There exist a several number of applications enabled by sensor networks: Surveillance systems, forest fire systems, Environmental monitoring, target tracking, robotics and military operations. This huge development in wireless sensor networks was due to its reliability and low cost. Each sensor node of the networks can measure targets states and communicate with each other to share collected information and doing computations [
1,
2]. According to the deployment method of nodes, wireless sensor towers can be divided into random deployment deterministic deployment, according to the node mobile capabilities, wireless sensor networks can be divided into static networks and dynamic networks [
3]. Coverage problem is the basic problem of any type of wireless sensor network. The coverage problems of static wireless sensor networks can be divided into three categories: point coverage, area coverage and barrier coverage [
4]. It is required that when a moving target traverses the network deployment area along an arbitrary path, the probability of the target not to be discovered is the smallest. So, for any sensor network, the detection probability of the target in the network when it passes through the network needs to be examined. Measuring the quality of sensor network coverage provide the concept of worst-case coverage to characterize the network ability to perceive a target [
5]. To measure the possibility of a certain target otherwise if it’s detected by a sensor network or not, many documents have cited exposure. In the literature [
6], the exposure degree of the target is calculated considering it as the target energy collected by the sensor network, and Dijkstra’s algorithm is used to find the minimum exposure path of the target. In the literature [
7], exposure is regarded as the distance between the standard path and the sensor node, two paths are calculated: the maximum clearance path and the maximum support path. In [
8] a two-dimensional rectangular area is considered to be guarded by a set of sensors, that may be surveillance cameras or sensors. And the minimal exposure path is calculated by first computing an approximate "feasible region" of interest using the sensors' sensing ranges, and then searching for the minimum exposure path in a systematic manner using a grid within this feasible area. It should be noticed that [
9] barrier sweep coverage was investigated using mobile sensors, with the barrier being modeled as a finite-length continuous curve on a plane. The sink node utilized sensor node exposure metrics to compute the lowest exposure path, and the function fitness was created using a combination of the computed minimal exposed path and the ratio of covered to uncovered grids in [
10] algorithm. When using traditional methods to calculate the maximum clearance path, the planar target traveling on the path may be incorrectly considered as not covered by nodes. This paper proposes a coverage analysis for plane target based on Clifford algebra. So, its calculation is applied to the study of the traversal problem of two-dimensional planar targets. Therefore, using Clifford geometric algebra which is a tool that does not depend on a specific coordinate system can be proposed [
11]. The coverage analysis model and the method that is consistent with different targets in dimensional space can effectively solve the problem of sensor network coverage performance analysis through the complete relative information between sensor nodes and targets. On this basis, this paper uses Clifford geometric algebra. Representation of the planar target and the rate of coverage for each node to the planar target are given, and a sensor network maximum clearance path algorithm based on the planar target is proposed. The Voronoi diagram of the network is implemented to represent the planar target traversing through the sensor network [
12]. Experiments show that the use of Clifford geometric algebra effectively solves the problem of searching for the optimal path of the plane target in the sensor network, which reflects the network coverage performance.
Clifford algebra was founded by WK. Clifford at the end of the nineteenth century. It is also called exterior algebra. It was extended of Grassman algebra. Clifford algebra provides calculations for space geometry without depending on coordinates to obtain a geometric symbol representation. On the other hand, it can be easily extended to higher-dimensional space for geometric calculations and analysis [
13]. It has become an important research tool in theoretical mathematics and physics [
11,
14]. The most popular algebraic structure today for Euclidean n-space is the inner product space
\({R}_{n}\). This powerful extension of this structure is represented in [
15,
16].
The remaining part of the paper is structured out as follows: In Sect.
3, the plane target in a wireless sensor network is presented and the coverage rate of the nodes in the wireless sensor network is calculated. In Sect.
4, the maximum clearance path is obtained based on the representation of the plane target using Clifford algebra. Experimental methods and presented algorithm are introduced in Sect.
5. Finally, Results and discussion are provided in Sect.
6.