# US 2025/0159629 A1 · Time synchronization method for wireless load testing system

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- Number: US 2025/0159629 A1
- Document ID: US20250159629A1
- Status: Published application
- Kind: A1
- Application number: 18/954,451
- Filed: 2024-11-20
- Published: 2025-05-15
- Earliest claimed: 2023-11-15
- Assignees: Shaanxi Electric Appliance Institute
- Applicants: Shaanxi Electric Appliance Institute
- Inventors: Chaoying ZHANG; Wei LI; Guoxuan MA; Zhongbing ZHAO; Weijian LIANG; Jingyi REN
- Web page: https://patentgrep.com/patent/US20250159629A1

## CPC

- H04W 56/0015: {one node acting as a reference for the others}
- H04J 3/0602: {Systems characterised by the synchronising information used}
- H04J 3/0658: {Clock or time synchronisation among packet nodes}
- H04L 41/145: {involving simulating, designing, planning or modelling of a network}
- H04L 43/106: using time related information in packets, e.g. by adding timestamps
- H04W 84/18: Self-organising networks, e.g. ad-hoc networks or sensor networks
- Y02D 30/70: in wireless communication networks
- H04W: WIRELESS COMMUNICATION NETWORKS (broadcast communication H04H; communication systems using wireless links for non-selective communication, e.g. wireless extensions H04M1/72)
- H04J: MULTIPLEX COMMUNICATION (transmission in general H04B; peculiar to transmission of digital information H04L5/00; systems for the simultaneous or sequential transmission of more than one television signal H04N7/08; in exchanges H04Q11/00; stereophonic systems H04S)
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)
- Y02D: CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE

## Abstract

A time synchronization method for a wireless load testing system includes two stages: a stage of constructing a wireless sensor network system and a stage of suppressing communication delay to achieve precise network-wide time synchronization. The method employs a relative skew estimator based on Bayesian estimation theory to suppress the effect of time delay in wireless communication, thereby enhancing the estimation accuracy of the relative skew estimator while reducing memory requirements. By applying the average consensus protocol, high-precision network-wide time synchronization is achieved, and the overall method enhances the robustness to time delay and has higher accuracy. The method solves the problems of reduced time synchronization accuracy and time synchronization failure of partial sub-nodes due to time delay of the traditional time synchronization algorithms in complex spatial layout.

## Claims

### Claim 1

A time synchronization method for a wireless load testing system, comprising the following steps:
S1, constructing a network model based on a consensus algorithm for updating virtual logic clocks of nodes;
S2, constructing a node virtual logic clock updating model based on a timestamp exchange mechanism based on a pseudo-periodic communication scheme;
S3, constructing a relative skew estimator based on Bayesian theory, and estimating undetermined parameters in the updating the virtual logic clocks of the nodes, such that the logic clocks of each sensor node approximate a common clock; and
S4, updating logical skew compensation and offset compensation of the nodes.

### Claim 2 (depends on 1)

The method according to claim 1, wherein the network model based on the consensus algorithm in step S1 comprises:
assuming communication topology is an undirected graph G=(N,ε) in a wireless network, where N={1, 2, . . . , N}represents a set of sensor nodes, and ε⊆N×N represents a set of effective communication links; and αij represents a non-empty adjacency element, and if and only if there is a directed link in G, a set of direct neighbor nodes of a sub-node i is expressed as Ni={j|(i,j)}∈ε, where (i,j)∈ε represents that the node i communicate with a node j in one hop, for the state of a certain sub-node i, the consensus algorithm is adopted to construct the following linear model:
x
i
(
k
+
1
)
=
x
i
(
k
)
+
∑
j
∈
N
i
a
ij
[
x
j
(
k
)
-
x
i
(
k
)
]
;
where k is the number of iterations; and xi(k) represents the linear model obtained after k iterations of the node i. if the linear model based on the consensus algorithm is applied to a clock update equation, the clocks of the nodes are driven to a common clock.

### Claim 3 (depends on 1)

The method according to claim 1, wherein the step S2 specifically comprises:
S21, constructing a clock model;
wherein, each sensor node having a local hardware clock whose first-order dynamic function is expressed as:
c
i
(
t
)
=
α
i
⁢
t
+
β
i
;
wherein ci(t) is the hardware clock reading at absolute reference time t, and αi and βi are local hardware clock skew and offset, respectively; the clock model is established as follows by using hardware clock data of any two nodes to obtain indirect information of the nodes:
c
j
(
t
)
=
α
j
α
i
⁢
c
j
(
t
)
+
(
β
j
-
α
j
α
i
⁢
β
i
)
=
α
ij
⁢
c
j
(
t
)
+
β
ij
;
wherein
,
α
ij
=
α
j
α
i
,
β
ij
=
β
j
-
α
j
α
i
⁢
β
i
;
since the local hardware clock cannot be manually modified, it is proposed that the node maintains a virtual logic clock to represent the synchronization time, the model is as follows:
c
^
j
(
t
)
=
α
i
⁢
c
i
(
t
)
+
β
i
=
α
i
⁢
α
i
(
t
)
+
α
i
⁢
β
i
+
β
i
;
wherein, αi and βi represent skew compensation and offset compensation, respectively, and αi=αiαi and βi=αiβi+βi are defined as virtual logical clock skew and offset, respectively; and
S22, updating compensation parameters of virtual logical clocks of nodes;
wherein, the compensation parameters of the virtual logic clock model are updated periodically and iteratively, such that the logic clocks of each sensor node approximate a common clock, c(t)=αt+β;
the compensation parameters of the virtual logic clocks of the nodes are updated, such that (αi,βi) satisfies:
{
lim
k
→
∞
α
i
(
k
)
⁢
α
i
=
α
¯
lim
k
→
∞
α
i
(
k
)
⁢
β
i
+
β
i
(
k
)
=
β
¯
;
wherein, c(t) represents the common clock, and α and β represent the updated compensation parameters of the virtual logic clocks of the nodes; and
S23, proposing a timestamp exchange mechanism based on a pseudo-periodic communication scheme;
wherein, each node broadcasts time information with a media access control (MAC) layer timestamp to neighbor nodes in each synchronization period T, the neighbor nodes record local clocks immediately after receiving the information;
assuming a k-th broadcast of the node i with communication delay to a neighbor node j, ci(tki)=kT represents the k-th transmission time of the node i, where tki represents the transmission instant at the corresponding absolute moment, and assuming the node j obtains the k-th message at its local time cj(tkij), where tki represents the instant time at which the node j receives the message within the absolute time, so tkij>tki, and
t
k
ij
=
t
k
i
+
d
ij
(
t
k
ij
)
=
t
k
i
+
d
ij
r
(
t
k
ij
)
+
d
ij
f
,
k
=
1
,
2
,
…
;
where, dij(tkij) represents the communication delay, and is composed of random delay dijr(tkij) and fixed delay dijf; and
based on the communication delay, it is assumed that for any communication link between any two nodes, the delay exists as a positive and bounded independent random variable, 0<dij(tkij)≤Md, where Md is a positive real constant; in addition, it is assumed that each node neither updates the virtual logical clock of the node nor obtains the time information sent by the neighbor nodes of the node until a time duration is greater than Md.

### Claim 4 (depends on 3)

The method according to claim 3, wherein step S3 comprises:
assuming each node i periodically broadcasts time information to its neighbor node j, where the time information includes a node identification (ID), an information transmission sequence number, a current hardware clock value, a logical skew compensation value and an offset compensation value; considering that the communication delay includes random delay and fixed delay, the time information exchanged between the node i and the node j is reconstructed as:
c
j
(
t
k
ij
)
=
α
ij
⁢
c
i
(
t
k
i
)
+
β
ij
+
d
ij
r
(
t
k
ij
)
+
d
ij
f
;
analyzing the effect of other unknown parameters of relative skew by subtracting the time information, to obtain the following formula:
c
j
(
t
k
ij
)
-
c
j
(
t
k
-
1
ij
)
=
α
ij
(
c
i
(
t
k
i
)
-
c
i
(
t
k
-
1
i
)
)
+
(
d
ij
r
(
t
k
ij
)
-
d
ij
r
(
t
k
-
1
ij
)
)
;
in the actual time synchronization process, when a message from the node i is not received by the neighbor node j within the time duration Md, the synchronization message will be considered as discarded; and
based on Bayesian estimation theory, an error function of the to-be-estimated parameter αij is expressed as e=αij−αij;
and then a quadratic function is defined as C(e)=e2=(αij−αij)2;
the relative skew is estimated by a Bayesian mean square error R=E(C(e))=E((αij−αij)2);
by applying the relative skew to a probability density function p(Δcj(n),αij), according to Bayesian principle, it is obtained that
p
⁡
(
Δ
⁢
c
j
(
n
)
,
α
ij
)
=
p
⁡
(
α
ij
❘
Δ
⁢
c
j
(
n
)
⁢
p
⁢
Δ
⁢
c
j
(
n
)
)
;
and
B
mse
(
α
ij
)
=
∫
(
∫
(
α
ij
-
α
ij
)
2
⁢
p
⁡
(
α
ij
❘
Δ
⁢
c
j
(
n
)
⁢
d
⁡
(
α
ij
)
)
×
p
⁡
(
Δ
⁢
c
j
(
n
)
)
⁢
d
(
(
Δ
⁢
c
j
(
n
)
)
;
since p(Δcj(n))≥0 holds for all Δcj(n), if the integral in parentheses is minimized for each Δcj(n), then Bmse will be minimized, and the estimator of minimizing Bmse is the average of the posterior joint conditions of
α
ij
=
E
⁡
(
α
ij
❘
Δ
⁢
c
j
(
n
)
)
;
α
ij
=
E
⁡
(
α
ij
❘
Δ
⁢
c
j
(
n
)
)
=
σ
α
ij
2
⁢
T
(
N
-
1
)
⁢
T
2
⁢
σ
α
ij
2
+
2
⁢
σ
2
⁢
∑
n
=
1
N
-
1
Δ
⁢
c
j
(
n
)
+
2
⁢
σ
2
⁢
μ
α
ij
⁢
T
(
N
-
1
)
⁢
T
2
⁢
σ
α
ij
2
+
2
⁢
σ
2
;
an equivalent recursive solution to the above formula is as follows:
α
ij
(
n
)
=
α
ij
(
n
-
1
)
-
σ
α
ij
2
⁢
T
2
(
n
-
1
)
⁢
T
2
⁢
σ
α
ij
2
+
2
⁢
σ
2
×
(
α
ij
(
n
-
1
)
-
Δ
⁢
c
j
(
n
-
1
)
T
.

### Claim 5 (depends on 4)

The method according to claim 4, wherein step S4 specifically comprises:
when the node j obtains the n-th synchronization packet from the node i, the node j performs the n-th skew and offset compensation update at tnij using the following update rules:
α
j
(
t
+
)
=
(
1
-
a
⁡
(
n
)
⁢
ρ
a
)
⁢
α
j
(
t
)
+
a
⁡
(
n
)
⁢
ρ
a
⁢
α
ij
-
1
(
n
)
⁢
α
i
(
t
)
;
and
β
j
(
t
+
)
=
β
j
(
t
)
+
a
⁡
(
n
)
⁢
ρ
0
[
c
i
^
(
t
n
i
)
-
c
ˆ
j
(
t
n
ij
)
]
,
i
∈
N
j
,
t
=
t
n
ij
;
where, ρα∈(0,1) and ρ0∈(0,1) are tuning parameters, α(n)∈(n-1)−u is an attenuation factor, where u∈(0,1), is αj the skew compensation of the node i at t, and the initial condition for any node j∈N is set to αj(0)=1 and βj(0)=1.