Research on Stability-Enhanced Clustering Algorithm Based on Distributed Node Status Judgment in MWSN

Abstract

Node mobility improves the self-deployment capability of the network; meanwhile, it also leads to frequent interruption of communication links and severe packet loss. Mitigating the negative impact of node movement on cluster stability is a new challenge. Existing clustering protocols try to use multi-hop data transmission, but they do not deal with the increase in communication overhead. This paper proposes a distributed node status judgment-based weighted clustering algorithm to solve the problems of easily broken communication links and excessive node reaffiliation in mobile wireless sensor networks (MWSNs). The protocol establishes intra-cluster second-level communication in order to solve the problem of the sudden interruption of dynamic communication links. A node status judgment algorithm was constructed to analyze the motion behavior of sensor nodes, distinguish the node states, and screen multiple communication nodes, thereby alleviating the transmission delay caused by complex routing. The extended Kalman filter (EKF) was used to filter the sensor noise in a non-ideal environment and to predict the actual position of nodes. The simulation results explain that the proposed protocol can effectively reduce node reaffiliation and the dominant set’s update frequency when the node runs at medium and high speeds while simultaneously maintaining low energy consumption.

1. Introduction

In addition to abundant sensors and excellent information collection capabilities [1], MWSN has gained more attention due to its wide range of application scenarios [2,3,4] and node mobility capability. The mobility of sensor nodes not only improves the deployment capability of regional networks but also challenges the stability of network clustering. The high-speed movement of the node makes it possible to leave the communication range of the cluster head (CH) at any time, which affects the data transmission of the node and network connectivity. In addition, the frequent replacement of CHs by member nodes will also increase energy consumption and shorten network life. Due to their low price, sensor nodes are generally used in large numbers, and due to the environmental limitations of the application scenario, timely battery replacement cannot be achieved. Given the above problems, MWSN needs a clustering communication protocol with low power consumption and high transmission efficiency [5]. The construction of the protocol especially needs to consider how to effectively alleviate the impact of node movement on cluster stability and link connection time. Due to the open deployment environment of the sensor network, a distributed protocol should be used in the sensor network design in order to avoid the damage of a single point of failure [6,7].

Many clustering routing protocols [5,8,9,10,11,12,13,14,15] were developed to alleviate the impact of node movement on clustering. These protocols fall broadly into three categories, depending on the different methods, namely multi-hop routing [8,9,10], improved weighted algorithm with movement factor [5,11,12], and hybrid protocols combining active and reactive protocols [13,14,15]. The weighted clustering algorithm comprehensively considers the parameters of network nodes. It expects to determine the optimal dominant set for different application scenarios through perfect parameter adjustment and the weight design of different parameters, while noting that for mobile wireless sensor networks, the influence of node migration factors should be considered [12]. In practice, the weight cannot be the only factor for selecting CHs, and the optimal dominant set in the moving status is not fixed. Hybrid protocols handle node movement and find optimal routing and data transfer. Using hybrid protocols for different network scenarios can help improve network performance and bring the application value of protocols into full play. Hybrid protocols often combine metaheuristic optimization with different performances to ensure energy efficiency and improve the optimal selection of cluster heads or communication paths [15]. However, hybrid protocols also inevitably lead to more complex protocol designs, and achieving efficient collocation between protocols is worth further discussion. Multi-hop communication can effectively alleviate the negative impact of node movement and improve network connectivity. The main issues discussed are the design of the multi-hop communication mechanism and the selection of the number and location of the vice cluster heads (VCHs). A multi-hop communication mechanism can improve the link stability and reduce the data transmission process’s energy consumption; simultaneously, it will complicate communication routing within the cluster and thus increase the data transmission delay [9].

Most of these protocols focus on finding the optimal communication route in a dynamic environment or improving the CH selection strategy, ignoring the impact of high-speed movement on the quality of communication links [16]. To address the problem of communication links being easily interrupted due to high-speed node movement, this paper tries to establish multi-hop routing in the cluster. The data is forwarded through relay nodes in the cluster to mitigate the direct impact of node movement on the communication link, and new state constraints are set to avoid overly complex communication routing within the cluster.

This paper proposes a distributed node status judgment-based weighted clustering algorithm (DSJWCA) based on the above ideas. The protocol uses the method of second-level communication within the cluster. The CH keeps in touch with the member nodes far away from its communication range through data forwarding by relay nodes. However, large-scale multi-hop communication will make intra-cluster communication routing more complicated and increase the data transmission delay. Given the problems caused by this mechanism, the protocol uses the node status judgment algorithm to distinguish the node status. The identity design and state partition of nodes in sensor networks positively affect network performance [6,17]. Only when the distance between the member node and the CH reaches the threshold and the member node is in an “unsafe” status is the member node allowed to communicate with the CH through the relay node. The status judgment relates to the moving speed and yaw angle between nodes. In addition, there is noise interference in sensor data acquisition in the non-ideal environment. This protocol uses the extended Kalman filter combined with the Gauss-Markov (GM) model to predict the actual position of the node. The protocol considers that the actual movement of the node has certain traceability. Then, for the permanent failures other than energy exhaustion that may occur during the operation of sensor nodes in non-ideal environments, this paper conducts some research in the simulation combined with the Weibull reliability model. Finally, detailed simulation experiments and data analysis are carried out in this paper. Compared with similar protocols, the proposed protocol significantly improves the update of the dominant set and the node reaffiliation.

2. Related Works

There are many clustering protocols developed for MWSN [6,8,16,18,19,20,21,22,23]. The protocol design of hierarchical wireless sensor networks using the clustering method can be roughly divided into two main stages: the clustering phase and the communication phase. The clustering phase includes two main parts: CH selection and intra-cluster node allocation. The communication phase completes the transmission and forwarding of intra-cluster and inter-cluster data.

The clustering phase’s main task is to determine the dominant set and divide the nodes in the network based on the CH. MAINAK [16] first proposed using weights to determine the dominant set in order to stabilize the topology. This weighted clustering algorithm comprehensively considers node degree, transmission power, mobility, and residual energy and selects the node with the lowest weight as the CH by weighting the above information. The protocol does not search for CHs according to a fixed period but makes aperiodic on-demand calls. In addition, the protocol has an expected threshold for the number of CHs in the network. Similarly, Rajakumar et al. [19] also comprehensively consider various influencing factors in the network in order to select dynamic brokers, but the difference is that this scheme contains up to 10 parameters. Undoubtedly, such a scheme will bring substantial computational overhead to sensor networks. On this basis, the MBC protocol proposed by Deng [21] has further requirements for selecting nodes in the cluster. CH will consider the expected connection time, distance, and residual energy of all nodes within its communication range to determine whether to continue to accept the node. The authors hope to improve cluster stability by adding the expected connection time to the weighting formula when selecting CHs. The consideration of node mobility improves the protocol’s applicability in high-mobility scenarios. The algorithm will incur huge control overhead in multiple mobile nodes. Sabor et al. [22] combined the improved weight calculation formula and immune optimization algorithm (MOIA) to predict CH’s position in the target region. Meanwhile, cluster size is adjusted according to the moving speed of the sensor node. However, the clustering phase of the algorithm has a high cost because of the over-complete consideration of various factors. Rady and Shokair et al. [6] adopt a two-stage method to select CHs in the clustering process. In the first stage, the remaining energy of the sensor node, link connection time, migration factor, and other information are used to find the VCH. Next, the protocol uses the MOIA algorithm to ascertain the unique CH in the set of VCH in the second stage.

Improving the communication phase of the existing clustering protocols mainly focuses on time allocation and data transmission mode. Kim and Chung [18] used time slots to divide the intra-cluster communication process. All member nodes will send data according to the requested information sent by the CH within the allocated TDMA time slot. To control CH’s energy consumption, the member nodes that have sent the data will stay in sleep mode until the next TDMA time slot. Nevertheless, the author does not mention the routing overhead. Cakici [23] hopes to improve end-to-end delay performance by finding the network’s most reliable route and maintaining the communication’s reliability. However, the long end-to-end delay makes the clustered network unbearable when the topology changes frequently. In order to avoid the loss of more data packets, the CH will delete the member node from its communication list [21]. When the time slot is exhausted, the packet sent by the member node is still not received. Given the dynamic network topology caused by node movement, Tran et al. [8] proposed a dynamic network multi-hop protocol. The scheme also uses real-time time slot scheduling and studies multi-hop network architecture and dynamic network topology management. Different schemes prove that multi-hop communication can be applied to dynamic topological networks.

In addition, the design of fault tolerance measures is also worth noting. Awwad et al. [20] introduced an adaptive scheduling mechanism to allow disconnected nodes to join new clusters faster, responding to a join message from a new node waiting to join the cluster within the contention timeslot. In order to avoid the sudden failure of the CH and improve the stability of the cluster, Sabor et al. [22] searched for a node with high residual energy and low mobility in the cluster as a VCH during the clustering phase.

A detailed analysis of the existing clustering–routing algorithms is shown in

Table 1. Comparison of the proposed algorithm and existing clustering algorithms.

Papers Referred	Cluster Communication (Inter/Intra-Cluster)	Organizational Form	Cluster Stability	Packet Delivery Ratio	Routing Overhead
Rady and Shokair et al. [6]	multi/single hop	distributed	unstable	yes	yes
MAINAK [16]	multi/single hop	centralized	unstable	no	no
Kim and Chung [18]	multi/single hop	distributed	unstable	yes	no
Awwad et al. [20]	multi/single hop	distributed	stable	yes	no
Deng [21]	multi/single hop	distributed	unstable	no	yes
Sabor et al. [22]	multi/single hop	distributed	stable	yes	yes
Proposed	multi/multi hop	distributed	stable	yes	yes

^“Yes” and “no” indicate whether the work considers the corresponding performance indicator.

. In short, the current clustering protocols have made good progress in improving the transmission efficiency of communication links and saving energy consumption. However, further research is still needed on reducing the reaffiliation in the scenario of high-speed node movement and avoiding the situation where the link is easily broken.

3. Using Models and Assumptions

Before expounding on the detailed design of the DSJWCA protocol, it first introduces some models used in this paper, including the network model, fault model, node mobility model, weight calculation formula, and radio energy consumption model. It then expounds on the scenario assumptions used by the protocol.

3.1. Network Model

MWSN comprises a fixed base station (BS) and many tiny, low-power, and inexpensive sensors, as shown in Figure 1. Sensor nodes form clusters according to specific rules and periodically receive and forward data information from the target area. The member nodes are responsible for obtaining and sending data to the CH. The CH needs to complete the integration and forwarding of data within the cluster and is also responsible for data forwarding between CHs if the network uses multi-hop communication [24]. This protocol considers the wireless channel symmetric [21]; the power required to transmit and receive data is the same when the distance between two nodes remains unchanged. In addition, BS, as a resource-rich node, does not consider its working mode and energy consumption.

3.2. Fault Model

There are many reasons for the failure of wireless sensor nodes in the natural environment. In addition to energy depletion, the failure of node hardware components, unexpected events, and permanent or short-term signal shielding by obstacles [25] can incapacitate nodes. This paper’s transient and Byzantine faults are not considered; only permanent faults are considered. In modeling a node failure, the node reliability is considered to obey the Weibull distribution [26]. The probability density function of the Weibull distribution [27] is formulated as follows:

$$f\left(t\right)=\frac{\beta }{\eta }{\left(\frac{t}{\eta }\right)}^{\beta -1}{e}^{-{\left(\frac{t}{\eta }\right)}^{\beta }}$$

(1)

This formula represents the possibility of sensor node failure at time t, where the shape parameter $\beta$ represents the trend of the function and the scale of parameter $\eta$ represents the offset degree of the function. Generally, $\beta > 2$ is required in the research of wireless sensor networks.

3.3. Node Mobility Model

Many models try to honestly describe the movement status of nodes, including the random waypoint model and GM model [28]. Considering that the moving angle of sensor nodes does not abruptly change in the actual movement and that the node status update is related to the prior motion status, the GM model with traceability is more suitable for the application scenario in this paper. The node movement angle and velocity update formulas of the GM model are as follows:

$$V_n=\alpha V_{n-1}+\left(1-\alpha \right)V+\sqrt{1-{\alpha }^2}{V}_{x_{n-1}}$$

(2)

$${\theta }_n=\alpha {\theta }_{n-1}+\left(1-\alpha \right)\theta +\sqrt{1-{\alpha }^2}{\theta }_{x_{n-1}}$$

(3)

where $\alpha$ is the weight factor in the range of $\left[0,1\right]$, $V_n$ and ${\theta }_n$ respectively represent the node moving speed and angle at the current time; $V_{n-1}$ and ${\theta }_{n-1}$ respectively represent the node moving speed and angle at the previous time; $V_{x_{n-1}}$ and ${\theta }_{x_{n-1}}$ respectively represent the speed and angle variables following the distribution of Gaussian random variables. The position calculation formula of the sensor node can be deduced according to Equations (2) and (3), and the specific expression is as follows:

$$S_n=\left(X_n,Y_n\right)=\left(X_{n-1}+V_{n-1}cos{\theta }_{n-1},Y_{n-1}+V_{n-1}sin{\theta }_{n-1}\right)$$

(4)

In the process of node movement, the algorithm considers that there are already several known targets in the target area distributed in the network, and the sensor node will maintain a trend to obtain information on known targets in the future. Figure 2 shows the movement trajectory of a sensor node approaching a known target under the GM model.

3.4. Weight Calculation Formula

This section will briefly introduce the weight calculation formula mentioned in the WCA protocol. This weight is used to find the CH in the clustering phase. The calculation formula [16] is as follows:

$$W\left(i\right)={\phi }_1\times deg\left(i\right)+{\phi }_2\times dis\left(i\right)+{\phi }_3\times vel\left(i\right)+{\phi }_4\times E_{residual}\left(i\right)$$

(5)

$W_i$ represents the weight of the node. Nodes with smaller $W_i$ have a higher probability of becoming CHs. $deg\left(i\right)$ is the degree of node, $dis\left(i\right)$ is the sum of distances between a node and other nodes in its communication range, $vel\left(i\right)$ is the node’s average velocity, and $E_{residual}\left(i\right)$ is the remaining energy of the node. It should be noted that the free coefficient has the following restrictions in Equation (5).

$${{\displaystyle \sum }}_{j=1}^4{\phi }_j=1$$

(6)

According to the node mobility characteristics of MWSN, the mobility factor and energy density-related information are added to the weight calculation formula. The nodes with lower mobility and higher energy are selected as the CHs in order to reduce the communication’s energy consumption while stabilizing the clustering and letting the packets flow through areas with higher power. For node mobility, we improve the weight calculation formula regarding local density and the local residual energy of nodes. Set S represents all sensor nodes in the target network, and a node and its neighbors form set C, where $de{g}_{int}\left(i\right)$ and $de{g}_{ext}\left(i\right)$ represent the node’s internal degree and external degree. It is defined as:

$$de{g}_{int}\left(i\right)=\left|Neighbor\left(s_i\right)\right|$$

(7)

$$Neighbor\left(s_i\right)=\left\{s_j|dis\left(s_i,s_j\right)\le R_i\wedge s_j\in \left(S-s_i\right)\right\}$$

(8)

$$de{g}_{ext}\left(i\right)=\left|\left\{\left(s_m,s_n\right)\right\}\in S|s_m\in C,s_n\in S∕C\right|$$

(9)

where $R_i$ represents the communication range of the node, and the local density of node is related to $de{g}_{int}\left(i\right)$ and $de{g}_{ext}\left(i\right)$; its expression is:

$$de{g}_{loc}\left(i\right)=2\times de{g}_{int}{\left(i\right)}^2 /\left({\vartheta }_i\left({\vartheta }_i-1\right)\left(de{g}_{int}\left(i\right)+de{g}_{ext}\left(i\right)\right)\right)$$

(10)

where ${\vartheta }_i$ represents the sum of a node and its neighbor nodes. Forcing packets to flow through higher energy-density areas can reduce network energy consumption. The energy density of a node is defined as:

$$E_{density}\left(j\right)=\sum \left\{E_{residual}\left(i\right),\forall i\in Neighbor\left(j\right)\wedge H\left(i\right)<H\left(j\right)\right\}+E_{residual}\left(j\right)$$

(11)

where $H\left(i\right)$ represents the hop values of the node. Therefore, combined with some improved parameters, the original weight calculation formula can be modified as follows:

$$W_i={\phi }_1\times de{g}_{loc}\left(i\right)+{\phi }_2\times dis\left(i\right)+{\phi }_3\times vel\left(i\right)+{\phi }_4\times E_{density}\left(i\right)$$

(12)

3.5. Radio Energy Consumption Model

In addition to the clustering phase, packet transmission and forwarding between nodes consumes substantial energy. This paper adopts a realistic radio model closer to the actual communication scenario. In this model, the radio transmission power of a node changes with the communication distance. Each node has four energy modes: send, transmit, sleep, and idle modes, and the symbols are $P_{rx}$, $P_{tx}$,$P_{sleep}$ and $P_{idle}$. A sensor node’s energy consumption is related to its status and packet communication distance. Each member node will generate a K-bits packet, transmit it to the corresponding CH in the ratio of $R_d$(bps) in its allocated time slot, and keep sleep mode in the time slot of other member nodes. Therefore, the energy consumption of member nodes [6] is expressed as follows:

$$E=E_{tx}+E_{idle}+E_{sleep}=\left\{T_d{P}_{tx}\right\}+\left\{\left(T_{slot}-T_d\right)P_{idle}\right\}+\left\{\left(T_{fr}\left(i\right)-T_{slot}\right)P_{sleep}\right\}$$

(13)

where $T_d=\mathrm{K}/R_d$ is the data transmission/acceptance time, $T_{slot}$ is a time slot, and $T_{fr}\left(i\right)$ is the sum of time slots of all member nodes of CH. In addition, the CH keeps its receiver open to accept data packets from its member nodes or lower-level CHs. Then the CH merges the data received from the member and relay nodes and sends it on to the BS or higher-level CHs. Therefore, each CH’s energy consumption is expressed as follows:

$$\begin{array}{cc}\hfill E=E_{rx}+E_{agg}& +E_{tx}+E_{idle}\hfill \\ & =\left\{m_i{T}_d{P}_{rx}+relay\left(i\right)T_d{P}_{rx}\right\}+\left\{\left(m_{i}1\right)E_{DA}K\right\}+\left\{\left(R_{pk}\left(i\right)+1\right)T_d{P}_{tx}\right\}\hfill \\ & +\left\{m_i\left(T_{slot}-T_d\right)P_{idle}+R_{pk}\left(i\right)\left(T_{slot}-T_d\right)P_{idle}\right\}\hfill \end{array}$$

(14)

where $E_{agg}$ represents the energy consumed by merging data, $m_i$ represents the number of member nodes of CH, $R_{pk}\left(i\right)$ represents the sum of the number of relay data packets from low-level CHs, and $E_{DA}$ represents the energy required by merging 1 bit data.

3.6. Assumptions

The DSJWCA protocol has the following assumptions for application scenarios:

• Non-ideal environments, including sensor nodes, may have noise when obtaining information, and sensor nodes may have other permanent faults except energy depletion [29] (transient and Byzantine faults are not considered);
• Except for BS, all sensor nodes can change their position after being deployed in the network;
• Some sensor nodes near the known target will approach it within a period to obtain information about the known target in the region;
• A popular movement model, the GM model, is used for sensor node movement, which does not consider the angular velocity change during movement.

4. Detailed Design of Protocol

This section elaborates on the distributed node status judgment-based weighted clustering protocol. First, the operation flow of the protocol is introduced, and then the node status judgment algorithm is explained in detail. Finally, the prediction process of the actual position of the node using EKF under the GM model is given.

4.1. Protocol Process

The DSJWCA protocol operation flow consists of three phases. The setup phase completes the CH, VCH selection, and CH communication routing construction, and the steady-state phase is mainly responsible for data packet transmission and forwarding. The DSJWCA protocol also sets up a fault-tolerant phase to allow the CH to update member nodes’ status and to re-enter the cluster for the node that lost connection. Figure 3 shows a schematic diagram of the operation flow of the protocol.

4.1.1. Setup Phase

The node weight calculation and the selection of CHs and VCHs are first performed. Non-CH nodes must decide which cluster to join according to location, CH weights, and other related information. This phase also needs to complete the construction of the CH communication route.

Calculate the node weight in the network according to the improved weight calculation formula and select the node with the smaller value as the CH. The CH broadcasts the $Hello\_Msg\left(ID,W\right)$ message to nodes within its communication radius. The node that only receives one CH message will return the $Join\_Msg\left(ID,x,y,V,\theta \right)$ message to apply for joining the cluster. If a node receives packets sent by multiple CHs simultaneously, it needs to judge the CH weight, mobility factor, link connection time, and other information. As an essential fault-tolerant measure against the CH’s sudden failure, the selection of the VCH needs to consider many factors, such as the node weight and its relative position. When the CH is determined, the member node in the cluster, whose node weight is second only to the weight of the CH, is determined as the VCH. The pseudocode for this phase of operation is as shown in Algorithm 1.

Algorithm 1. Setup Phase.

Input: $\forall i\in S_{live}:ID,x,y,V,\theta ,MF,E_{residual}\left(i\right),de{g}_{int}\left(i\right),de{g}_{ext}\left(i\right)$.

Output: (1) Set of CH, VCH;(2) Result of Clusters Building.

1:  for i = 1:1:$S_{live}$

2:    Calculate the weight of $S_i$ based on Equation (12);

3:  end for

4:  CHs = $CH\_Selection\left(ID,x,y,W\right)$;

5:  Calculate the hop values of CH using flooding;

6:  $N{H}_{best}$ = $Const\_routing\_tree\left(ID,x,y,hop\right)$;

7:  for each CH j

8:    BS sends $\left\{CH\_stat\_Msg\left(N{H}_{best}\left(j\right)\right)\right\}$ to $CHs\left(j\right)$;

9:    $CHs\left(j\right)$ broadcasts $\left\{Adv\_Msg\left(ID,x,y,V,\theta \right)\right\}$ to CHs;

10:  end for

11:  $CH\left(i\right)$ broadcasts $\left\{Hello\_Msg\left(ID,W\right)\right\}$ to $node\left(j\right)$ within its radius;

12:  for i = 1:$S_{live}$

13:     if $node\left(i\right)$ receives only one packet from $CH\left(j\right)$

14:       $node\left(i\right)$ sends $\left\{Join\_Msg\left(ID,x,y,V,\theta \right)\right\}$ to $CH\left(j\right)$;

15:     else

16:       LCT = $Cal\_lct\left(i,CHs\right)$;

17:       H_idea = $judge\left(LCT,W,MF\right)$;

18:       $node\left(i\right)$ sends $\left\{Join\_Msg\left(ID,x,y,V,\theta \right)\right\}$ to $CHs\left(H\_idea\right)$;

19:     end if

20:  end for

21:  Calculate $N{o}_{slot}$;

22:  for each CH i

23:    VCH = $Select\_VCH\left(ID,W\right)$;

24:    $CHs\left(i\right)$ sends $\left\{Sche\_Msg\left(TDMA,N{o}_{slot},VCH\right)\right\}$ to $nodes\left(CHs\left(i\right)\right)$;

25:  end for

4.1.2. Steady-State Phase

In this phase, the protocol considers all nodes to maintain time synchronization. The communication of the member nodes is divided into several timeslots. The node can only send or forward data packets to the CH in its timeslot, and the other timeslots keep sleep status to reduce energy consumption. The CH, unlike the member nodes, needs to keep the receiver in the operational status, realize the reception and integration of the data packets from the member nodes in the cluster, and forward the data packets sent by other CHs as a relay node.

In addition to data communication, member nodes may re-select CHs. As the communication link is maintained within the cluster using second-level communication, member nodes can maintain communication even if they leave the communication radius of the CH. Nevertheless, the CH may also fail to receive data packets within the timeslot, including the interference of noise in a non-ideal environment on the communication link and the transmission time being too long, resulting in the incomplete transmission of data packets before the end of the time slice. After successfully receiving the data packet, the CH will send an ACK message to the member nodes to confirm the successful reception of the data packet. Different from protocols such as LEACH-M and MBC, when the CH does not receive a data packet during intra-cluster communication, it will send messages to the member node for multiple timeslots in order to inquire about the current status. During this period, if the CH successfully receives the message returned by the member node, it is considered that the link communication between the nodes is abnormal; otherwise, the node is invalid.

In this phase, besides the member nodes’ departure or failure, the CH’s sudden loss also needs to be considered, as it will negatively impact the routing communication of the entire network and the stability of the cluster. An additional member node will be selected as the VCH in the clustering phase in order to prevent the CH’s sudden failure, and the weight of the VCH is second only to the CH. Unlike the non-fixed periodic replacement of the CH, the VCH will be replaced in each clustering phase to ensure that it can form the optimal dominant set when it acts as the CH. To obtain the current status of the CH, the VCH will send messages to the CH from time to time.

When the member node does not receive the ACK message returned by the CH after sending the data packet, the node will notify the VCH of the event and send the data packet. The VCH will immediately broadcast information in the cluster to suspend the allocation of timeslots and ask about the CH status. Suppose the CH replies to the inquiry status message of the VCH. In that case, it is considered that the communication link between the CH and the member nodes is disturbed, and the VCH will forward the data packets to be sent and restore the timeslot allocation. Suppose the VCH does not receive the status reply message from the CH. In that case, it is considered that the CH is in a failed status, and the VCH broadcasts the CH failure message in the cluster and reorganizes the communication routes. The CH replacement process is also performed when $E_{residual}\left(CH\right)<0.2E_0$ or $E_{residual}\left(CH\right)-E_{residual}\left(VCH\right)<E_{density}\left(CH\right)/de{g}_{int}\left(CH\right)$.

4.1.3. Fault-Tolerant Phase

In order to ensure a steady communication link between nodes and reduce the packet drop rate, a fault-tolerant phase is set before each round of communication to check the node status and communication link. The member nodes in the cluster that use second-level communication forward data packets through the relay node to keep in touch with the CH. If the member node status is “unsafe” and out of CH communication coverage, the node sends $Hello\_Msg\left(ID,x,y,V,\theta \right)$ packets to the surrounding nodes to find the CHs within its communication radius. The CH that receives the $Hello\_Msg$ data packet will return the $CH\_Msg\left(ID,x,y,V,\theta ,W\right)$ data packet with its information, and the member nodes compare the received data packet to determine whether to change the CH.

4.2. Node Status Judgment Algorithm

MWSN does not have a fixed topology, because its node mobility leads to easily broken communication links and high network delay. The communication radius of the CH cannot be expanded indefinitely, and the increase in the communication distance means that higher transmit power is required, resulting in more energy consumption. Displacement may cause the node to leave the CH communication coverage during packet transmission. However, the CH has not found the interruption of the communication link, resulting in the loss of data packets. Therefore, all measures need to be carried out before the communication link is not interrupted.

In this paper, intra-cluster second-level communication is used to extend the connection time of node communication links. It selects an appropriate relay node within the cluster and forwards the data packets of nodes that have left the communication radius of the CH and have not re-entered the cluster or are in an “unsafe” status.

To avoid the complication of intra-cluster communication routing and consider the communication pressure of the CH, it is necessary to set rules to control the number of nodes to forward data. After each round of the setup phase ends, member nodes will judge whether they need to update their status according to the set threshold. With the dynamic change of node communication radius and moving speed [30], it is expressed as:

$$D_{th}=R_j-V_{max}\times round$$

(15)

Among them, $R_j$ represents the communication radius of the corresponding CH, and $V_{max}$ represents the member node’s maximum velocity. The CH will discover the link interruption of member nodes within one round because of TDMA time slot communication, so in actual operation, the value range of the round is $\left[1,2\right]$. The hotspot problem is common in WSNs with multi-hop communication, and it can be solved by unequal clustering [31]. A CH’s communication radius changes dynamically with its residual energy and the number of neighbor and successor nodes. The function of about $R_j$ can be expressed as:

$$R_j=\left[1-\alpha \left(\frac{D_{max}-D_{BS}\left(j\right)}{D_{max}-D_{min}}\right)-\beta \left(1-\frac{E_{residual}\left(j\right)}{E_{max}}\right)+\rho \left(1-\frac{Neighbor\left(j\right)}{Neighbo{r}_{max}}\right)+\gamma \left(1-\frac{Br\left(j\right)}{B{r}_{max}}\right)\right]R_{max}$$

(16)

where $\alpha$, $\beta$,$\rho$, and $\gamma$ are weights in the range of $\left(0,1\right)$, $D_{max}$ and $D_{min}$ are the maximum and minimum distances from the CH to the BS, respectively, and $D_{BS}\left(j\right)$ is the distances from the CH j to the BS. $E_{max}$,$Neighbor\left(j\right)$, and $B{r}_{max}$ are the node’s initial energy and the maximum value of neighbor nodes and successor nodes, respectively, and $Br\left(j\right)$ represents the number of successor nodes of the CH j.

The node status judgment algorithm judges the node status by the relative distance between nodes and the node moving angle and speed. The algorithm considers that, when the member node maintains a special relationship with the CH’s moving angle, the member node may be in a safe status at the current time; otherwise, the member node is considered unsafe. Member nodes in an unsafe status need to find relay nodes in the cluster to establish second-level communication with the CH. In some particular angles, it is necessary to combine the relative movement speed for judgment. In the node status judgment algorithm, the range of the node movement angle when the safety status is satisfied is shown in Figure 4.

The figure shows the angle range required to satisfy the safety status when the member nodes are located at different positions, taking the CH moving yaw angle in the first quadrant as an example. The position of the CH (${\mathrm{P}}_{\mathrm{CH}}$) is the coordinate origin, and the yaw angle of the CH movement is $\mathsf{\alpha }$. When the member nodes are in the first quadrant and the third quadrant, it is necessary to judge the required angle range by combining the specific position of the member nodes. When the member node is in the second or fourth quadrants, it does not need to be judged separately. The angle ranges required for nodes in different quadrants to satisfy the safe status are as follows.

Case 1: When the node is in the upper half of the first quadrant, the node yaw angle range in the safe status is $-\left(\pi /2+{tan}^{-1}\left(\left|x\right|/\left|y\right|\right)\right)\le \theta \le \alpha$; when the node is in the lower half of the first quadrant, the node yaw angle range in the safe status is $\alpha \le \theta \le \pi +{tan}^{-1}\left(\left|y\right|/\left|x\right|\right)$.

Case 2: When the node is in the second quadrant, the node yaw angle range in the safe status is -${tan}^{-1}\left(\left|y\right|/\left|x\right|\right)\le \theta \le \alpha$.

Case 3: When the node is in the upper half of the third quadrant, the node yaw angle range in the safe status is ${tan}^{-1}\left(\left|y\right|/\left|x\right|\right)\le \theta \le \alpha$; when the node is in the lower half of the third quadrant, the node yaw angle range in the safe status is $\alpha \le \theta \le {tan}^{-1}\left(\left|y\right|/\left|x\right|\right)$.

Case 4: When the node is in the fourth quadrant, the node yaw angle range in the safe status is $\pi /2-\alpha \le \theta \le \pi /2+{tan}^{-1}\left(\left|x\right|/\left|y\right|\right)$.

When the yaw angle of CH movement is in other quadrants, the movement angles of nodes that satisfy the safe status have similar rules. The pseudocode of the node status judgment algorithm is shown in Algorithm 2.

Algorithm 2. Node status Judgment Algorithm.

Input: (1)$\forall S_i\in S\left(head\right).clustermem:E_{residual}\left(i\right),dist\left(i,head\right),V,\theta$; (2)$D_{max},D_{min},E_{max}$.

Output: (1) Relay node of $S_i$; (2) The route for data transfer.

1:  Calculate the communication radius of $CH\left(R_{head}\right)$ based on Equation (16);

2:  Calculate $D_{th}$ based on Equation (15);

3:  for i = 1:1: length($S\left(head\right).clustermem$)

4:     if ($dist\left(i,head\right)>D_{th}$)

5:        Determine the quadrant where the node resides;

6:        isSafe($S\left(i\right).angle,S\left(i\right).speed,S\left(head\right).angle,S\left(head\right).speed$);

7:        $S\left(i\right).relaynode$ = −1;

8:        if ($S\left(i\right).type$ == ‘unsafe’)

9:            Find N nodes closest to CH and form the set $R_i$;

10:          Find the node r with the lowest residual energy in the set $R_i$;

11:          $S\left(i\right).relaynode$ = r;

12:        end if

13:        if ($S\left(i\right).relaynode$ != −1)

14:          Establish the communication route between node r, node i and head;

15:          Update the routing information table stored in CH;

16:        end if

17:     end if

18:  end for

4.3. Node Location Prediction

The EKF uses partial differentiation to obtain the Jacobian matrix to linearize the nonlinear system, which estimates the system’s current status. The calculation steps used by EKF in position prediction [32] are as follows:

$$\mathrm{Location} \mathrm{prediction} x_t^{-}=f\left(x_{t-1}^{-},u_t,w_t\right)$$

(17)

$$\mathrm{Error} \mathrm{covariance} P_t^{-}=F_t{P}_{t-1}{F}_t^T+W_t{Q}_t{W}_t^T$$

(18)

$$\mathrm{Kalman} \mathrm{Gain} K_t=P_t^{-}{H}_t^T{\left(H_t{P}_t^{-}{H}_t^T+V_t{R}_t{V}_t^T\right)}^{-1}$$

(19)

$$\mathrm{Prediction} \mathrm{of} \mathrm{measured} \mathrm{values}\left(\mathrm{updated}\right) x_t=x_t^{-}+K_t\left(z_t-h\left(x_{t-1}^{-},v_t\right)\right)$$

(20)

$$\mathrm{Error} \mathrm{covariance}\left(\mathrm{updated}\right) P_t=\left(E-K_t{H}_t\right)P_t^{-}$$

(21)

Table 2. Description of EKF symbols.

Symbol	Description
$x_t^{-}$	predicted position at time t
$x_t$	the position of the filter prediction at time t
$z_t$	measurement position at time t
$u_t$	input command at time t
$w_t$	process noise at time t
$Q_t$	process noise covariance matrix
$P_t$	error covariance of filter estimates at time t
$P_t^{-}$	error covariance at time t
$v_t$	measurement error at time t
$K_t$	Kalman gain at time t
E	identity matrix
$H_t$	measurement matrix at time t
$H_t^T$	transpose matrix of $H_t$

The table shows some parameters contained in the EKF iteration formula and their interpretations.

gives the specific meaning of each parameter in EKF.

In addition to the above symbols, the calculation formula of EKF also includes some Jacobian matrices, which are defined as follows:

$$F_t=\frac{\delta f\left(x_{t-1}^{-},0,0\right)}{\delta x}$$

(22)

The Jacobian matrix is a matrix composed of the first-order partial derivatives of each dependent variable concerning each independent variable in a multivariate function and can be expressed as:

$$J=\left(\begin{array}{ccc}\frac{\delta f}{\delta x_1}& \cdots & \frac{\delta f}{\delta x_n}\end{array}\right)=\left(\begin{array}{ccc}\frac{\delta f_1}{\delta x_1}& \cdots & \frac{\delta f_1}{\delta x_n}\\ ⋮& \ddots & ⋮\\ \frac{\delta f_m}{\delta x_1}& \cdots & \frac{\delta f_m}{\delta x_n}\end{array}\right)$$

(23)

The motion of sensor nodes under known targets is purposeful. The movement angle and speed of the node under the GM model will not change suddenly. Each new update of the node movement status is related to the previous one while maintaining a uniform linear motion within a sampling time. Based on this motion model, the status quantity of the target can be expressed as:

$$\overrightarrow{x}\left(t\right)={\left(x,y,\nu ,\theta ,w\right)}^T$$

(24)

where $\theta$ is the angle between the target node and the x-axis in the current coordinate system, the value range is [0, 2), and the counterclockwise direction is positive. $w$ is the yaw angular velocity, considered $w$ = 0 under this model. The simplified status function expression is:

$$\overrightarrow{x}\left(t+\Delta t\right)=\left(\begin{array}{c}\begin{array}{c}\frac{\nu }{w}sin\left(w\Delta t+\theta \right)-\frac{\nu }{w}sin\left(\theta \right)+x_t\\ -\frac{\nu }{w}cos\left(w\Delta t+\theta \right)+\frac{\nu }{w}cos\left(\theta \right)+y_t\end{array}\\ \begin{array}{c}\nu \\ w\Delta t+\theta \\ w\end{array}\end{array}\right),w\ne 0$$

(25)

In EKF, the multivariate Taylor series expansion is used to linearize the nonlinear model. In practice, the expansion term of the advanced series is often ignored, and only the first-order Jacobian matrix is considered for approximate linearization. When $w$ = 0, according to Equations (22) and (23), the Jacobian matrix can be solved as:

$$J_F=\left(\begin{array}{ccccc}1& 0& \Delta tcos\left(\theta \right)& -\Delta t\nu sin\left(\theta \right)& 0\\ 0& 1& \Delta tsin\left(\theta \right)& \Delta t\nu cos\left(\theta \right)& 0\\ 0& 0& 1& 0& 0\\ 0& 0& 0& 1& \Delta t\\ 0& 0& 0& 0& 1\end{array}\right)$$

(26)

A similar partial differentiate can solve Jacobian matrices $J_H$, $J_W$, and $J_V$. In addition, process noise also interferes with position prediction in the movement model. The process noise indicates that the system may face errors caused by model simplification after running for a specified period. The noise sources in the model process include linear acceleration and yaw angular acceleration. The acceleration is assumed to satisfy a Gaussian distribution with a mean of 0 and a variance of ${\sigma }_a^2$ and ${\sigma }_w^2$, respectively. In the status transition formula, the effect of acceleration on the status is as follows:

$$noise=G\cdot \mu =\left(\begin{array}{cc}\begin{array}{c}\frac{1}{2}\Delta t^{2}cos\left(\theta \right)\\ \frac{1}{2}\Delta t^{2}sin\left(\theta \right)\end{array}& \begin{array}{c}0\\ 0\end{array}\\ \begin{array}{c}\Delta t\\ 0\\ 0\end{array}& \begin{array}{c}0\\ \frac{1}{2}\Delta t^2\\ \Delta t\end{array}\end{array}\right)\cdot \left(\begin{array}{c}{\mu }_a\\ {\mu }_w\end{array}\right)$$

(27)

The covariance matrix is derived from the process noise, and its expression is:

$$Q_t=E\left[noise\cdot nois{e}^T\right]=E\left[G\mu {\mu }^T{G}^T\right]=G\cdot E\left[\mu {\mu }^T\right]\cdot G^T$$

(28)

where ${\mu }_a$ and ${\mu }_w$ are the linear and yaw angular accelerations, respectively. $E\left[\mu {\mu }^T\right]=\left(\begin{array}{cc}{\sigma }_a^2& 0\\ 0& {\sigma }_w^2\end{array}\right)$.

5. Simulation and Results

This chapter uses MATLAB software to run different simulation programs in order to test the performance of the DSJWCA protocol under different parameters.

5.1. Evaluation Indicators

Use the following indicators to assess the performance of the DSJWCA protocol and the comparison protocol:

• Average energy expenditure (AEE): Only the energy consumption involved in data receiving and forwarding between sensor nodes based on Equations (13) and (14) is considered;
• End-to-end delay (EED): The time spent from the first digit of the packet generated by the source node until the receiving node fully receives the packet;
• Dominant Set Update (DSU): A dominant set is a collection of CH that will be updated when a node can no longer be a neighbor of the current dominant set.

5.2. Simulation Results

In order to study the reliability and performance of the protocol, this paper will compare the proposed protocol with WCA [16], LEACH-M [19], CBR-mobile [20], MBC [21], and JNSMIC [7] under the same scenario. The nodes are moved using the GM model, and the initial nodes are randomly deployed in the scenario. Each simulation in this article will be run ten separate times to allow for occasional errors. The simulation is also combined with the Weibull reliability model to test the operation of WSN under a non-ideal environment. The relevant parameters of the proposed protocol in Equation (1) are $\beta$ = 3 and $\eta$ = 1000. The weights in the weight calculation formula of Equation (12) are $\phi 1$ = 0.35, $\phi 2$ = 0.2, $\phi 3$ = 0.2 and $\phi 4$ = 0.25, respectively. Other network and simulation parameters are shown in

Table 3. Radio and network parameters.

Parameter	Value
Sensor deployment Scope	150 $\times$ 150 ${\mathrm{m}}^2$
BS location	[75,75]m
Maximum communication radius ($R_{max}$)	40 m
The initial energy of node	1 J
Transmission power ($P_{tx}$):0,−5,−10,−15 dBm	93,72,57,49.5 mW
Received power ($P_{rx}$)	81 mW
Idle power ($P_{idle}$)	3 mW
Sleep power ($P_{sleep}$)	6 $\mathsf{\mu }\mathrm{W}$
Aggregated energy ($E_{DA}$)	5 nJ/bit/slot
Data packet length ($L_d$)	1000 bits
Control packet length ($L_c$)	100 bits
Data rate ($R_d$)	40 Kbit/s
Mobility model	Gauss-Markov (GM) Model

.

5.2.1. Influence of Node Moving Speed

MWSN contains 100 nodes with a maximum communication radius of 40 m. The performance variation of the proposed algorithm and other algorithms was studied by adjusting the maximum moving speed of nodes in the range of 1–8 m/s. Figure 5, Figure 6 and Figure 7 show the influences of AEE, EED, DSU, and the proposed protocol caused by the change in movement speed.

Figure 5a noted that the DSJWCA protocol has lower energy consumption than other protocols. The change of node moving speed affects the AEE of different protocols, among which the WCA and LEACH-M protocols considerably change. As moving speed increases, the quality of communication links between nodes deteriorates, increasing the packet drop rate and leading to more energy consumption due to frequent clustering. As, in the clustering phase and when considering node movement and link connection time, the number of nodes that lost connection is relatively small, it can be seen that the AEE performance of MBC, JNSMIC, and the proposed protocol is stable. In contrast, although the AEE of the proposed and JNSMIC protocols are both lower, the proposed protocol’s consumption is increased due to second-level communication. The faster the movement speed, the more energy is needed, so the AEE of the proposed protocol increased slightly under the high-speed mobility scenario. This is caused by sacrificing part of the energy to improve the link quality.

As shown in Figure 5b, the EED of the WCA and LEACH-M protocol increases rapidly with the increase in node movement speed. High-speed moving nodes will bring significant challenges to communication links and clustering stability. MBC considers more about re-clustering nodes that have lost connection and are more active in dealing with node-link interruption, so the EED of the network has good feedback, but the EED is still relatively high in general. In terms of EED, JNSMIC is stable and performs better than other protocols because the link connection time is considered when selecting nodes in the cluster. Similarly, the proposed protocol in the fault-tolerant phase also performed well in EED. However, the multi-hop communication in the cluster leads to a certain degree of complexity in the communication network, accompanied by an inevitable increase in EED, but with good overall performance.

Figure 6 shows that increased node movement speed inevitably leads to more frequent CH updates. JNSMIC protocol dramatically improves CH selection’s accuracy by regularly partitioning the network. Both MBC and the proposed protocol select CHs based on weight. Compared with the MBC protocol, the proposed protocol not only considers the local energy change in the network but also improves the weight of the node mobility factor. At the same time, under the effect of second-level communication, communication links are not suddenly interrupted, and the probability of member nodes replacing CHs is reduced, reducing the speed of updating the dominant set to a certain extent.

Figure 7 shows that the reaffiliation of nodes is positively correlated with the moving speed. When a node moves slowly, it has a low probability of falling out of the CH’s communication range, so reaffiliation is also low. However, the link connection time will decrease when the node moves faster, and the clustering stability will decrease. Although the MBC protocol considers the link connection time of nodes in the clustering phase, it has a poor effect on nodes moving at high speed. JNSMIC establishes communication links for nodes with lost connections separately in the fault-tolerance phase but has no other decisive measures except selecting nodes with less mobility as CHs in the clustering phase. In contrast, the proposed protocol sets a second-level communication mechanism in a cluster to reduce the influence of high-speed node movement. Member nodes out of the communication range of CHs should first consider forwarding data through relay nodes rather than finding other CHs again.

5.2.2. Influence of Node Communication Radius

There are 100 nodes in the network, and the maximum moving speed of nodes is 3 m/s. The performance changes of proposed and comparative protocols are analyzed by changing the maximum communication radius of CHs within the range of 10–50 m. The changes in the DSU and reaffiliation of WCA, MBC, JNSMIC, and the proposed protocol under different communication radii are shown in Figure 8.

With the increase in the communication radius of CH, DSU and reaffiliation show different changing trends. The change of reaffiliation is no longer a simple increase or decrease, but rather it shows a trend of increasing and then decreasing with the increase of communication radius. When the communication radius of nodes is small, there will be more clusters in the network, and it is easy for nodes to move away from the communication radius of the CH. At the same time, the small communication radius also leads to small communication coverage of the CH. For these reasons, member nodes that have lost connection do not easily join new clusters and can only apply to new CH. As a result, the DSU of the sensor network is currently enormous. However, as the communication coverage of the whole network increases, the DSU of the sensor network will decrease. The above reasons also increase reaffiliation when the communication radius increases but gradually decrease after reaching the peak value. This phenomenon occurs because, when the moving speed of nodes is unchanged, broader communication coverage can make member nodes stay longer in their coverage area compared with a smaller communication radius.

Figure 8a shows that when the dominant set saturates the network communication coverage, the DSU of different protocols is very small. However, when the communication radius is small, the proposed protocol showed good capability to precisely select CHs, which reduced the replacement speed of CHs and the energy consumption of nodes simultaneously. In Figure 8b, these protocols showed similar results of node reaffiliation under the outer communication radius. However, the proposed protocol had a smaller peak value and a more stable overall curve. Simulation data show that the DSJWCA protocol has advantages in maintaining clustering stability and improving link connection time. This benefits from establishing the second-level communication within the cluster and plays a significant role in fault-tolerant measures such as the sudden failure of CHs and the active response of member nodes that lose connection.

5.2.3. Network Lifetime Comparison

There are 100 nodes in the network, the movement speed of nodes is 5 m/s, and the maximum communication radius is 40 m. Figure 9 shows the network lifetime of the different protocols in this scenario. WCA seeks CHs by calculating their weights. Although this protocol has no fixed period for CH selection, large-scale data computation consumes lots of energy. LEACH-M protocol extends the network lifetime by modifying the network operation process. Member nodes can only forward data in the allocated time slot and keep sleep in the other time slot, saving unnecessary energy consumption. JNSMIC protocol uses the MOIA algorithm to obtain the optimal dominant set. The protocol can modify the communication radius of nodes according to the moving speed and position of member nodes in the cluster. Better connectivity brings less energy consumption. The proposed protocol prolongs link connection time by using the mechanism of intra-cluster second-level communication. A relatively complex intra-cluster communication route consumes part of the node energy. However, unnecessary energy consumption can also be reduced by controlling the number of in-cluster second-level communication nodes. According to the simulation data, the intra-cluster communication energy consumption does not seriously affect the network lifetime. On the contrary, the link stability and low dominant set update reduce the clustering process and a lot of weight calculation.

6. Conclusions

This paper proposes a distributed node status judgment-based weighted clustering protocol in order to improve the connectivity and stability of wireless sensor networks. The protocol reduces the influence of node movement on cluster stability by using second-level communication within the cluster, improves link connection time, and reduces packet drop rate. In terms of CH selection, an improved weight calculation formula is used to comprehensively consider the mobility factor of sensor nodes, local density, residual energy density, link connection time, and other information. At the same time, the node status judgment algorithm is used to effectively control the number of second-level communication nodes in the cluster, reduce the complexity of intra-cluster communication, reduce energy consumption, and reduce node reaffiliation.

In addition, to avoid the sudden failure of CHs, the protocol builds the set of VCH to replace the CH to complete data collection and forwarding. Considering the noise of sensor data acquisition in a non-ideal environment, EKF is used to eliminate noise interference and predict the actual position of sensor nodes under the GM mobility model. The simulation results combined with the Weibull reliability model showed that the proposed protocol with the node status judgment algorithm performed better than WCA, LEACH-M, MBC, and JNSMIC protocols regarding reaffiliation, dominant set update, and average energy consumption. Subsequent work will address routing selection under a multi-hop communication network and the network problems faced in open environments.