A method for estimating the speed and clock drift of a moving node based on bidirectional wireless communication

Abstract

The application provides a motion node speed and clock drift estimation method based on bidirectional wireless communication, and the method comprises the following steps: establishing a motion model of a master node and a slave node; establishing a communication model of the master node and the slave node; obtaining a relative motion speed of the master node and the slave node, a radio frequency Doppler observed by the master node to the slave node, and a radio frequency Doppler observed by the slave node to the master node based on the motion model and the communication model of the master node and the slave node; taking the relative motion speed of the master node and the slave node and the relative clock drift of the master node and the slave node as a state vector, and establishing a state equation based on the state vector; taking the radio frequency Doppler observed by the master node to the slave node and the radio frequency Doppler observed by the slave node to the master node as an observation vector, and establishing an observation equation based on the observation vector; and performing Kalman filtering based on the state equation and the observation equation to obtain an estimated node speed and clock drift.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of radio communication technology, in particular to a method for estimating the velocity and clock drift of a moving node based on bidirectional wireless communication. BACKGROUND

[0002] With the development of aerospace test, navigation, communication, power and other scientific technologies, more and more engineering and scientific fields need precise time synchronization. For example: the world's time laboratories need nanosecond or sub-nanosecond high-precision time synchronization; atomic clocks of satellite launch, measurement and control, and test ranges need to be calibrated; high-precision time synchronization is needed between navigation satellites, between satellites and the ground, and between ground stations; in addition, autonomous formation spacecraft, networked aircraft, etc. also need precise baseline measurement and time synchronization. There is no mature commercial product of time synchronization terminal based on bidirectional precise ranging in China.

[0003] The clock drift is estimated through the satellite time system, so that the clock is corrected, and the dependence on the satellite time system is high. SUMMARY

[0004] The present application provides a method for estimating the velocity and clock drift of a moving node based on bidirectional wireless communication, which can solve the technical problems in the prior art.

[0005] The present application provides a method for estimating the velocity and clock drift of a moving node based on bidirectional wireless communication, which comprises:

[0006] establishing a motion model of a master node and a slave node;

[0007] establishing a communication model of the master node and the slave node;

[0008] obtaining the relative motion velocity of the master node and the slave node, the radio frequency Doppler observed by the master node to the slave node, and the radio frequency Doppler observed by the slave node to the master node based on the motion model and the communication model of the master node and the slave node;

[0009] taking the relative motion velocity of the master node and the slave node and the relative clock drift of the master node and the slave node as a state vector, and establishing a state equation based on the state vector;

[0010] taking the radio frequency Doppler observed by the master node to the slave node and the radio frequency Doppler observed by the slave node to the master node as an observation vector, and establishing an observation equation based on the observation vector;

[0011] performing Kalman filtering based on the state equation and the observation equation to obtain the estimated node velocity and clock drift.

[0012] Preferably, the motion model of the master node and the slave node is established by the following formula:

[0013] V(x)=V0,x≥0

[0014] L(x) = L0 + V0x, x ≥ 0

[0015] In the formula, V(x) represents the relative motion speed of the master and slave nodes, x represents the global time, V0 represents the relative motion speed of the master and slave nodes at x = 0, L(x) represents the distance between the master and slave nodes, and L0 represents the distance between the master and slave nodes at x = 0, wherein the master and slave nodes are opposite to the positive direction of the speed.

[0016] Preferably, the communication model of the master node and the slave node is established by the following formula:

[0017] t z (x) = x, x ≥ 0

[0018] t c (x) = (1 + Δf) · x, x ≥ 0

[0019] Δt z (x) = t z (x) - x = 0, x ≥ 0

[0020] Δt c (x) = t c (x) - x = Δf · x, x ≥ 0

[0021] F Rz (x) = F R , x ≥ 0

[0022] F Rc (x) = (1 + Δf) F R , x ≥ 0

[0023] In the formula, t z (x) represents the local time of the master node, x represents the global time, t c (x) represents the local time of the slave node, Δf represents the relative clock drift of the master and slave nodes, Δt z (x) represents the clock difference of the master node, Δt c (x) represents the clock difference of the slave node, F Rz (x) represents the transmission radio frequency of the master node, F R represents the standard radio frequency point set by the communication system, and F Rc (x) represents the transmission radio frequency of the slave node.

[0024] Preferably, the radio frequency Doppler observed by the master node to the slave node is obtained by the following formula:

[0025]

[0026] The radio frequency Doppler observed by the slave node to the master node is obtained by the following formula:

[0027]

[0028] wherein D cz (k) denotes the radio Doppler observed by the master node to the slave node, F Rc [(k-1)T+T c ] denotes the transmission radio frequency of the slave node at x=(k-1)T+T c , k denotes the round of communication, T denotes the period of bidirectional communication, T c 0 denotes the initial time of transmission of the slave node, V[(k-1)T+T c ] denotes the relative velocity of the master and slave nodes at x=(k-1)T+T c , c denotes the speed of light, F Rz [(k-1)T+T c )] denotes the transmission radio frequency of the master node at x=(k-1)T+T c , F R 0 denotes the standard radio frequency point set by the communication system, V0 denotes the relative velocity of the master and slave nodes at x=0, Δf denotes the relative clock drift of the master and slave nodes, D zc (k) denotes the radio Doppler observed by the slave node to the master node, F Rz [(k-1)T+T z ] denotes the transmission radio frequency of the master node at x=(k-1)T+T z , T z 0 denotes the initial time of transmission of the master node, V[(k-1)T+T z ] denotes the relative velocity of the master and slave nodes at x=(k-1)T+T z , F Rc [(k-1)T+T z )] denotes the transmission radio frequency of the slave node at x=(k-1)T+T z .

[0029] Preferably, the state vector is obtained by the following formula:

[0030] X k = [V k Δf k ] T

[0031] wherein X k denotes the state vector of the kth round, V k denotes the relative velocity of the master and slave nodes at x=kT, Δf k denotes the relative clock drift of the master and slave nodes at x=kT, k denotes the round of communication, and T denotes the period of bidirectional communication.

[0032] Preferably, the state equation is established by the following formula:

[0033] X k = ΦX k-1 +W

[0034]

[0035] wherein X k , X k-1 represent the state vectors of the k, k-1 rounds respectively, k represents the round number of the communication, Φ represents the state transition matrix, and W represents the system excitation noise sequence.

[0036] Preferably, the observation vector is obtained by the following formula:

[0037] Z k = [D cz (k), D zc (k)] T

[0038] wherein Z k represents the observation vector of the k round, D cz (k) represents the radio frequency Doppler observed by the master node to the slave node, and D zc (k) represents the radio frequency Doppler observed by the slave node to the master node.

[0039] Preferably, the observation equation is established by the following formula:

[0040] Z k = HX k + V

[0041] wherein,

[0042] wherein Z k represents the observation vector of the k round, H represents the observation matrix, X k represents the state vector of the k round, V represents the measurement noise sequence, F R represents the standard radio frequency point set by the communication system, and c represents the light speed.

[0043] By applying the technical scheme of the present application, the Doppler effect in the data link communication process is utilized, that is, the influences of the node movement speed and the crystal oscillator frequency deviation (clock drift) on the Doppler frequency deviation are decomposed through bidirectional Doppler observation, and the node movement speed and the clock drift can be estimated more accurately through multiple observation and filtering, thereby providing support for time synchronization. The present application can realize dynamic clock drift estimation between nodes by using the data link system under the satellite denial condition, and can further provide data support for cooperative navigation and time synchronization under the satellite denial condition. Meanwhile, the present application can be used in the complex electromagnetic environment in the battlefield, and can solve the problems of satellite signal interference and unreliable satellite clock correction. BRIEF DESCRIPTION OF DRAWINGS

[0044] The accompanying drawings, which are included to provide a further understanding of the embodiments of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the principles of the application. It is appreciated that the appended drawings are only examples and serve only to illustrate the embodiments of the present application. Other embodiments can be derived from these drawings by one of ordinary skill in the art without paying creative labor.

[0045] Figure 1 A flow chart of a method for estimating velocity and clock drift of a moving node based on two-way wireless communication is shown according to an embodiment of the present application;

[0046] Figure 2 A schematic diagram of a method for estimating velocity and clock drift of a moving node based on two-way wireless communication is shown according to an embodiment of the present application;

[0047] Figure 3 A schematic diagram of a moving node is shown according to an embodiment of the present application;

[0048] Figure 4 A timing diagram of a node communication is shown according to an embodiment of the present application;

[0049] Figure 5 A flow diagram of a node interaction is shown according to an embodiment of the present application;

[0050] Figure 6 A plot of velocity estimation is shown according to an embodiment of the present application;

[0051] Figure 7 A plot of error of velocity estimation is shown according to an embodiment of the present application;

[0052] Figure 8 A plot of clock drift estimation is shown according to an embodiment of the present application;

[0053] Figure 9 A plot of error of clock drift estimation is shown according to an embodiment of the present application. DETAILED DESCRIPTION

[0054] It should be noted that the embodiments and features of the embodiments in the present application can be combined with each other in the case of no conflict. The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the drawings of the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The description of the at least one example embodiment is actually only illustrative, but not as any limitation on the present application and its application or use. 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.

[0055] It should be noted that the terms used herein are only intended to describe 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 reference to the presence of a feature, step, operation, device, component and / or combinations thereof.

[0056] Unless specifically stated otherwise, the relative arrangement of components and steps, numerical expressions, and numerical values set forth in the various embodiments described herein are not limiting. It should be understood that the various parts shown in the drawings are not necessarily drawn to scale. Techniques, methods, and devices known to those of ordinary skill in the relevant art can not be discussed in detail, but should be considered as part of the description 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. Therefore, other examples of the exemplary embodiments can have different values. It should be noted that similar reference numbers and letters represent similar items in the following drawings, and therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0057] As shown in Figure 1 and Figure 2 The present application provides a method for estimating the velocity of a moving node and clock drift based on bidirectional wireless communication, the method comprising:

[0058] S10, establishing a motion model of a master node and a slave node;

[0059] S20, establishing a communication model of the master node and the slave node;

[0060] S30, obtaining the relative motion velocity of the master node and the slave node, the radio frequency Doppler observed by the master node to the slave node, and the radio frequency Doppler observed by the slave node to the master node based on the motion model and the communication model of the master node and the slave node;

[0061] S40. Using the relative motion velocity of the master and slave nodes and the relative clock drift of the master and slave nodes as state vectors, establish state equations based on the state vectors.

[0062] S50. The radio frequency Doppler observed by the master node to the slave node and the radio frequency Doppler observed by the slave node to the master node are used as observation vectors, and the observation equation is established based on the observation vectors.

[0063] S60. Kalman filtering is performed based on the state equation and observation equation to obtain the estimated node velocity and clock drift.

[0064] This invention utilizes the Doppler effect in data link communication, specifically by decomposing the influence of node motion velocity and crystal oscillator frequency drift (clock drift) on Doppler frequency drift through bidirectional Doppler observation. Through multiple observations and filtering, the node motion velocity and clock drift can be estimated relatively accurately, thus providing support for time synchronization. This invention enables dynamic clock drift estimation between nodes using a data link system under satellite denial conditions, further providing data support for cooperative navigation and time synchronization under satellite denial. Simultaneously, this invention can be applied in complex electromagnetic environments on the battlefield, solving the problems of satellite signal interference and unreliable satellite clock repair.

[0065] According to one embodiment of the present invention, in S10 of the present invention, the motion model of the master node and the slave node includes the relative motion velocity expression of the master and slave nodes and the distance expression between the master and slave nodes.

[0066] like Figure 3 The diagram shows the node motion state. In this embodiment, ranging during the aircraft cooperative networking process is used to determine the relative motion relationship between nodes. For ease of analysis, this embodiment assumes the master node is stationary. During high-speed motion, the change in node velocity is a very small order of magnitude compared to the absolute value of the velocity, and the instantaneous maneuverability of nodes is weak during high dynamics. Therefore, it can be considered as uniform linear motion over a certain period of time. The expression for the relative velocity of the master and slave nodes is:

[0067] V(x) = V0, x ≥ 0

[0068] The distance expression between master and slave nodes is:

[0069] L(x) = L0 + V0x, x ≥ 0

[0070] In the formula, V(x) represents the relative velocity between the master and slave nodes, x represents the global time, V0 represents the relative velocity between the master and slave nodes at x = 0, L(x) represents the distance between the master and slave nodes, and L0 represents the distance between the master and slave nodes at x = 0. It is stipulated that the positive direction of the velocity is when the master and slave nodes are moving in opposite directions.

[0071] According to one embodiment of the present invention, in S20 of the present invention, the communication model between the master node and the slave node includes the local time of the master node and the local time expression of the slave node, the clock difference of the master node and the clock difference expression of the slave node, the transmit radio frequency of the master node and the transmit radio frequency of the slave node.

[0072] like Figure 4 The diagram shown is a timing diagram of node communication. Figure 4 middle, These represent the pseudorange delay of the communication from the slave node to the master node in the i-th round and the pseudorange delay of the communication from the master node to the slave node in the i-th round, respectively.

[0073] like Figure 5 The diagram shows the information flow during node interaction. In this embodiment, it is assumed that the master node's clock drift is zero, and the slave node's clock drift is also stable within a certain time period, denoted as Δf. The period of bidirectional communication is T, and the slave node's clock drift occurs at (k-1)T+T. c Launched at time (k-1)T+T, the master node is at time (k-1)T+T z Launch at time, T c <T z <T,

[0074] The expressions for the master node's local time and the slave node's local time are as follows:

[0075] t z (x) = x, x ≥ 0

[0076] t c (x)=(1+Δf)·x,x≥0

[0077] The expressions for master node clock bias and slave node clock bias are as follows:

[0078] Δt z (x)=t z (x)-x=0,x≥0

[0079] Δt c (x)=t c (x)-x=Δf·x,x≥0

[0080] As we know from hardware design principles, the antenna radio frequency will change proportionally with clock drift. Therefore, the expressions for the master node's transmit radio frequency and the slave node's transmit radio frequency are as follows:

[0081] F Rz (x)=F R x≥0

[0082] F Rc (x)=(1+Δf)F R x≥0

[0083] In the formula, tz (x) represents the master node local time, x represents the global time, t c (x) represents the slave node local time, Af represents the master-slave node relative clock drift, At z (x) represents the master node clock difference, At c (x) represents the slave node clock difference, F Rz (x) represents the master node transmitting radio frequency, F R represents the standard radio frequency point set by the communication system, F Rc (x) represents the slave node transmitting radio frequency.

[0084] According to an embodiment of the present application, in S30 of the present application, the radio frequency Doppler observed by the master node to the slave node is obtained by the following formula:

[0085]

[0086] The radio frequency Doppler observed by the slave node to the master node is obtained by the following formula:

[0087]

[0088] In the formula, D cz (k) represents the radio frequency Doppler observed by the master node to the slave node, F Rc [(k-1)T+T c ] represents the slave node transmitting radio frequency at x = (k-1)T+T c , k represents the communication round, T represents the period of bidirectional communication, T c represents the initial time of slave node transmission, V[(k-1)T+T c ] represents the relative motion speed of the master-slave node at x = (k-1)T+T c , c represents the speed of light, F Rz [(k-1)T+T c )] represents the master node transmitting radio frequency at x = (k-1)T+T c , F R represents the standard radio frequency point set by the communication system, V0 represents the relative motion speed of the master-slave node at x = 0, Af represents the master-slave node relative clock drift, D zc (k) represents the radio frequency Doppler observed by the slave node to the master node, F Rz [(k-1)T+T z ] represents the master node transmitting radio frequency at x = (k-1)T+T z , T z represents the initial time of master node transmission, V[(k-1)T+T z ] represents the relative motion speed of the master-slave node at x = (k-1)T+T zthe relative motion speed of the master and slave nodes at time x=kT Rc [(k-1)T+T z )] represents the transmitting radio frequency of the slave node at time x=(k-1)T+T z

[0089] According to an embodiment of the present application, in S40 of the present application, the state vector is obtained by the following formula:

[0090] X k =[V k Δf k ] T

[0091] In the formula, X k represents the state vector of the kth round, V k represents the relative motion speed of the master and slave nodes at time x=kT, Δf k represents the relative clock drift of the master and slave nodes at time x=kT, and k represents the round number of communication, and T represents the period of bidirectional communication.

[0092] According to an embodiment of the present application, in S40 of the present application, the state equation is established by the following formula:

[0093] X k =ΦX k-1 +W

[0094]

[0095] In the formula, X k and X k-1 represent the state vectors of the kth and (k-1)th rounds respectively, k represents the round number of communication, Φ represents the state transition matrix, and W represents the system excitation noise sequence.

[0096] According to an embodiment of the present application, in S50 of the present application, the observation vector is obtained by the following formula:

[0097] Z k =[D cz (k),D zc (k)] T

[0098] In the formula, Z k represents the observation vector of the kth round, D cz (k) represents the radio frequency Doppler observed by the master node to the slave node, and D zc (k) represents the radio frequency Doppler observed by the slave node to the master node.

[0099] According to an embodiment of the present application, in S50 of the present application, the observation equation is established by the following formula:

[0100] Z​k =HX k +V

[0101] in,

[0102] In the formula, Z k Let H represent the observation vector in the k-th round, and let X represent the observation matrix. k Let V represent the state vector of the k-th round, and let F represent the measurement noise sequence. R The standard radio frequency point set by the communication system is indicated by 'c', and 'c' represents the speed of light.

[0103] To gain a further understanding of the present invention, the following description is provided in conjunction with... Figure 6-9 The present invention provides a detailed description of the motion node velocity and clock drift estimation method based on bidirectional wireless communication.

[0104] In this embodiment, the experimental setup is to set the bidirectional communication period T = 1s, and the transmission time from the slave node is T. c =0ms, master node transmit time T z =900ms, initial distance between master and slave nodes L0 = 1000m, relative velocity between master and slave nodes V0 = 4000m / s, relative clock drift between master and slave nodes Δf = 1ppm. The mean of the observed noise is zero, and the variance R0 = [40 2 ;40 2 ] Filtering estimation is performed under the condition of ] .

[0105] like Figure 6-9 As shown in the simulation results, the relative velocity and clock drift estimation algorithm can accurately estimate the velocity and clock drift characteristics of a moving target.

[0106] In summary, this invention provides a method for estimating the velocity and clock drift of moving nodes based on two-way wireless communication. It utilizes the Doppler effect during two-way communication, specifically by decomposing the influence of node velocity and crystal oscillator frequency drift (clock drift) on the Doppler frequency drift through two-way Doppler observations. Through multiple observations and filtering, the node velocity and clock drift can be estimated relatively accurately, thus providing support for time synchronization. This invention enables dynamic clock drift estimation between nodes using a data link system under satellite denial conditions, further providing data support for cooperative navigation and time synchronization under satellite denial. Simultaneously, this invention can be applied in complex electromagnetic environments on the battlefield, solving the problems of satellite signal interference and unreliable satellite clock repair.

[0107] For purposes of the description hereinafter, spatial or directional terms, for example, "above", "below", "upper", "lower", and the like, can be used, and relate to the device as illustrated in the figures. However, it is to be understood that no absolute or relative orientation of the device is intended or implied, unless specifically described as such. Terms concerning attachments, coupling and the like, such as "connected" and "coupled" and the like, are to be construed in accordance with their normal meanings, that is, as referring to an indirect or direct connection or coupling. Any reference to "comprising" or "containing" is to be construed as meaning "comprising or containing, but not limited to". Any reference to "comprising" or "containing" is to be construed as meaning "comprising or containing, but not limited to".

[0108] In addition, it should be pointed out that the use of the terms "first", "second" and the like, to describe various elements in the claims, is merely intended to distinguish between two steps or entities of the application, and is not intended to limit the scope of the present application, unless specifically stated otherwise. Thus, the terms "first", "second", and the like, are not intended to limit the scope of the present application, unless specifically stated otherwise.

[0109] The preferred embodiments herein disclosed are not intended to limit the scope of the application, which is set forth in the claims hereinafter. Various changes in form and details of the application can be made without departing from the spirit and scope of the application. Therefore, the scope of the application is defined not by the detailed description of the preferred embodiments but by the appended claims.

Claims

1. A method for estimating the velocity and clock drift of moving nodes based on two-way wireless communication, characterized in that, The method includes: Establish a motion model for the master node and slave nodes; Establish a communication model between the master node and the slave node; The relative motion velocity of the master and slave nodes, the radio frequency Doppler observed by the master node and the radio frequency Doppler observed by the slave node are obtained based on the motion model and communication model of the master node and slave node. The relative motion velocity of the master and slave nodes and the relative clock drift of the master and slave nodes are used as state vectors, and state equations are established based on the state vectors. The radio frequency Doppler observed by the master node from the slave node and the radio frequency Doppler observed by the slave node from the master node are used as observation vectors, and observation equations are established based on the observation vectors. Kalman filtering is performed based on the state equation and the observation equation to obtain the estimated node velocity and clock drift. The radio frequency Doppler observed by the master node from the slave node is obtained by the following formula: The radio frequency Doppler observed from the node to the master node is obtained using the following formula: In the formula, D cz (k) represents the radio frequency Doppler observed by the master node from the slave node, F Rc [(k-1)T+T c ] indicates that in x = (k-1)T+T c The time interval is determined by the node's transmit radio frequency, k represents the number of communication rounds, and T represents the period of bidirectional communication. c V[(k-1)T+T] represents the initial time of transmission from the node. c ] indicates that in x = (k-1)T+T c The relative velocity between the master and slave nodes at any given moment, where c represents the speed of light, and F represents the speed of light. Rz [(k-1)T+T c ] indicates that in x=(k-1)T+T c The master node's transmit radio frequency, F R The standard radio frequency point set by the communication system is represented by V0, the relative velocity of the master and slave nodes at x = 0, Δf, and the relative clock drift of the master and slave nodes are represented by D. zc (k) represents the radio frequency Doppler observed from the node to the master node, F Rz [(k-1)T+T z ] indicates that in x = (k-1)T+T z The master node's transmit radio frequency at time T z V[(k-1)T+T] represents the initial launch time of the master node. z ] indicates that in x = (k-1)T+T z The relative velocity of the master and slave nodes at any given moment, F Rc [(k-1)T+T z ] indicates that in x=(k-1)T+T z The radio frequency transmitted from the node at all times.

2. The method according to claim 1, characterized in that, The motion model of the master node and slave node is established by the following formula: V(x) = V0, x ≥ 0 L(x) = L0 + V0x, x ≥ 0 In the formula, V(x) represents the relative motion velocity of the master and slave nodes, x represents the global time, V0 represents the relative motion velocity of the master and slave nodes at x=0, L(x) represents the distance between the master and slave nodes, and L0 represents the distance between the master and slave nodes at x=0. The direction of the velocity is the positive direction of the movement of the master and slave nodes in opposite directions.

3. The method according to claim 1 or 2, characterized in that, The communication model between the master node and the slave node is established using the following formula: t z (x)=x,x≥0 t c (x)=(1+Δf)·x,x≥0 Δt z (x)=t z (x)-x=0,x≥0 Δt c (x)=t c (x)-x=Δf·x,x≥0 F Rz (x)=F R ,x≥0 F Rc (x)=(1+Δf)F R ,x≥0 In the formula, t z (x) represents the master node's local time, x represents the global time, and t c (x) represents the local time of the slave node, Δf represents the relative clock drift between the master and slave nodes, and Δt represents the local time of the slave node. z (x) represents the master node clock bias, Δt c (x) represents the clock difference from the node, F Rz (x) represents the master node's transmit radio frequency, F R F represents the standard radio frequency point set by the communication system. Rc (x) represents the transmit radio frequency of the node.

4. The method according to claim 1, characterized in that, The state vector is obtained using the following formula: X k =[V k Δf k ] T In the formula, X k V represents the state vector in the k-th round. k Δf represents the relative velocity between the master and slave nodes at time x = kT. k This represents the relative clock drift between the master and slave nodes at time x = kT, where k represents the number of communication rounds and T represents the period of bidirectional communication.

5. The method according to claim 4, characterized in that, The state equation is established using the following formula: X k =ΦX k-1 +W In the formula, X k X k-1 Let represent the state vectors of the k-th and (k-1)-th rounds, respectively, where k represents the number of rounds of communication, Φ represents the state transition matrix, and W represents the system excitation noise sequence.

6. The method according to claim 1, characterized in that, The observation vector is obtained using the following formula: Z k =[D cz (k),D zc (k)] T In the formula, Z k Let D represent the observation vector in the k-th round. cz (k) represents the radio frequency Doppler observed by the master node from the slave node, D zc (k) represents the radio frequency Doppler observed from the node to the master node.

7. The method according to claim 6, characterized in that, The observation equation is established using the following formula: Z k =HX k +V in, In the formula, Z k Let H represent the observation vector in the k-th round, and let X represent the observation matrix. k Let V represent the state vector of the k-th round, and let F represent the measurement noise sequence. R The standard radio frequency point set by the communication system is indicated by 'c', and 'c' represents the speed of light.

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