A clock detection based spoofing jamming detection method

By using a clock detection-based method and utilizing the clock bias and clock drift information of satellite navigation and positioning devices, the problem of inaccurate positioning of satellite navigation and positioning devices under deception interference is solved, enabling rapid detection and elimination of deception signals and improving the reliability of positioning.

CN119716915BActive Publication Date: 2025-12-19BEIJING AUTOMATION CONTROL EQUIP INST
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Patent Information

Application Number
CN202411858610.5
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-12-17
Publication Date
2025-12-19
Estimated Expiration
2044-12-17

AI Technical Summary

Technical Problem

Satellite navigation and positioning devices cannot accurately locate themselves when encountering deception or interference.

Method used

By using a clock detection-based method, the clock difference and clock drift information obtained from the position and velocity calculation of the satellite navigation and positioning device are continuously calculated. When the calculated clock difference information is inconsistent with the extrapolated clock difference information, it is considered that the satellite navigation and positioning device has been deceived and interfered with, and a warning is issued to the user.

Benefits of technology

It improves the reliability of satellite navigation and positioning, can quickly detect and eliminate spoofing signals, has a simple algorithm, and is suitable for implementation on DSP or FPGA hardware platforms.

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Abstract

The application provides a clock detection-based deception jamming detection method, which utilizes the clock error and clock drift information of a satellite navigation positioning device obtained by position and speed calculation of the satellite navigation positioning device to continuously calculate the clock error, and when the calculated clock error information is inconsistent with the calculated clock error information, it is considered that the satellite navigation positioning device is subjected to deception jamming, a warning is sent to the user, and the positioning reliability is improved. The method can quickly detect the deception signal in the presence of deception jamming, has a certain deception signal elimination capability, the algorithm is simple to apply, there is no complex or huge calculation formula, the real-time performance and calculation amount can be guaranteed on the DSP or FPGA hardware platform for algorithm programming implementation, that is, easy to implement in engineering.
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Description

TECHNICAL FIELD

[0001] The present application relates to the field of satellite navigation technology, and in particular to a spoofing interference detection method based on clock detection. BACKGROUND

[0002] In the use environment of military satellite navigation positioning devices, the situation of human-made spoofing interference is often faced. Spoofing interference is to broadcast signals same as or similar to real satellite navigation signals, so that the satellite navigation positioning device receives and uses the spoofing signals, resulting in incorrect positioning, and achieving the purpose of spoofing interference.

[0003] At present, the satellite navigation positioning device cannot be correctly positioned when encountering spoofing interference. SUMMARY

[0004] The present application provides a spoofing interference detection method based on clock detection, which can solve the technical problem that the satellite navigation positioning device cannot be correctly positioned when encountering spoofing interference.

[0005] The present application provides a spoofing interference detection method based on clock detection, which comprises:

[0006] S10, the satellite navigation positioning device acquires satellite navigation signals, and performs bit synchronization and frame synchronization on the tracking satellite based on the satellite navigation signals;

[0007] S20, on the basis of completing the frame synchronization of the satellite navigation positioning device and the tracking satellite, the pseudo-range and ephemeris parameters of each satellite are acquired;

[0008] S30, the transmission time of each satellite is acquired based on the pseudo-range of each satellite, and the position information of each satellite is obtained based on the transmission time of each satellite and the ephemeris parameters;

[0009] S40, the position velocity solution equation of the satellite navigation positioning device is established based on the position information and pseudo-range of each satellite, and the position information and clock difference of the satellite navigation positioning device; the position velocity solution equation of the satellite navigation positioning device is linearized to obtain the first observation equation about the position and the second observation equation about the velocity;

[0010] S50, the first observation equation is subjected to least square iteration to obtain the position information and clock difference of the satellite navigation positioning device; and the second observation equation is subjected to least square iteration to obtain the velocity information and clock drift of the satellite navigation positioning device;

[0011] S60, it is judged whether the continuous positioning time of the satellite navigation positioning device including the current time is greater than the first preset time, if yes, turn to S70, otherwise, turn to S10;

[0012] S70, judging whether the clock bias and the clock drift both satisfy the detection condition, if yes, there is no spoofing interference, taking the position information and the speed information of the satellite navigation positioning device as the positioning result, otherwise, there is spoofing interference, turning to S10.

[0013] Preferably, the method further comprises: if the continuous lock loss time of the satellite navigation positioning device is greater than the second preset time, no longer performing the clock bias and clock drift detection, and turning to S10.

[0014] Preferably, judging whether the clock bias satisfies the detection condition comprises:

[0015] judging whether the absolute value of the difference between the clock bias of the least square solution at the current moment and the clock bias of the recursion at the current moment is less than a preset clock bias threshold, if yes, judging that the clock bias satisfies the detection condition, otherwise, judging that the clock bias does not satisfy the detection condition.

[0016] Preferably, the clock bias of the recursion at the current moment is obtained by the following formula:

[0017] dtSm=dt+ddtSm*T

[0018] the preset clock bias threshold is obtained by the following formula:

[0019] DTthresh=PPB*T*n*(n+1) / 2+n / 2*PPB*T*T

[0020] In the formula, dtSm is the clock bias of the recursion at the current moment, dt is the clock bias of the least square solution at the current moment, ddtSm is the average value of the clock drift in the continuous positioning time, T is the positioning solution period, DTthresh is the preset clock bias threshold, PPB is the frequency offset of the crystal oscillator, and n is the recursion times of the clock bias.

[0021] Preferably, judging whether the clock drift satisfies the detection condition comprises:

[0022] in the case that the number of satellites of the single positioning system is equal to four or the number of satellites of the double positioning system is equal to five, judging whether the absolute value of the difference between the clock drift of the least square solution at the current moment and the clock drift of the least square solution at the last moment is less than a first preset clock drift threshold, if yes, judging that the clock drift satisfies the detection condition, otherwise, judging that the clock drift does not satisfy the detection condition;

[0023] in the case that the number of satellites of the single positioning system is greater than four or the number of satellites of the double positioning system is greater than five, judging whether the absolute value of the difference between the clock drift of the least square solution at the current moment and the clock drift of the least square solution at the last moment is less than a second preset clock drift threshold, if yes, judging that the clock drift satisfies the detection condition, otherwise, judging that the clock drift does not satisfy the detection condition;

[0024] The first preset clock drift threshold is smaller than the second preset clock drift threshold, the single positioning system is a single positioning system using Beidou or GPS, and the double positioning system is a combined positioning system using Beidou and GPS.

[0025] Preferably, a position and speed solving equation of the satellite navigation positioning device is established by the following formula:

[0026]

[0027] In the formula, ρ J is the pseudo-range of the Jth satellite, J=1, 2,..., n, n is the total number of satellites after elimination, X J , Y J , and Z J are the X, Y, and Z coordinates of the Jth satellite respectively, X U , Y U , and Z U are the X, Y, and Z coordinates of the satellite navigation positioning device respectively, C is the speed of light, and t u is the clock error.

[0028] Preferably, the first observation equation about the position is obtained by the following formula:

[0029] z1=Hx1+ε

[0030] In the formula, z1 is the first observation, H is the coefficient matrix, x1 is the first state quantity, and ε is the measurement error.

[0031] x1=(X U , Y U , Z U , t u )

[0032]

[0033] In the formula, z1 is the first observation, H is the coefficient matrix, x1 is the first state quantity, and ε is the measurement error. are the X, Y, and Z unit vectors of the satellite navigation positioning device pointing to the Jth satellite respectively.

[0034] Preferably, the second observation equation about the speed is obtained by the following formula:

[0035] z2=Hx2+ε

[0036] In the formula, z2=B

[0037]

[0038] In the formula, z2 is the second observation, x2 is the second state quantity, B is the Doppler observation, and ε is the measurement error. are the X, Y, and Z speeds of the satellite navigation positioning device respectively, and t u ′ is the clock drift.

[0039] The application uses the clock error and clock drift information of the satellite navigation positioning device obtained by the position and speed calculation of the satellite navigation positioning device to continuously calculate the clock error, and when the calculated clock error information is inconsistent with the calculated clock error information, it is considered that the satellite navigation positioning device is interfered by fraud, and a warning is sent to the user, thereby improving the reliability of positioning. The method can quickly detect fraud signals in the presence of fraud interference, has certain fraud signal elimination capability, and the algorithm is simple to apply, without complex or large amount of calculation formula, and the real-time and calculation amount can be guaranteed on the DSP or FPGA hardware platform for algorithm programming implementation, that is, easy to implement in engineering. BRIEF DESCRIPTION OF DRAWINGS

[0040] The accompanying drawings, which are included to provide a further understanding of the embodiments of the application, constitute a part of the specification and illustrate the embodiments of the application and, together with the text description, serve to explain the principles of the application. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor.

[0041] Figure 1 A flowchart of a clock detection-based fraud interference detection method according to an embodiment of the application is shown. DETAILED DESCRIPTION

[0042] It should be noted that the embodiments and features in the present application can be combined with each other without conflict. The technical solutions in the embodiments of the present application will be described clearly and completely with reference to the drawings of the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, not all. The description of the at least one exemplary embodiment is actually only illustrative, not as any limitation on the application and use of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0043] It should be noted that the terms used herein are only for the purpose of describing specific embodiments, and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and it should also be understood that when the terms "comprise" and / or "include" are used in the specification, there is a feature, step, operation, device, component and / or combination thereof.

[0044] The relative arrangement of parts and steps, numerical expressions, and numerical values set forth in the examples herein are not meant to limit the scope of the present application unless otherwise specifically indicated. It is to be understood that the dimensions of the various parts shown in the drawings are not drawn to scale for ease of illustration. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art can not be discussed in detail, but should be considered within the scope of the present application. In all examples shown and discussed herein, any specific value should be interpreted as merely an example, and not as a limitation. Thus, other examples of the exemplary embodiments can have different values. It is noted that like numbers and letters refer to like elements throughout the several views of the drawings, and thus, once an element is defined in one drawing, it is not necessary to discuss it further in subsequent drawings.

[0045] As Figure 1 illustrated, the present application provides a clock detection-based spoofing interference detection method, the method comprising:

[0046] S10, a satellite navigation positioning device captures a satellite navigation signal, and performs bit synchronization and frame synchronization on a tracking satellite based on the satellite navigation signal;

[0047] S20, on the basis of completing frame synchronization of the satellite navigation positioning device and the tracking satellite, obtaining pseudo-range and ephemeris parameters of each satellite;

[0048] S30, obtaining the transmission time of each satellite based on the pseudo-range of each satellite, and obtaining the position information of each satellite based on the transmission time of each satellite and the ephemeris parameters;

[0049] S40, establishing a satellite navigation positioning device position and velocity solving equation based on the position information and pseudo-range of each satellite, the position information and clock error of the satellite navigation positioning device; linearizing the satellite navigation positioning device position and velocity solving equation to obtain a first observation equation about position and a second observation equation about velocity;

[0050] S50, performing least squares iteration on the first observation equation to obtain the position information and clock error of the satellite navigation positioning device; performing least squares iteration on the second observation equation to obtain the velocity information and clock drift of the satellite navigation positioning device;

[0051] S60, judging whether the continuous positioning time of the satellite navigation positioning device including the current time is greater than a first preset time, if yes, turning to S70, otherwise, turning to S10;

[0052] S70, judging whether the clock error and the clock drift both satisfy a detection condition, if yes, there is no spoofing interference, and the position information and velocity information of the satellite navigation positioning device are taken as a positioning result, otherwise, there is spoofing interference, and turning to S10.

[0053] The application utilizes the clock difference and clock drift information of the satellite navigation positioning device obtained by the position and speed solution of the satellite navigation positioning device, continuously calculates the clock difference, and when the calculated clock difference information is inconsistent with the calculated clock difference information, it is considered that the satellite navigation positioning device is interfered by spoofing, and a warning is sent to the user, thereby improving the reliability of positioning. The method can quickly detect spoofing signals in the presence of spoofing interference, has certain spoofing signal elimination capability, the algorithm is simple to apply, there is no complex or large amount of calculation formula, and the real-time and calculation amount can be guaranteed on the DSP or FPGA hardware platform for algorithm programming implementation, that is, easy to implement in engineering.

[0054] In order to have a further understanding of the application, the following will combine Figure 1 The clock-based spoofing interference detection method of the application will be described in detail, which specifically includes the following steps:

[0055] Step one, satellite acquisition, tracking and synchronization

[0056] The satellite navigation positioning device acquires the satellite navigation signal, and performs bit synchronization and frame synchronization on the tracking satellite based on the satellite navigation signal; wherein the frame synchronization is performed after the bit synchronization is completed;

[0057] Step two, observation extraction

[0058] On the basis of completing the frame synchronization of the satellite navigation positioning device and the tracking satellite, the pseudorange, Doppler observation and ephemeris parameter of each satellite after completing the frame synchronization are obtained;

[0059] Step three, satellite position and speed calculation

[0060] Based on the pseudorange of each satellite, the transmission time of each satellite is obtained, and according to the satellite position calculation method provided by the satellite navigation interface control file (ICD), the position information and speed information of each satellite are obtained based on the transmission time and ephemeris parameter of each satellite;

[0061] Step four, satellite navigation positioning device position and speed solution

[0062] According to the available satellites after step five, the satellite navigation positioning device position and speed solution equation is established:

[0063]

[0064] In the formula, ρ J is the pseudorange of the Jth satellite, J=1, 2,..., n, n is the total number of satellites after elimination, X J , Y J , Z J are the X, Y and Z coordinates of the Jth satellite, respectively, XU , Y U , Z U are X, Y, Z coordinates of the satellite navigation positioning device respectively, C is the speed of light, t u is the clock error;

[0065] The position and velocity solving equation of the satellite navigation positioning device is linearized to obtain a first observation equation about the position:

[0066] z1 = Hx1 + ε

[0067] wherein, is an n x 1 vector,

[0068] x1 = (X U , Y U , Z U , t u ) is a 4 x 1 vector,

[0069]

[0070] In the formula, z1 is the first observation, H is the coefficient matrix, x1 is the first state quantity, ε is the measurement error, are X, Y, Z unit vectors of the satellite navigation positioning device pointing to the Jth satellite respectively;

[0071] wherein, Similarly, the calculation ε is an n x 1 measurement error vector, which can contain random (ranging random jitter) and deterministic (bias) items at the same time;

[0072] The position and velocity solving equation of the satellite navigation positioning device is linearized to obtain a second observation equation about the velocity:

[0073] z2 = Hx2 + ε

[0074] wherein, z2 = B, is an n x 1 vector,

[0075] is a 4 x 1 vector,

[0076] In the formula, z2 is the second observation, x2 is the second state quantity, B is the Doppler observation, are X, Y, Z velocities of the satellite navigation positioning device respectively, t u ' is the clock drift;

[0077] The first observation equation is iterated by least squares to obtain the position information of the satellite navigation positioning device, and the second observation equation is iterated by least squares to obtain the velocity information of the satellite navigation positioning device;

[0078] Step five, judging whether the continuous positioning time of the satellite navigation positioning device including the current time is greater than 5s (i.e. whether the continuous positioning is within 5s), if yes, go to step six, otherwise, go to step one;

[0079] Step six, judging whether the clock difference and the clock drift both satisfy the detection condition, if yes, there is no spoofing interference, and the position information and the speed information of the satellite navigation positioning device are taken as the positioning result, otherwise, there is spoofing interference, and go to step one;

[0080] In this step, the judgment whether the clock drift satisfies the detection condition includes:

[0081] In the case that the number of satellites in the single positioning system is equal to four or the number of satellites in the double positioning system is equal to five, judging whether the absolute value of the difference between the clock drift of the least square solution at the current time and the clock drift of the least square solution at the last time is less than 0.5m / s, if yes, judging that the clock drift satisfies the detection condition, otherwise, judging that the clock drift does not satisfy the detection condition, considering that the clock drift is abnormal, and the spoofing interference may exist;

[0082] In the case that the number of satellites in the single positioning system is greater than four or the number of satellites in the double positioning system is greater than five, judging whether the absolute value of the difference between the clock drift of the least square solution at the current time and the clock drift of the least square solution at the last time is less than 20m / s, if yes, judging that the clock drift satisfies the detection condition, otherwise, judging that the clock drift does not satisfy the detection condition, considering that the clock drift is abnormal, and the spoofing interference may exist;

[0083] In this step, the judgment whether the clock difference satisfies the detection condition includes:

[0084] A sliding window is set, and the window size is the clock difference of the least square solution of the current time and the previous 10 times, and the clock difference is recursively calculated in real time by the following formula:

[0085] dtSm=dt+ddtSm*T

[0086] The preset clock difference threshold is obtained by the following formula:

[0087] DTthresh=PPB*T*n*(n+1) / 2+n / 2*PPB*T*T

[0088] In the formula, dtSm is the recursively calculated clock difference at the current time, dt is the clock difference of the least square solution at the current time, ddtSm is the average value of the clock drift in the continuous positioning time, T is the positioning solution period, and is taken as 0.5s, DTthresh is the preset clock difference threshold, PPB is the crystal oscillator frequency offset, and the value is 48m / s, and n is the clock difference recursive times, and n is equal to the calculation time divided by T;

[0089] If the absolute value of the difference between the clock difference calculated by the least square method at the current time and the clock difference calculated by the recursive method at the current time is less than the preset clock difference threshold, it is determined that the clock difference satisfies the detection condition, otherwise, it is determined that the clock difference does not satisfy the detection condition, and it is considered that the clock difference is abnormal, and there may be a spoofing interference.

[0090] In the case that the clock difference satisfies the detection condition, the clock difference calculated by the least square method at the current time and the clock difference calculated by the recursive method at the current time are continuously updated.

[0091] In the case that the continuous lock loss time of the satellite navigation positioning device is greater than 10 min, the clock difference and clock drift detection is not performed, and the process goes to S10.

[0092] When there is a spoofing interference, a warning is sent to the satellite navigation positioning device, otherwise, no warning is performed, and the positioning result is normally output.

[0093] The embodiment only uses the clock information itself, and the spoofing interference detection can be performed in the positioning or non-positioning state of the satellite navigation positioning device; and as long as the satellite navigation positioning device is continuously positioned for 5 s after being started, the spoofing signal can be detected by the method.

[0094] In summary, the present application provides a spoofing interference detection method based on clock detection, the clock difference and clock drift information of the satellite navigation positioning device obtained by the satellite navigation positioning device position and speed calculation are used to continuously calculate the clock difference, when the calculated clock difference information is inconsistent with the calculated clock difference information, it is considered that the satellite navigation positioning device is subjected to spoofing interference, a warning is sent to the user, and the positioning reliability is improved. The method can quickly detect the spoofing signal in the case that there is a spoofing interference, and has a certain spoofing signal elimination capability, the algorithm is simple to apply, there is no complex or large amount of calculation formula, and the real-time performance and calculation amount can be guaranteed on the DSP or FPGA hardware platform, that is, easy to implement in engineering.

[0095] For the sake of brevity, spatially relative terms, such as "beneath", "below", "lower", "above", "upper" and the like, can be used herein for describing an element's position as relating to the position of other elements. It is to be understood that a spatially relative term is intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if a device described herein is inverted, then an element described as "below" or "beneath" another element or group of elements would then be oriented "above" and "over" the other element or group of elements. Thus, the example term "below" can encompass both an orientation of above and below. The device can be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.

[0096] In addition, it should be noted that the use of the terms "first", "second" and the like does not denote any order, quantity, combination or the like, but is merely intended to distinguish between different parts, and therefore cannot be understood as limiting the scope of protection of the present application.

[0097] The preferred embodiments of the present application have been described above with the purpose of illustrating the principles of the present application, and should not be construed in a limiting sense. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application should be included in the scope of protection of the present application.

Claims

1. A clock detection based spoofing jamming detection method, characterized in that, The method comprises: S10, a satellite navigation positioning device captures a satellite navigation signal, and performs bit synchronization and frame synchronization on a tracking satellite based on the satellite navigation signal; S20, on the basis of completing frame synchronization between the satellite navigation positioning device and the tracking satellite, pseudo distances and ephemeris parameters of each satellite are obtained; S30, a transmission time of each satellite is obtained based on the pseudo distance of each satellite, and position information of each satellite is obtained based on the transmission time of each satellite and the ephemeris parameters; S40, satellite navigation positioning device position and velocity solving equations are established based on the position information and the pseudo distance of each satellite, the position information and the clock bias of the satellite navigation positioning device; the satellite navigation positioning device position and velocity solving equations are linearized to obtain a first observation equation about position and a second observation equation about velocity; S50, the first observation equation is subjected to least square iteration to obtain the position information and the clock bias of the satellite navigation positioning device; the second observation equation is subjected to least square iteration to obtain the velocity information and the clock drift of the satellite navigation positioning device; S60, whether the continuous positioning time of the satellite navigation positioning device including the current time is greater than a first preset time is judged, if yes, turn to S70, otherwise, turn to S10; S70, whether the clock bias and the clock drift both satisfy a detection condition is judged, if yes, there is no spoofing interference, the position information and the velocity information of the satellite navigation positioning device are taken as a positioning result, otherwise, there is spoofing interference, and turn to S10; Wherein, whether the clock bias satisfies the detection condition comprises: whether an absolute value of a difference between the clock bias solved by least square at the current time and the clock bias recursively calculated at the current time is less than a preset clock bias threshold is judged, if yes, it is judged that the clock bias satisfies the detection condition, otherwise, it is judged that the clock bias does not satisfy the detection condition; the clock bias recursively calculated at the current time is obtained by the following formula: dtSm=dt+ddtSm*T the preset clock bias threshold is obtained by the following formula: DTthresh=PPB*T*n*(n+1) / 2+n / 2*PPB*T*T In the formula, dtSm is the clock bias recursively calculated at the current time, dt is the clock bias solved by least square at the current time, ddtSm is an average value of clock drift in the continuous positioning time, T is a positioning solving period, DTthresh is the preset clock bias threshold, PPB is a crystal oscillator frequency offset, and n is a clock bias recursion number; whether the clock drift satisfies the detection condition comprises: in the case that the number of satellites in a single positioning system is equal to four or the number of satellites in a double positioning system is equal to five, whether an absolute value of a difference between the clock drift solved by least square at the current time and the clock drift solved by least square at the last time is less than a first preset clock drift threshold is judged, if yes, it is judged that the clock drift satisfies the detection condition, otherwise, it is judged that the clock drift does not satisfy the detection condition; in the case that the number of satellites in a single positioning system is greater than four or the number of satellites in a double positioning system is greater than five, whether an absolute value of a difference between the clock drift solved by least square at the current time and the clock drift solved by least square at the last time is less than a second preset clock drift threshold is judged, if yes, it is judged that the clock drift satisfies the detection condition, otherwise, it is judged that the clock drift does not satisfy the detection condition; The first preset clock drift threshold is less than the second preset clock drift threshold, the single positioning system is a single positioning system using Beidou or GPS, and the double positioning system is a combined positioning system using Beidou and GPS.

2. The method of claim 1, wherein, The method further comprises: in a case where the continuous lock loss time of the satellite navigation positioning device is greater than the second preset time, no longer performing clock difference and clock drift detection, and switching to S10.

3. The method of claim 1, wherein, A position and speed solving equation of the satellite navigation positioning device is established by the following formula: wherein ρ J is the pseudo-range of the Jth satellite, J = 1, 2,..., n, n is the total number of satellites after elimination, X J , Y J , and Z J are the X, Y, and Z coordinates of the Jth satellite, respectively, X U , Y U , and Z U are the X, Y, and Z coordinates of the satellite navigation positioning device, respectively, C is the speed of light, and t u is the clock error.

4. The method of claim 3, wherein, A first observation equation about position is obtained by the following formula: z1=Hx1+ε wherein x1 = (X U , Y U , Z U , t u ) wherein z1 is a first observation, H is a coefficient matrix, x1 is a first state quantity, and ε is a measurement error, are unit vectors of the X, Y, Z directions of the satellite navigation positioning device pointing to the Jth satellite, respectively.

5. The method of claim 4, wherein, A second observation equation about speed is obtained by the following formula: z2=Hx2+ε Wherein, z2=B where z2 is a second observation, x2 is a second state quantity, B is a Doppler observation, are the X, Y, Z velocities of the satellite navigation positioning device, respectively, t u is the clock drift.

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