the limited service capabilities of a single satellite, there are defects such as limited coverage and insufficient dynamic adaptability. Its coverage and data processing capabilities are difficult to meet the future 6G network's needs for global seamless connectivity and high-precision navigation.

[0004] To solve the above problems, the integrated communication and navigation technology based on low-orbit satellite constellations has become a new direction to break through the above bottlenecks. By building a multi-satellite collaborative networking architecture, we can make full use of the global coverage, low transmission delay and high dynamic reconstruction capabilities of low-orbit satellites to achieve deep coupling of communication signals and navigation signals at the physical layer. Compared with traditional methods, multi-satellite collaboration can significantly improve the utilization rate of space resources, enhance anti-interference capabilities, and improve positioning accuracy, speed measurement accuracy and data transmission efficiency. It is suitable for a variety of application scenarios such as smart transportation, drone management, precision agriculture, and emergency communications. Therefore, a communication and navigation integration method for low-orbit satellite constellations is proposed, which can not only provide a more efficient and reliable solution for the future 6G space-ground integrated network, but also promote the integrated development of satellite communication and navigation technologies, improve the intelligence level of global information infrastructure, and lay a core technical foundation for building a 6G ubiquitous intelligent network covering the entire space, land, and sea. Summary of the invention

[0005] The purpose of the present invention is to meet the growing demand for global communication and high-precision navigation, to solve the problems of waste of spectrum resources, high system complexity, insufficient coordination capability, etc. in traditional separate communication and navigation systems, and to propose a communication and navigation integration method for low-orbit satellite constellations.

[0006] The specific technical solution adopted in the present invention is as follows:

[0007] The present invention provides a communication and navigation integration method for a low-orbit satellite constellation, which is as follows:

[0008] S1: In the low-orbit satellite constellation system, K dual-function low-orbit satellites equipped with N-dimensional uniform antenna arrays are set up to form a low-orbit satellite constellation service group, which jointly provides communication and navigation fusion services for L single-antenna communication users and M single-antenna navigation users within the coverage area;

[0009] S2: Each low-orbit satellite node in the low-orbit satellite constellation service group uses inter-satellite links to build a collaborative network, and obtains the channel state information h from the kth low-orbit satellite to the lth communication user in real time through channel estimation or user feedback. k,l , and the channel state information g from the kth low-orbit satellite to the mth navigation user k,m ;

[0010] S3: Based on the obtained channel state information, the low-orbit satellite constellation system uses a multi-satellite collaborative communication and navigation integrated beam design method to jointly optimize and design communication transmission beams v for all low-orbit satellites in the low-orbit satellite constellation service group. k,l and navigation transmit beam w k ; where v k,l is the communication transmission beam of the kth low-orbit satellite for the lth communication user, w k Transmit the navigation beam for the kth low-orbit satellite;

[0011] S4: According to the beam design scheme obtained by the multi-satellite collaborative communication and navigation integrated beam design method, each low-orbit satellite in the low-orbit satellite constellation service group constructs and transmits a communication-navigation dual-function signal in, is the communication data signal for the lth communication user, is the navigation data signal of the kth low-orbit satellite after pseudo-random code spread;

[0012] S5: Based on the received communication-navigation dual-function signal, the communication user decodes to obtain the communication data information, the navigation user obtains the navigation data information through pseudo-random decoding, and obtains the position coordinates and clock deviation of the navigation user itself based on the pseudo-range measurement method, and then uses the Doppler frequency shift maximum likelihood estimation to obtain the navigation user's own motion velocity vector.

[0013] Preferably, in S3, a multi-satellite collaborative communication and navigation integrated beam design method is specifically as follows:

[0014] S31: Calculate the average communication transmission rate of the lth communication user in, is the noise variance of the signal received by the lth communication user, |·| represents the absolute value;

[0015] S32: Definition Defining intermediate variables and According to the average communication transmission rate limit, let Among them, tr(·) represents the trace of the matrix, log 2 (·) represents the logarithm operation with base 2, μl is the minimum average communication transmission rate requirement of the lth communication user;

[0016] S33: Define intermediate variables in, is a continuous convex approximation expansion point, represents the operation of calculating gradients,<A·B> =tr(A Τ B) represents the inner product operation of matrix A and matrix B, and the average communication transmission rate limit is converted to μ l +η l -ξ l ≤0;

[0017] S34: According to the transmission power limit of low-orbit satellites, Among them, P k is the maximum transmission power of the kth low-orbit satellite; definition κ k is a K-dimensional row vector whose only k-th element is 1 and other elements are 0; I N is the N-dimensional identity matrix, represents the Kronecker product operation;

[0018] S35: Calculate the positioning error of the mth navigation user respectively Timing Error and speed measurement error

[0019] S36: The design goal is to minimize the weighted average navigation error of M navigation users in, and are the weights of positioning, timing and speed measurement respectively; an auxiliary variable U is introduced m ,Ω m ,Ω′ m and Ω′ m ',make and Then the design goal is equivalent to minimizing

[0020] S37: Use the interior point method or directly call the CVX toolkit to solve and obtain The smallest solution is the solution V that can minimize the weighted average navigation error of M navigation users. l and W, and then perform Gaussian decomposition to obtain the communication transmission beam v of the k-th low-orbit satellite for the l-th communication user. k,l and the navigation transmission beam w of the kth low-orbit satellite k .

[0021] Furthermore, in S35, the positioning error Timing Error and speed measurement error The calculation method is as follows:

[0022] S351: Calculate the delay vector τ for the mth navigation user m The equivalent Fisher information matrix Among them, τ m =[τ 1,m ; τ 2,m ;…τ K,m ] represents the delay vector of the mth navigation user, f m =[f 1,m ;f 2,m ; ...f K,m ] represents the Doppler shift vector about the mth navigation user,

[0023] [A] i,j represents the element in the i-th row and j-th column of matrix A, [a] i,j represents the i-th element in vector a, t is the time index, and are the channel delay and Doppler shift from the kth low-orbit satellite to the mth navigation user, represents the equivalent receiving noise variance of the mth navigation user, Diag(a) represents the operation of converting vector a into a diagonal matrix;

[0024] S352: Calculate the Fisher information matrix for the mth navigation user speed in γ m is the velocity vector of the mth navigation user;

[0025] S353: Calculate the positioning error Timing Error and speed measurement error in, Λ′=[0,0,0,1],J m is the Jacobian matrix of the linear mapping from position and time errors to time delays, (A) -1 Represents the inverse matrix of matrix A.

[0026] The present invention has the following beneficial effects:

[0027] The present invention proposes a communication and navigation integration method for low-orbit satellite constellations, which breaks through the problems of resource waste, high system complexity and low coordination efficiency caused by the independent operation of traditional communication and navigation systems. Real-time information interaction and joint beam design between satellites are realized through inter-satellite links, and communication-navigation dual-function signals are transmitted in a coordinated manner to improve the spectrum utilization and data transmission efficiency of the communication system, while enhancing the positioning, speed measurement and timing accuracy of navigation users. In addition, the multi-satellite collaborative communication and navigation integrated beam design method proposed in the present invention can effectively reduce the computational complexity and improve navigation accuracy and communication reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a system block diagram of the communication and navigation integration method for low-orbit satellite constellations;

[0029] Figure 2 It is a comparison of the weighted average navigation error obtained by the proposed method when the dimensions of the satellite antenna array and the maximum transmission power are different;

[0030] Figure 3 The weighted average navigation error obtained by the proposed method is compared when the satellite constellation orbit altitude and the communication user transmission rate requirements are different. DETAILED DESCRIPTION

[0031] The present invention is further described and illustrated below in conjunction with the accompanying drawings and specific embodiments. The technical features of each embodiment of the present invention can be combined accordingly without conflicting with each other.

[0032] The present invention provides a communication and navigation integration method for a low-orbit satellite constellation. The specific steps are as follows:

[0033] S1: In the low-orbit satellite constellation system, K dual-function low-orbit satellites equipped with N-dimensional uniform antenna arrays are set up to form a low-orbit satellite constellation service group, which jointly provides communication and navigation fusion services for L single-antenna communication users and M single-antenna navigation users within the coverage area.

[0034] S2: Each low-orbit satellite node in the low-orbit satellite constellation service group uses inter-satellite links to build a collaborative network, and obtains the channel state information h from the kth low-orbit satellite to the lth communication user in real time through channel estimation or user feedback. k,l, and the channel state information g from the kth low-orbit satellite to the mth navigation user k,m .

[0035] S3: Based on the obtained channel state information, the low-orbit satellite constellation system uses a multi-satellite collaborative communication and navigation integrated beam design method to jointly optimize the design of communication transmission beams for all low-orbit satellites in the low-orbit satellite constellation service group. k,l and navigation transmit beam w k ; where v k,l is the communication transmission beam of the kth low-orbit satellite for the lth communication user, w k is the navigation transmission beam of the kth low-orbit satellite.

[0036] As a preferred embodiment of the present invention, a multi-satellite collaborative communication and navigation integrated beam design method is specifically as follows:

[0037] S31: Calculate the average communication transmission rate of the lth communication user in, is the noise variance of the signal received by the lth communication user, |·| represents the absolute value;

[0038] S32: Definition Defining intermediate variables and According to the average communication transmission rate limit, let Among them, tr(·) represents the trace of the matrix, log 2 (·) represents the logarithm operation with base 2, μl is the minimum average communication transmission rate requirement of the lth communication user;

[0039] S33: Define intermediate variables in, is a continuous convex approximation expansion point, represents the operation of calculating gradients,<A·B> =tr(A Τ B) represents the inner product operation of matrix A and matrix B, and the average communication transmission rate limit is converted to μ l +η l -ξ l ≤0;

[0040] S34: According to the transmission power limit of low-orbit satellites, Among them, P k is the maximum transmission power of the kth low-orbit satellite; definition κ k is a K-dimensional row vector whose only k-th element is 1 and other elements are 0; I N is the N-dimensional identity matrix, represents the Kronecker product operation;

[0041] S35: Calculate the positioning error of the mth navigation user respectively Timing Error and speed measurement error

[0042] As a preferred embodiment of the present invention, the positioning error Timing Error and speed measurement error The calculation method is as follows:

[0043] S351: Calculate the delay vector τ for the mth navigation user m The equivalent Fisher information matrix Among them, τ m =[τ 1,m ; τ 2,m ;…τ K,m ] represents the delay vector of the mth navigation user, f m =[f 1,m ;f 2,m ; ...f K,m ] represents the Doppler shift vector about the mth navigation user,

[0044] [A] i,j represents the element in the i-th row and j-th column of matrix A, [a] i,j represents the i-th element in vector a, t is the time index, and are the channel delay and Doppler shift from the kth low-orbit satellite to the mth navigation user, represents the equivalent receiving noise variance of the mth navigation user, Diag(a) represents the operation of converting vector a into a diagonal matrix;

[0045] S352: Calculate the Fisher information matrix for the mth navigation user speed in γ m is the velocity vector of the mth navigation user;

[0046] S353: Calculate the positioning error Timing Error and speed measurement error in, Λ′=[0,0,0,1],J m is the Jacobian matrix of the linear mapping from position and time errors to time delays, (A) -1 Represents the inverse matrix of matrix A.

[0047] S36: The design goal is to minimize the weighted average navigation error of M navigation users in, and are the weights of positioning, timing and speed measurement respectively; an auxiliary variable U is introduced m ,Ω m ,Ω′ m and Ω′ m ',make and Then the design goal is equivalent to minimizing

[0048] S37: Use the interior point method or directly call the CVX toolkit to solve and obtain The smallest solution is the solution V that can minimize the weighted average navigation error of M navigation users. l and W, and then perform Gaussian decomposition to obtain the communication transmission beam v of the k-th low-orbit satellite for the l-th communication user. k,l and the navigation transmission beam w of the kth low-orbit satellite k .

[0049] S4: Based on the beam design scheme obtained by a multi-satellite collaborative communication and navigation integrated beam design method, each low-orbit satellite in the low-orbit satellite constellation service group constructs and transmits a communication-navigation dual-function signal in, is the communication data signal for the lth communication user, is the navigation data signal of the kth low-orbit satellite after pseudo-random code spread;

[0050] S5: Based on the received communication-navigation dual-function signal, the communication user decodes to obtain the communication data information, the navigation user obtains the navigation data information through pseudo-random decoding, and obtains the navigation user's own position coordinates and clock deviation based on the pseudo-range measurement method, and then uses the Doppler frequency shift maximum likelihood estimation to obtain the navigation user's own motion velocity vector.

[0051] Example

[0052] In this embodiment, a system block diagram of a communication and navigation integration method for a low-orbit satellite constellation is shown in FIG. Figure 1As shown in the figure, the low-orbit satellite constellation system deploys K dual-function low-orbit satellites equipped with N-dimensional uniform antenna arrays to provide communication and navigation fusion services for L single-antenna communication users and M single-antenna navigation users within the coverage area. Each low-orbit satellite node realizes real-time information interaction and integrated networking through inter-satellite links, and collaboratively designs and jointly transmits communication-navigation dual-function signals. Through the satellite-to-ground downlink, the communication user decodes and obtains the communication data information, and the navigation user obtains the navigation data information through pseudo-random decoding to obtain the navigation user's own position coordinates, clock deviation and motion velocity vector.

[0053] The specific technical solution of a communication and navigation integration method for a low-orbit satellite constellation adopted in this embodiment is as follows:

[0054] 1) In the low-orbit satellite constellation system, K dual-function low-orbit satellites equipped with N-dimensional uniform antenna arrays form a low-orbit satellite constellation service group, which jointly provide communication and navigation fusion services for L single-antenna communication users and M single-antenna navigation users within the coverage area.

[0055] 2) Each low-orbit satellite node in the low-orbit satellite constellation service group of step 1) builds a collaborative network using inter-satellite links, and obtains the channel state information h from the kth low-orbit satellite to the lth communication user in real time through channel estimation or user feedback. k,l , and the channel state information g from the kth low-orbit satellite to the mth navigation user k,m .

[0056] 3) Based on the obtained channel state information, the low-orbit satellite constellation system uses a multi-satellite collaborative communication and navigation integrated beam design method to jointly optimize the communication transmission beam design for all low-orbit satellites in the service group. k,l and navigation transmit beam w k , where v k,l is the communication transmission beam of the kth low-orbit satellite for the lth communication user, w k is the navigation transmission beam of the kth low-orbit satellite.

[0057] In this embodiment, in the above step 3), a multi-satellite collaborative communication and navigation integrated beam design method is:

[0058] 31) Calculate the average communication transmission rate of the lth communication user in is the noise variance of the signal received by the lth communication user, |·| represents the absolute value;

[0059] 32) Definition Defining intermediate variables and According to the average communication transmission rate limit, let where tr(·) represents the trace of the matrix, log 2 (·) represents the logarithm operation with base 2, μl is the minimum average communication transmission rate requirement of the lth communication user;

[0060] 33) Define intermediate variables in is a continuous convex approximation expansion point, represents the operation of calculating gradients,<A·B> =tr(A Τ B) represents the inner product operation of matrix A and matrix B, and the average communication transmission rate limit is converted to μ l +η l -ξ l ≤0;

[0061] 34) According to the transmission power limit of low-orbit satellites, Where P k is the maximum transmission power of the kth low-orbit satellite, and is defined κ k is a K-dimensional row vector whose only k-th element is 1 and other elements are 0. N is the N-dimensional identity matrix, represents the Kronecker product operation;

[0062] 35) Calculate the positioning error of the mth navigation user respectively Timing Error and speed measurement error

[0063] In this embodiment, in the above step 35), the positioning error Timing Error and speed measurement error The calculation method is:

[0064] 351) Calculate the delay vector τ for the mth navigation user m The equivalent Fisher information matrix where τ m =[τ 1,m ; τ 2,m ;…τ K,m ] represents the delay vector of the mth navigation user, f m =[f 1,m ;f 2,m ; ...f K,m ] represents the Doppler shift vector about the mth navigation user,

[0065] [A] i,jrepresents the element in the i-th row and j-th column of matrix A, [a] i,j represents the i-th element in vector a, t is the time index, and are the channel delay and Doppler shift from the kth satellite to the mth navigation user, represents the equivalent receiving noise variance of the mth navigation user, Diag(a) represents the operation of converting vector a into a diagonal matrix;

[0066] 352) Calculate the Fisher information matrix for the mth navigation user speed in γ m is the velocity vector of the mth navigation user;

[0067] 353) Calculate the positioning error Timing Error and speed measurement error in Λ′=[0,0,0,1],J m is the Jacobian matrix of the linear mapping from position and time errors to time delays, (A) -1 Represents the inverse matrix of matrix A.

[0068] 36) The design goal is to minimize the weighted average navigation error of M navigation users in and are the weights of positioning, timing and speed measurement respectively. Introduce auxiliary variable U m ,Ω m ,Ω′ m and Ω′ m ',make and Then the design goal is equivalent to minimizing

[0069] 37) Use the interior point method or directly call the CVX toolkit to solve and obtain The smallest solution is the solution V that can minimize the weighted average navigation error of M navigation users. l and W, and then perform Gaussian decomposition to obtain the communication transmission beam v of the k-th low-orbit satellite for the l-th communication user. k,l and the navigation transmission beam w of the kth satellite k .

[0070] 4) According to the beam design scheme obtained in step 3), each low-orbit satellite in the low-orbit satellite constellation service group constructs and transmits a communication-navigation dual-function signal in is the communication data signal for the lth communication user, is the navigation data signal of the kth satellite after pseudo-random code spreading.

[0071] 5) Based on the received communication-navigation dual-function signal, the communication user decodes to obtain the communication data information, and the navigation user obtains the navigation data information through pseudo-random decoding, and obtains the navigation user's own position coordinates and clock deviation based on the pseudo-range measurement method, and then uses the Doppler frequency shift maximum likelihood estimation to obtain the navigation user's own motion velocity vector.

[0072] Computer simulations show that Figure 2 As shown, in the communication and navigation integration method for low-orbit satellite constellations proposed by the present invention, the larger the antenna array deployed on the satellite, the smaller the weighted average navigation error. Furthermore, as the maximum transmission power of the satellite increases, the weighted average navigation error decreases significantly. In addition, Figure 3 It shows that in the method proposed in the present invention, as the transmission rate requirements of communication users and the orbit height of the satellite constellation decrease, the navigation performance is significantly improved.

[0073] The present invention is based on the low-orbit satellite constellation architecture. Each low-orbit satellite node realizes real-time information interaction and integrated networking through inter-satellite links, and collaboratively designs and jointly transmits communication-navigation dual-function signals. For communication service scenarios, communication users achieve high-speed information transmission services by demodulating communication signals. For navigation application scenarios, navigation users use the received multi-star collaborative navigation signals to achieve high-precision positioning, timing and speed measurement. Therefore, the present invention is oriented to low-orbit satellite constellations and provides an effective communication and navigation integration solution for 6G non-terrestrial networks.

[0074] The above-described embodiment is only a preferred solution of the present invention, but it is not intended to limit the present invention. A person skilled in the relevant technical field may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent replacement or equivalent transformation falls within the protection scope of the present invention.

Claims

1. A communication and navigation integration method for a low-orbit satellite constellation, characterized in that: The details are as follows: S1: In the low-orbit satellite constellation system, K dual-function low-orbit satellites equipped with N-dimensional uniform antenna arrays are set up to form a low-orbit satellite constellation service group, which jointly provides communication and navigation fusion services for L single-antenna communication users and M single-antenna navigation users within the coverage area; S2: Each low-orbit satellite node in the low-orbit satellite constellation service group uses inter-satellite links to build a collaborative network, and obtains the channel state information h from the kth low-orbit satellite to the lth communication user in real time through channel estimation or user feedback. k,l , and the channel state information g from the kth low-orbit satellite to the mth navigation user k,m ; S3: Based on the obtained channel state information, the low-orbit satellite constellation system uses a multi-satellite collaborative communication and navigation integrated beam design method to jointly optimize and design communication transmission beams v for all low-orbit satellites in the low-orbit satellite constellation service group. k,l and navigation transmit beam w k ; Among them, v k,l is the communication transmission beam of the kth low-orbit satellite for the lth communication user, w k Transmit the navigation beam for the kth low-orbit satellite; S4: According to the beam design scheme obtained by the multi-satellite collaborative communication and navigation integrated beam design method, each low-orbit satellite in the low-orbit satellite constellation service group constructs and transmits a communication-navigation dual-function signal in, is the communication data signal for the lth communication user, is the navigation data signal of the kth low-orbit satellite after pseudo-random code spread; S5: Based on the received communication-navigation dual-function signal, the communication user decodes to obtain the communication data information, the navigation user obtains the navigation data information through pseudo-random decoding, and obtains the position coordinates and clock deviation of the navigation user itself based on the pseudo-range measurement method, and then uses the Doppler frequency shift maximum likelihood estimation to obtain the navigation user's own motion velocity vector.

2. The communication and navigation integration method for a low-orbit satellite constellation according to claim 1, characterized in that: In S3, a multi-satellite collaborative communication and navigation integrated beam design method is specifically as follows: S31: Calculate the average communication transmission rate of the lth communication user in, is the noise variance of the signal received by the lth communication user, |·| represents the absolute value; S32: Definition Defining intermediate variables and According to the average communication transmission rate limit, let Where tr(·) represents the trace of the matrix, log2(·) represents the logarithm operation with base 2, and μl is the minimum average communication transmission rate requirement of the lth communication user; S33: Define intermediate variables in, is a continuous convex approximation expansion point, Indicates the calculation of gradient operation, A·B>=tr(A Τ B) represents the inner product operation of matrix A and matrix B, and the average communication transmission rate limit is converted to μ l +η l -ξ l ≤0; S34: According to the transmission power limit of low-orbit satellites, Among them, P k is the maximum transmission power of the kth low-orbit satellite; definition κ k is a K-dimensional row vector whose only k-th element is 1 and other elements are 0; I N is the N-dimensional identity matrix, represents the Kronecker product operation; S35: Calculate the positioning error of the mth navigation user respectively Timing Error and speed measurement error S36: The design goal is to minimize the weighted average navigation error of M navigation users in, and are the weights of positioning, timing and speed measurement respectively; an auxiliary variable U is introduced m ,Ω m ,Ω′ m and Ω′ m ',make and Then the design goal is equivalent to minimizing S37: Use the interior point method or directly call the CVX toolkit to solve and obtain The smallest solution is the solution V that can minimize the weighted average navigation error of M navigation users. l and W, and then perform Gaussian decomposition to obtain the communication transmission beam v of the k-th low-orbit satellite for the l-th communication user. k,l and the navigation transmission beam w of the kth low-orbit satellite k .

3. The communication and navigation integration method for a low-orbit satellite constellation according to claim 2, characterized in that: In S35, the positioning error Timing Error and speed measurement error The calculation method is as follows: S351: Calculate the delay vector τ for the mth navigation user m The equivalent Fisher information matrix Among them, τ m =[τ 1,m ; τ 2,m ;…τ K,m ] represents the delay vector of the mth navigation user, f m =[f 1,m ;f 2,m ; ...f K,m ] represents the Doppler shift vector about the mth navigation user, [A] i,j represents the element in the i-th row and j-th column of matrix A, [a] i,j represents the i-th element in vector a, t is the time index, and are the channel delay and Doppler shift from the kth low-orbit satellite to the mth navigation user, represents the equivalent receiving noise variance of the mth navigation user, Diag(a) represents the operation of converting vector a into a diagonal matrix; S352: Calculate the Fisher information matrix for the mth navigation user speed in γ m is the velocity vector of the mth navigation user; S353: Calculate the positioning error Timing Error and speed measurement error in, Λ′=[0,0,0,1],J m is the Jacobian matrix of the linear mapping from position and time errors to time delays, (A) -1 Represents the inverse matrix of matrix A.

Images