A hybrid measurement dynamic positioning method for low earth orbit satellites

Abstract

A low-orbit satellite hybrid measurement dynamic positioning method, according to the known satellite information, the system state equation and the combined observation equation of the dynamic user are constructed, based on the extended Kalman filtering algorithm, the dynamic user receiver position, clock error, frequency difference are obtained, aiming at the difference between the low-orbit satellite constellation coverage characteristics and the medium-orbit satellite constellation, and the characteristics of high relative motion speed of low-orbit satellite, a method for real-time dynamic navigation and positioning of single low-orbit satellite based on pseudo-range and Doppler hybrid measurement data and user inertial navigation device measurement information is proposed.

Description

TECHNICAL FIELD

[0001] The application relates to a mixed measurement dynamic positioning method of a low-orbit satellite and belongs to the field of low-orbit satellite navigation. BACKGROUND

[0002] The satellite navigation system is applied everywhere, and brings a revolutionary influence on the positioning and navigation mode in various fields of industrial production and military application. Therefore, the vulnerability of the satellite navigation system and the reliable alternative mode in extreme cases are paid more and more attention. On the other hand, in recent years, low-orbit satellites have developed rapidly. The low-orbit satellite is different from the medium-orbit and high-orbit navigation satellite. The orbit height is low, and the coverage number is much lower than that of the medium-orbit and high-orbit satellite under the same number. Meanwhile, the low-orbit satellite has a high speed and a short transit time. This provides a possibility for navigation and positioning service based on the low-orbit satellite, and the navigation and positioning based on the low-orbit satellite has a certain implementation difficulty. SUMMARY

[0003] The application solves the technical problem that the low-orbit satellite navigation and positioning is difficult in the prior art.

[0004] The application solves the above technical problem by the following technical scheme.

[0005] A mixed measurement dynamic positioning method of a low-orbit satellite comprises the following steps.

[0006] (1) constructing a system state equation of a dynamic user to be positioned according to the position, speed, mixed observation pseudo-range and pseudo-range rate of a single low-orbit satellite, and the dynamic user speed measured by an inertial navigation device;

[0007] (2) establishing a combined observation equation of the dynamic user, including a pseudo-range observation equation, an observation equation of a Doppler observation value equivalent to a pseudo-range rate, and a system observation equation;

[0008] (3) obtaining the position, clock difference and frequency difference of the dynamic user receiver based on an extended Kalman filtering algorithm.

[0009] In the step (1), the system state equation of the dynamic user to be positioned is specifically as follows.

[0010] X=[x,y,z,δt,δt f ] T

[0011] X k =Φ k,k-1 ·X k-1 +B·U

[0012]

[0013] U=[vux ,v uy ,v uz ,0,0,0] T

[0014]

[0015] where X is the state vector including three-dimensional position components and clock and frequency errors, Φ is the state transition matrix, U is the user velocity measured by the inertial navigation device, and B is the relationship matrix between the input and the state.

[0016] In step (2), the pseudo-range observation equation is:

[0017]

[0018]

[0019] where ρ j is the geometric distance between the dynamic user and the satellite, δt r is the equivalent distance caused by the clock error, and δt is the pseudo-range measurement noise.

[0020] The observation equation for the equivalent conversion of the Doppler observation value to the pseudo-range rate is:

[0021]

[0022]

[0023] where is the geometric distance variation rate between the dynamic user and the satellite, δt f is the receiver frequency error, and δt is the pseudo-range rate measurement noise.

[0024] The system observation equation is:

[0025] Z = H · X + V

[0026]

[0027]

[0028]

[0029] where Z is obtained from the pseudo-range and the pseudo-range rate equivalent to the Doppler, H is the observation matrix, V is the observation noise, and δt is the calculated pseudo-range and pseudo-range rate from the last updated estimated value.

[0030] The dynamic user receiver position is obtained through single Kalman filtering, specifically:

[0031] R uk =[X k (1),X k (2),X k (3)] T

[0032] In the formula, R uk is the kth user position filtering result, (X k (1), X k (2), X k (3)) is the first three components of the kth filtering result of the system state quantity X, and represents the kth receiver absolute position filtering result.

[0033] The clock difference and frequency difference calculation method of the dynamic user receiver is as follows:

[0034] delta t k = delta t k-1 + X k (4)

[0035] delta t fk = X k (5)

[0036] In the formula, delta t k-1 is the k-1th clock difference calculation result, X k (4) is the user receiver clock difference, equal to the fourth component of the kth filtering result of the system state quantity X, and X k (5) is the user receiver frequency difference, equal to the fifth component of the kth filtering result of the system state quantity X.

[0037] The method further comprises the following step (4): repeating the step (3) until the low-orbit satellite is invisible, maintaining the positioning result as an initial value under the assistance of the inertial navigation, and taking the positioning result as an initial value for filtering positioning when the next low-orbit satellite is visible.

[0038] Compared with the prior art, the method has the following advantages:

[0039] (1) The low-orbit satellite hybrid measurement dynamic positioning method provided by the application is based on pseudo-range and Doppler hybrid measurement data and user inertial navigation device measurement information, and is used for real-time dynamic navigation positioning of a single low-orbit satellite.

[0040] (2) The application constructs system state equation and dynamic user combined observation equation according to known satellite information, obtains dynamic user receiver position, clock difference and frequency difference based on extended Kalman filtering algorithm, and proposes a positioning method based on pseudo-range and Doppler mixed measurement based on typical low-orbit satellite single coverage, thereby providing a technical approach for low-orbit satellite used for dynamic navigation positioning. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 A flow chart of the mixed measurement dynamic positioning method of low-orbit satellite provided by the application is shown in the figure. DETAILED DESCRIPTION

[0042] The mixed measurement dynamic positioning method of low-orbit satellite is a method for real-time dynamic navigation positioning of single low-orbit satellite based on pseudo-range and Doppler mixed measurement data and user inertial navigation device measurement information, which is proposed in view of the characteristics that the coverage characteristics of low-orbit satellite constellation are different from those of medium-orbit and high-orbit satellite constellation and the high relative motion speed of low-orbit satellite. The specific steps are as follows:

[0043] (1) Constructing the system state equation of the dynamic user to be positioned according to the position, speed, mixed observation pseudo-range and pseudo-range rate of single low-orbit satellite, and the dynamic user speed obtained by inertial navigation device measurement;

[0044] The system state equation of the dynamic user to be positioned is specifically as follows:

[0045] X = [x, y, z, δt, δt f ] T

[0046] X k = Φ k,k-1 ·X k-1 +B·U

[0047]

[0048] U = [v ux ,v uy ,v uz ,0,0,0] T

[0049]

[0050] In the formula, the state variable X is three-dimensional position component and clock difference and clock drift, Φ is state transition matrix, U is user speed measured by inertial navigation device and is system input variable, B is the relationship matrix between input variable and system state;

[0051] (2) Establishing the combined observation equation of dynamic user, including pseudo-range observation equation, observation equation of Doppler observation value equivalent conversion pseudo-range rate and system observation equation;

[0052] The pseudo-range observation equation is:

[0053]

[0054]

[0055] In the formula, ρ j is the geometric distance between the dynamic user and the satellite, δt r is the equivalent distance caused by the clock error, is the pseudo-range measurement noise;

[0056] The observation equation for converting the Doppler observation value into the pseudo-range rate is:

[0057]

[0058]

[0059] In the formula, ρ is the geometric distance rate between the dynamic user and the satellite, δt f is the equivalent distance rate caused by the clock frequency error, is the pseudo-range rate measurement noise;

[0060] The system observation equation is:

[0061] Z = H · X + V

[0062]

[0063]

[0064]

[0065] In the formula, the observation Z is obtained from the pseudo-range and the Doppler converted pseudo-range rate, H is the observation matrix; V is the observation noise, is the calculated value of the pseudo-range and the pseudo-range rate obtained from the last updated to-be-estimated quantity;

[0066] (3) Based on the extended Kalman filtering algorithm, the dynamic user receiver position, the clock error and the frequency error are obtained, specifically as follows:

[0067] The dynamic user receiver position is obtained through single Kalman filtering calculation, specifically as follows:

[0068] R uk = [X k (1), X k (2), X k (3)] T

[0069] In the formula, R ukFor the k-th user location filtering result, (X) k (1),X k (2),X k (3) represents the first three components of the k-th filtering result of the system state variable X, which characterizes the k-th receiver absolute position filtering result.

[0070] The calculation methods for clock bias and frequency bias of dynamic user receivers are as follows:

[0071] δt k =δt k-1 +X k (4)

[0072] δt fk =X k (5)

[0073] In the formula, δt k-1 X represents the clock difference calculation result for the (k-1)th iteration. k (4) is the user receiver clock error, which is equal to the fourth component of the k-th filtering result of the system state variable X. k (5) is the frequency difference of the user receiver, which is equal to the fifth component of the system state variable X of the k-th filtering result.

[0074] The following is a further explanation with reference to specific embodiments:

[0075] In the current embodiment, such as Figure 1 As shown, for a single usable low-Earth orbit (LEO) satellite, a method for dynamic positioning of the LEO satellite is presented, which integrates pseudorange and Doppler measurement data, including the known satellite position and velocity obtained from Doppler frequency shift conversion, the hybrid observation pseudorange and pseudorange rate, and the dynamic user velocity measured by inertial navigation devices. Specifically:

[0076] User algorithms for obtaining broadcast ephemeris data from low-Earth orbit satellites are used to calculate arbitrary observation time t. k Satellite position (x) sk ,y sk ,z sk As known conditions, the pseudorange ρ and Doppler frequency shift Δf between the low-Earth orbit satellite and the user receiver are used as subjective measurements.

[0077] Analyze the characteristics of the user terminal to obtain the clock characteristics of the user receiver and the auxiliary measurement information of the user terminal's inertial navigation device.

[0078] Taking uniform motion as an example, the user terminal's velocity is provided by the inertial navigation system as a known input. During real-time positioning calculation, besides the user's position (x... u ,y u ,z u In addition, clock difference Δt and clock drift As a quantity to be solved;

[0079] Construct the system state equations for the dynamic user to be located. Define the state variable X during the positioning process as three-dimensional position components and clock bias and clock drift:

[0080] X=[x,y,z,δt,δt f ] T

[0081] The system state equation is:

[0082] X k =Φ k,k-1 ·X k-1 +B·U

[0083] In the formula, Φ is the state transition matrix; U is the user velocity measured by the inertial navigation device, which is the system input; B is the matrix showing the relationship between the input and the system state, as follows:

[0084]

[0085] U = [v ux ,v uy ,v uz ,0,0,0] T

[0086]

[0087] The combined observation equations for the user to be located are given, where:

[0088] The pseudorange observation equation is:

[0089]

[0090] In the formula, It is the geometric distance between the user and the satellite; δt r The equivalent distance caused by clock error; To reduce pseudorange measurement noise, Gaussian white noise is applied here.

[0091] Doppler observations are equivalently converted to pseudorange rate, and the observation equation is:

[0092]

[0093] In the formula, δt represents the rate of change of the geometric distance between the user and the satellite. f The equivalent distance rate caused by clock frequency error; To reduce the noise in the pseudorange rate measurement, Gaussian white noise was applied.

[0094] The system observation equation is:

[0095] Z = H·X + V

[0096] Where, Z is the observation, which is obtained from pseudo-range and Doppler converted pseudo-range rate; H is the observation matrix; V is the observation noise.

[0097]

[0098] The calculated value of pseudo-range and pseudo-range rate from the last updated estimated value.

[0099]

[0100]

[0101] The dynamic real-time positioning solution is performed by using Kalman filtering algorithm:

[0102] State one-step prediction:

[0103]

[0104] The pre-test estimated value of covariance matrix:

[0105]

[0106] Where, Q is the process noise matrix, which is composed of inertial navigation and clock drift noise:

[0107]

[0108] S t = 2h0, S t = 8π 2 h -2

[0109] Where, A is the Allan coefficient of different types of crystal oscillator, and the selection table of different types of crystal oscillator Allan coefficient is as follows:

[0110]

[0111] The initial value of P matrix:

[0112]

[0113] Filter gain matrix:

[0114]

[0115] Where, R is the measurement noise matrix:

[0116]

[0117] Observation update:

[0118]

[0119]

[0120] After the filtering, the user position calculated by the filtering is obtained:

[0121] R uk = [X k (1), X k (2), X k (3)] T

[0122] User receiver clock difference, frequency difference:

[0123] δt k = δt k-1 + X k (4)

[0124] δt fk = X k (5)

[0125] In the formula, δt k-1 is the clock difference calculation result of the k-1th time, X k (4) is the user receiver clock difference, equal to the 4th component of the system state quantity X the kth filtering result, X k (5) is the user receiver frequency difference, equal to the 5th component of the system state quantity X the kth filtering result.

[0126] The above steps are repeated to continue positioning until the low-orbit satellite is not visible, the positioning result is simply maintained under the aid of inertial navigation as the initial value, and is used as the initial value of the filtering positioning when the next star is visible.

[0127] Although the present application has been disclosed with the above preferred embodiments, it is not intended to limit the present application, and any person skilled in the art can make possible changes and modifications to the technical solutions of the present application by using the disclosed methods and technical contents without departing from the spirit and scope of the present application. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application, which does not depart from the content of the technical solutions of the present application, belongs to the protection scope of the technical solutions of the present application.

[0128] The contents not described in detail in the specification of the present application belong to the known technology of the person skilled in the art.

Claims

1. A hybrid measurement dynamic positioning method for low earth orbit satellites, characterized by The steps are as follows: (1) according to the position, speed, mixed observation pseudo-range, pseudo-range rate of single low earth orbit satellite, the dynamic user speed measured by corresponding inertial navigation device, the system state equation of the user to be positioned is constructed; (2) the combined observation equation of the dynamic user is established, including the pseudo-range observation equation, the pseudo-range rate observation equation equivalent to the Doppler observation value, and the system observation equation; (3) based on the extended Kalman filtering algorithm, the position, clock difference and frequency difference of the dynamic user receiver are obtained; The system state equation of the user to be positioned is specifically: X = [x, y, z, δt, δt f ] T X k = Φ k，k-1 · X k-1 + B · U U = [v ux ,v uy ,v uz ,0,0,0] T In the formula, the state variable X is three-dimensional position components x, y, z and clock difference δt, frequency difference δt f , X k is the kth filtering result of the system state variable X, and X k-1 , Φ kk-1 is the filtering coefficient, Φ is the state transition matrix; U is the user speed measured by the inertial navigation device, and v ux , v uy , v uz is the three-axis split speed; B is the relationship matrix between the input and the system state; The system observation equation is: Z=H·X+V wherein the observations Z are derived from pseudoranges p, Doppler observations, etc. wherein H is the observation matrix; V is the observation noise, are the computed values of the pseudorange and pseudorange rate from the last updated estimates of the parameters to be estimated. The dynamic real-time positioning solution is carried out by using the Kalman filtering algorithm: State one-step prediction: The prior estimate value of the covariance matrix: Wherein, Q is the process noise matrix composed of inertial navigation and clock drift noise: S t = 2h0, S t = 8π 2 h -2 The initial value of the P matrix: Filter gain matrix: In the formula, R is the measurement noise matrix: Observation update: After this filtering, the user position calculated by this filtering is obtained: R uk = [X k (1),X k (2),X k (3)] T User receiver clock difference and frequency difference: δt k = δt k-1 + X k (4) δt fk = X k (5) where δt k-1 is the clock error calculation result of the k-1th time, X k (4) is the clock error of the user receiver, equal to the 4th component of the kth filtering result of the system state variable X k (5) is the frequency error of the user receiver, equal to the 5th component of the kth filtering result of the system state variable X.

2. The dynamic positioning method of low earth orbit satellite mixed measurement according to claim 1, characterized in that: In step (2), the pseudo-range observation equation is: where p j is the geometric distance between the dynamic user and the satellite, δt r is the equivalent distance due to clock error, is the pseudorange measurement noise.

3. The dynamic positioning method of low earth orbit satellite mixed measurement according to claim 2, characterized in that: The pseudo-range rate observation equation equivalent to the Doppler observation value is: where is the rate of change of the geometric range between the dynamic user and the satellite, δt f is the receiver frequency difference, is the pseudorange rate measurement noise.

4. The dynamic positioning method of low earth orbit satellite mixed measurement according to claim 1, characterized in that: It further includes step (4), which repeats step (3) until the low earth orbit satellite is not visible, the positioning result is maintained under the assistance of inertial navigation as the initial value, and is used as the initial value of the next low earth orbit satellite filtering positioning.

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