A high-precision time synchronization method based on Doppler frequency shift

Abstract

This application discloses a high-precision time synchronization method based on Doppler frequency shift, comprising: a regular node sending a time synchronization request message to a time reference node; upon receiving the time synchronization request message, the time reference node recording the arrival time of the time synchronization request message at the air interface and estimating the Doppler frequency shift of the time synchronization request message; the time reference node replying with a time synchronization response message; upon receiving the time synchronization response message from the time reference node, the regular node recording the arrival time of the time synchronization response message at the air interface and estimating the Doppler frequency shift of the time synchronization response message; the regular node using the Doppler frequency shifts of the time synchronization request message and the time synchronization response message, as well as the transmission delays of the time synchronization request message and the time synchronization response message, to calculate the time synchronization error between the regular node and the time reference node, thereby achieving time synchronization. This solves the problem of message propagation path asymmetry and improves the time synchronization accuracy of mobile ad hoc networks.

Description

Technical Field

[0001] This application belongs to the field of wireless ad hoc network management technology, and in particular relates to a high-precision time synchronization method based on Doppler frequency shift. Background Technology

[0002] Time synchronization is fundamental to the efficient operation of wireless ad hoc networks (WLANs) and is a crucial means to improve network performance, ensure service quality, enhance security, and promote efficient management. In recent years, with the development of distributed service applications in WLANs, such as data fusion, deterministic scheduling, and power allocation, the role of time synchronization in ensuring data consistency, distributed computing, and collaboration has become increasingly prominent. For example, time synchronization ensures the consistency of event records and data packet timestamps in the network, which is essential for applications requiring precise time information, such as environmental monitoring in sensor networks and location and tracking in military applications. In application scenarios involving the collaborative work of multiple nodes, such as distributed database updates or parallel computing, time synchronization is fundamental to ensuring the smooth and correct execution of tasks.

[0003] For time synchronization in wireless ad hoc networks, experts and scholars have proposed various time synchronization protocols. The earliest time synchronization protocol can be traced back to the Network Time Protocol (NTP), proposed in 1985. This protocol is an application layer protocol. Two nodes that need to synchronize exchange time synchronization messages carrying timestamps, and the time synchronization error between the two nodes is calculated by using the difference in transmission delay between the forward and reverse timestamp messages. However, because the timestamps in the NTP protocol are injected by the protocol layer, the message transmission delay is affected by various factors such as message processing delay, queuing delay, access delay, and physical layer processing delay, resulting in poor time synchronization accuracy of the NTP protocol, which can only achieve millisecond-level synchronization accuracy.

[0004] To eliminate protocol stack processing latency such as message processing latency, queuing latency, and access latency, the IEEE proposed the Time Precision Synchronization (PTP) protocol—IEEE PTPv2—in 2002. Although this protocol belongs to the application layer, it can achieve microsecond-level time synchronization accuracy by eliminating protocol stack processing latency through physical layer hardware timestamp injection. However, in highly dynamic scenarios, the asymmetric propagation path problem exists, which will greatly reduce the time synchronization accuracy of IEEE PTPv2.

[0005] Both the NTP and IEEE PTPv2 protocols assume symmetrical bidirectional propagation paths, meaning that forward and backward propagation delays are equal. However, in mobile ad hoc wireless networks, node movement leads to asymmetrical bidirectional propagation delays, significantly reducing the time synchronization accuracy of both NTP and IEEE PTPv2 protocols.

[0006] To address the poor time synchronization accuracy caused by the asymmetry of propagation paths in wireless two-way time synchronization protocols, Japanese experts proposed the Wireless Two-Way Interferometric Time Synchronization (Wi-Wi) protocol in 2017. This protocol utilizes a low-frequency wireless channel to exchange time synchronization protocol messages, calculating the time synchronization error between two nodes by propagating the phase difference between forward and reverse messages. Theoretically, this protocol can achieve picosecond-level synchronization accuracy. However, the Wi-Wi protocol, based on radio frequency signal phase information, suffers from the following problems that severely affect its time synchronization accuracy: first, the phase ambiguity problem, where the phase difference has multiple possibilities of Δφ+2kπ, k=0,1,…; second, poor anti-interference performance, meaning that the phase estimation accuracy of the wireless radio frequency signal is poor due to interference signals. Summary of the Invention

[0007] The purpose of this application is to provide a high-precision time synchronization method based on Doppler frequency shift. By utilizing the Doppler frequency domain of the bidirectional time synchronization signal, the propagation delay difference of the bidirectional radio frequency signal caused by the relative motion of nodes is estimated, thereby solving the problem of poor time synchronization accuracy caused by the asymmetry of the message propagation path in the bidirectional time synchronization protocol and improving the time synchronization accuracy of highly mobile wireless ad hoc networks.

[0008] The objective of this application is achieved through the following technical solution:

[0009] A high-precision time synchronization method based on Doppler frequency shift, the time synchronization method comprising:

[0010] S1: Ordinary nodes send time synchronization request messages to time reference nodes. When time reference nodes receive time synchronization request messages, they record the arrival time of time synchronization request messages at the air interface and estimate the Doppler frequency shift of time synchronization request messages.

[0011] S2: The time reference node replies with a time synchronization response message. When the ordinary node receives the time synchronization response message from the time reference node, it records the arrival time of the time synchronization response message at the air interface and estimates the Doppler frequency shift of the time synchronization response message.

[0012] S3: Ordinary nodes use the Doppler shift of time synchronization request messages and time synchronization response messages, as well as the transmission delay of time synchronization request messages and time synchronization response messages, to calculate the time synchronization error between ordinary nodes and time reference nodes, thereby achieving time synchronization.

[0013] According to a preferred embodiment, in step S1, the time synchronization request message sent by the ordinary node includes: the ordinary node address, the time synchronization request message sequence number, and the sending timestamp t1;

[0014] Ordinary nodes use physical layer hardware to timestamp the time synchronization request message and send a timestamp t1.

[0015] According to a preferred embodiment, in step S1, after the time reference node detects the radio frequency signal destined for this node,

[0016] First, the physical layer hardware is used to mark the arrival time t2 of the corresponding radio frequency signal at the time reference node air interface, and the Doppler frequency shift Δf of the corresponding signal is estimated using a signal detection algorithm. R ,

[0017] Then, the ordinary node will record the time t2 when the radio frequency signal arrives at the time reference node's air interface and the Doppler frequency shift Δf. R The message body is uploaded to the protocol stack.

[0018] According to a preferred embodiment, in step S2, the time synchronization response message replied by the time reference node includes: the address of the ordinary node, the sequence number of the time synchronization request message, the arrival time t2 of the sequence number of the time synchronization request message, and the Doppler frequency shift Δf of the time synchronization request message. R , Time synchronization response message sending timestamp t3;

[0019] Furthermore, the timestamp for sending the time synchronization response message is injected by the physical layer hardware of the time reference node.

[0020] According to a preferred embodiment, in step S2, when a normal node detects a radio frequency signal destined for its own node,

[0021] First, the arrival time t4 of the RF signal at the time reference node air interface is marked using physical layer hardware, and the Doppler frequency shift Δf of the corresponding RF signal is estimated using a signal detection algorithm. A ,

[0022] Then, the ordinary node will record the time t4 when the radio frequency signal arrives at the time reference node's air interface and the Doppler frequency shift Δf. A The message body is uploaded to the protocol stack.

[0023] According to a preferred embodiment, step S3 further includes: when the ordinary node protocol stack receives the time synchronization response message, it performs message validity verification. If the verification is consistent with the information maintained by the node, the validity verification passes; otherwise, the message is discarded.

[0024] According to a preferred embodiment, message validity verification includes: checking whether the address of a normal node is consistent with the address of this node, and whether the sequence number of the time synchronization request message replied is consistent with the sequence number of the time synchronization request message most recently sent by this node;

[0025] According to a preferred implementation, after the time synchronization response message passes the validity verification...

[0026] By parsing the time synchronization response message, a normal node can obtain the arrival time t2 of the time synchronization request message at the time reference node and the Doppler frequency shift Δf of the time synchronization request message. R Time synchronization response message sending time t3;

[0027] Combining the time synchronization request message sending time t1 and the time synchronization request message transmission frequency f R 4. Time t4: Time synchronization response radio frequency signal arrives at the time reference node air interface; 5. Frequency f of the time synchronization response radio frequency signal. A This allows us to obtain the time synchronization error between ordinary nodes and time reference nodes.

[0028] According to a preferred embodiment, the time synchronization error between the ordinary node and the time reference node is calculated using the following formula:

[0029]

[0030] Where T1(R) and T2(R) represent the signal processing delay at the sending end and the signal processing delay at the receiving end of the time synchronization request message; T1(A) and T2(A) represent the signal processing delay at the sending end and the signal processing delay at the receiving end of the time synchronization response message.

[0031] The aforementioned main solution and its various further alternative solutions can be freely combined to form multiple solutions, all of which are solutions that can be adopted and are claimed in this application. Those skilled in the art, after understanding the solution of this application, will realize that there are many combinations based on the prior art and common general knowledge, all of which are technical solutions to be protected in this application, and will not be exhaustively listed here.

[0032] The beneficial effects of this application are:

[0033] The high-precision time synchronization method based on Doppler frequency shift proposed in this invention can effectively solve the problem of message propagation path asymmetry, improve the time synchronization accuracy of mobile ad hoc networks, and achieve ns-level synchronization accuracy under high mobility conditions. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the high-precision time synchronization method based on Doppler frequency shift proposed in this invention.

[0035] Figure 2 This is a schematic diagram of the time synchronization performance of the high-precision time synchronization method based on Doppler frequency shift proposed in this invention when the Doppler frequency shift estimation error is 0Hz.

[0036] Figure 3 This is a schematic diagram of the time synchronization performance of the high-precision time synchronization method based on Doppler frequency shift proposed in this invention when the Doppler frequency shift estimation error is 250Hz.

[0037] Figure 4 This is a schematic diagram illustrating the relationship between Doppler frequency shift estimation error and time synchronization accuracy when using this invention. Detailed Implementation

[0038] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.

[0039] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0040] This application discloses a high-precision time synchronization method based on Doppler frequency shift, the time synchronization method comprising the following steps.

[0041] Step S1: Ordinary nodes send a time synchronization request message to the time reference node. When the time reference node receives the time synchronization request message, it records the arrival time of the time synchronization request message at the air interface and estimates the Doppler frequency shift of the time synchronization request message.

[0042] Preferably, in step S1, the time synchronization request message sent by the ordinary node includes: the ordinary node address, the time synchronization request message sequence number, and the sending timestamp t1; the ordinary node injects the sending timestamp t1 into the time synchronization request message by using physical layer hardware to timestamp.

[0043] Preferably, in step S1, after the time reference node detects an RF signal destined for it, it first uses physical layer hardware to mark the time t2 when the corresponding RF signal arrives at the time reference node's air interface, and then uses a signal detection algorithm to estimate the Doppler frequency shift Δf of the corresponding signal. R Then, the ordinary node will record the time t2 when the radio frequency signal arrives at the time reference node's air interface and the Doppler frequency shift Δf. R The message body is uploaded to the protocol stack.

[0044] Step S2: The time reference node replies with a time synchronization response message. When the ordinary node receives the time synchronization response message from the time reference node, it records the arrival time of the time synchronization response message at the air interface and estimates the Doppler frequency shift of the time synchronization response message.

[0045] Preferably, in step S2, the time synchronization response message replied by the time reference node includes: the address of the ordinary node, the sequence number of the time synchronization request message, the arrival time t2 of the sequence number of the time synchronization request message, and the Doppler frequency shift Δf of the time synchronization request message. R The time synchronization response message is sent using a timestamp t3; and the timestamp of the time synchronization response message is injected by the physical layer hardware of the time reference node.

[0046] Preferably, in step S2, after a normal node detects a radio frequency signal destined for it, it first uses physical layer hardware to mark the time t4 when the radio frequency signal arrives at the time reference node's air interface, and then uses a signal detection algorithm to estimate the Doppler frequency shift Δf of the corresponding radio frequency signal. A Then, the ordinary node will record the time t4 when the radio frequency signal arrives at the time reference node's air interface and the Doppler frequency shift Δf. A The message body is uploaded to the protocol stack.

[0047] Step S3: Ordinary nodes use the Doppler shift of time synchronization request messages and time synchronization response messages, as well as the transmission delay of time synchronization request messages and time synchronization response messages, to calculate the time synchronization error between ordinary nodes and time reference nodes, thereby achieving time synchronization.

[0048] Preferably, step S3 further includes: when the ordinary node protocol stack receives the time synchronization response message, it performs message validity verification. If the verification is consistent with the information maintained by the node, the validity verification passes; otherwise, the message is discarded.

[0049] Furthermore, message validity verification includes: checking whether the address of a regular node is consistent with the address of this node, and whether the sequence number of the time synchronization request message replied is consistent with the sequence number of the time synchronization request message most recently sent by this node;

[0050] Preferably, after the time synchronization response message passes the validity check,

[0051] By parsing the time synchronization response message, a normal node can obtain the arrival time t2 of the time synchronization request message at the time reference node and the Doppler frequency shift Δf of the time synchronization request message. R Time synchronization response message sending time t3;

[0052] Combining the time synchronization request message sending time t1 and the time synchronization request message transmission frequency f R 4. Time t4: Time synchronization response radio frequency signal arrives at the time reference node air interface; 5. Frequency f of the time synchronization response radio frequency signal. A This allows us to obtain the time synchronization error between ordinary nodes and time reference nodes.

[0053] Specifically, ordinary nodes can calculate the transmission delay Δt of RTT-R messages and RTT-A messages. R and Δt A :

[0054] Δt R =t2-t1=T1(R)+T2(R)+T Rp -δ

[0055] Δt A =t4-t3=T1(A)+T2(A)+T Ap +δ

[0056] Where T1(R) and T1(A) are the signal processing delays at the sending end of the RTT-R message and the RTT-A message, respectively, and T2(R) and T2(A) are the signal processing delays at the receiving end of the RTT-R message and the RTT-A message, respectively. Rp and T Ap This indicates the air propagation delay of RTT-R and RTT-A messages.

[0057] Then, ordinary nodes can obtain the time synchronization error between themselves and the time reference node using the following method.

[0058] Let L represent the distance between the ordinary node and the time reference node at time t1, and L1 represent the relative movement distance between the ordinary node and the time reference node during the RTT-R radio frequency signal transmission. Then the following equation can be obtained:

[0059]

[0060] L=[Δt R -T1(R)-T2(R)+δ]×c+L1 (1)

[0061] In the two equations above, c represents the speed of light, and f R This represents the carrier frequency of the RTT-R radio frequency signal, a value known at both the transmitting and receiving ends. [Δt] R -T1(R)-T2(R)+δ]×c represents the propagation distance of the RTT-R radio frequency signal; This represents the relative speed between the ordinary node and the time reference node at the RTT-R signal reception time t2. Since the radio frequency signal propagation time is short (usually on the order of milliseconds), the relative speed between the two nodes can be considered to remain constant during the propagation of the radio frequency signal.

[0062] Let L2 represent the relative movement distance between the ordinary node and the time reference node from the time reference node detecting the RTT-R radio frequency signal at time t2 to the time reference node replying to the RTT-A message at time t3.

[0063]

[0064] In the above formula This represents the relative speed between the ordinary node and the time reference node at the RTT-A signal reception time t4. Similarly, since the propagation time of radio frequency signals in the air is relatively short, the relative speed between the ordinary node and the time reference node at the RTT-A message transmission time t3 can also be considered as v. A .at this time This represents the average relative speed between the ordinary node and the time reference node from time t2 to t3.

[0065] Let L3 represent the relative distance traveled between a regular node and a time reference node during RTT-A message transmission, then we can obtain:

[0066]

[0067] L=(Δt A -T1(A)-T2(A)-δ)×c+L1+L2+L3 (2)

[0068] Combining equations (1) and (2), we get:

[0069] [Δt R -T1(R)-T2(R)+δ]×c+L1=(Δt A -T1(A)-T2(A)-δ)×c+L1+L2+L3

[0070] Simplifying the above equation, we can obtain the time error between ordinary nodes and time reference nodes as follows:

[0071]

[0072] If the physical layers of ordinary nodes and time reference nodes use the same code rate, adjustment style, hardware clock frequency, and signal processing architecture, then T1(A) + T2(A) = T1(R) + T2(R), and the above formula can be simplified to:

[0073]

[0074] Otherwise, it is necessary to calculate and compensate for the processing delay of physical layer signal transmission and reception of radio frequency signals between ordinary nodes and time reference nodes.

[0075] Example 1

[0076] Assume that ordinary nodes and time reference nodes use the same physical layer signal processing architecture.

[0077] See Figure 1To achieve precise time synchronization, ordinary nodes send a Time Synchronization Request (RTT-R) message to the time reference node. This message contains the address of the ordinary node, the RTT-R message sequence number, and the sending timestamp t1. The RTT-R sending timestamp t1 of the ordinary node is injected by the underlying physical layer hardware.

[0078] After receiving an RTT-R message from a regular node, the time reference node records the message arrival time t2 when it detects a signal and estimates the signal Doppler frequency shift Δf. R The message body is then compared with the message arrival time t2 and the Doppler frequency shift Δf of the radio frequency signal. R Upload them together to the time synchronization module.

[0079] See Figure 1 The time synchronization module of the time reference node parses the RTT-R message to obtain the ordinary node address and the RTT-R message sequence number. Then, it replies with an RTT-A message using the same modulation scheme and code rate as the RTT-R message. This message contains the ordinary node address, the RTT-R message sequence number, the RTT-R message arrival time t2, and the Doppler frequency shift Δf of the RTT-R radio frequency signal. R The RTT-A message sending timestamp t3 is injected by the physical layer hardware of the time reference node.

[0080] When a normal node receives an RTT-A message, it records the message arrival time t3 upon detecting the signal and estimates the signal Doppler frequency shift Δf. A The message body is then linked to the message arrival time t3 and the Doppler frequency shift Δf of the radio frequency signal. A Upload them together to the time synchronization module.

[0081] The ordinary node time synchronization module parses the RTT-A message and performs a validity check based on the ordinary node address and RTT-R message sequence number within the RTT-A message. If both of these match the information maintained by this node, the validity check passes; otherwise, the message is discarded.

[0082] At this point, ordinary nodes can obtain the arrival time t2 of the RTT-R message and the Doppler frequency shift Δf of the RTT-R signal. R The RTT-A message transmission time t3. Combined with the RTT-R message transmission time t1 and the RTT-R message transmission frequency f... R , RTT-A RF signal TOA time t4, RTT-A RF signal frequency f A Information such as...

[0083] Assuming that the ordinary node and the time reference node use the same code rate, adjustment pattern, hardware clock frequency and signal processing architecture, T1(A) + T2(A) = T1(R) + T2(R). The ordinary node can use the following formula to calculate the time error between itself and the time reference node.

[0084]

[0085] See Figure 2 and Figure 3 This invention compares the high-precision time synchronization scheme based on Doppler frequency shift proposed in this invention with existing time synchronization methods that do not employ motion error compensation.

[0086] See Figure 2 and Figure 3 Existing time synchronization methods without motion error compensation exhibit linearly increasing time synchronization errors as the relative movement speed of nodes increases. However, the high-precision time synchronization scheme based on Doppler frequency shift proposed in this invention does not change with variations in the relative movement speed between nodes. Specifically, when the Doppler frequency shift estimation error is 0Hz, the high-precision time synchronization method based on Doppler frequency shift proposed in this invention can achieve zero-error time synchronization.

[0087] See Figure 4 The time synchronization error of the high-precision time synchronization scheme based on Doppler frequency shift proposed in this invention is linearly related to the Doppler frequency domain estimation error. The time synchronization error δ is related to the Doppler frequency shift estimation error Δf. d The numerical relationship is approximately δ = 0.004672 × Δf d .

[0088] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A high-precision time synchronization method based on Doppler frequency shift, characterized in that, The time synchronization method includes: S1: Ordinary nodes send time synchronization request messages to time reference nodes. When time reference nodes receive time synchronization request messages, they record the arrival time of time synchronization request messages at the air interface and estimate the Doppler frequency shift of time synchronization request messages. S2: The time reference node replies with a time synchronization response message. When the ordinary node receives the time synchronization response message from the time reference node, it records the arrival time of the time synchronization response message at the air interface and estimates the Doppler frequency shift of the time synchronization response message. S3: Ordinary nodes use the Doppler shift of time synchronization request messages and time synchronization response messages, as well as the transmission delay of time synchronization request messages and time synchronization response messages, to calculate the time synchronization error between ordinary nodes and time reference nodes, thereby achieving time synchronization; The time synchronization error between ordinary nodes and the time reference node is calculated using the following formula: Where T1(R) and T2(R) represent the signal processing delay at the sending end and the receiving end of the time synchronization request message; T1(A) and T2(A) represent the signal processing delay at the sending end and the receiving end of the time synchronization response message; t1 represents the time of sending the time synchronization request message; t2 represents the time of arrival of the time synchronization request message at the time reference node; t3 represents the time of sending the time synchronization response message; t4 represents the time of arrival of the time synchronization response radio frequency signal at the time reference node air interface; Δf R The Doppler frequency shift, Δf, represents the radio frequency signal transmitted to the time reference node. A f represents the Doppler frequency shift of the radio frequency signal sent to a normal node. R f represents the frequency at which time synchronization request messages are emitted. A This indicates the frequency of the time synchronization response radio frequency signal.

2. The time synchronization method as described in claim 1, characterized in that, In step S1, the time synchronization request message sent by the ordinary node includes: the ordinary node address, the time synchronization request message sequence number, and the sending timestamp t1; Ordinary nodes use physical layer hardware to timestamp the time synchronization request message and send a timestamp t1.

3. The time synchronization method as described in claim 1, characterized in that, In step S1, after the time reference node detects the radio frequency signal destined for this node, First, the physical layer hardware is used to mark the arrival time t2 of the corresponding radio frequency signal at the time reference node air interface, and the Doppler frequency shift Δf of the corresponding signal is estimated using a signal detection algorithm. R , Then, the ordinary node will record the time t2 when the radio frequency signal arrives at the time reference node's air interface and the Doppler frequency shift Δf. R The message body is uploaded to the protocol stack.

4. The time synchronization method as described in claim 1, characterized in that, In step S2, the time synchronization response message replied by the time reference node includes: the address of the ordinary node, the sequence number of the time synchronization request message, the arrival time t2 of the sequence number of the time synchronization request message, and the Doppler frequency shift Δf of the time synchronization request message. R , Time synchronization response message sending timestamp t3; Furthermore, the timestamp for sending the time synchronization response message is injected by the physical layer hardware of the time reference node.

5. The time synchronization method as described in claim 1, characterized in that, In step S2, when a normal node detects a radio frequency signal destined for it, First, the arrival time t4 of the RF signal at the time reference node air interface is marked using physical layer hardware, and the Doppler frequency shift Δf of the corresponding RF signal is estimated using a signal detection algorithm. A , Then, the ordinary node will record the time t4 when the radio frequency signal arrives at the time reference node's air interface and the Doppler frequency shift Δf. A The message body is uploaded to the protocol stack.

6. The time synchronization method as described in claim 1, characterized in that, Step S3 also includes: when the ordinary node protocol stack receives the time synchronization response message, it performs a message validity check. If the check is consistent with the information maintained by this node, the validity check passes; otherwise, the message is discarded.

7. The time synchronization method as described in claim 6, characterized in that, Message validity verification includes checking whether the address of a regular node is the same as the address of this node, and whether the sequence number of the time synchronization request message replied is the same as the sequence number of the time synchronization request message most recently sent by this node.

8. The time synchronization method as described in claim 6, characterized in that, Once the time synchronization response message passes the validity check... By parsing the time synchronization response message, a normal node can obtain the arrival time t2 of the time synchronization request message at the time reference node and the Doppler frequency shift Δf of the time synchronization request message. R Time synchronization response message sending time t3; Combining the time synchronization request message sending time t1 and the time synchronization request message transmission frequency f R 4. Time t4: Time synchronization response radio frequency signal arrives at the time reference node air interface; 5. Frequency f of the time synchronization response radio frequency signal. A This allows us to obtain the time synchronization error between ordinary nodes and time reference nodes.

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