# Detecting Anonymous Target and Predicting Target Trajectories in Wireless Sensor Networks

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. WSN Model for Anonymous Target Tracking

#### 3.1. Rudimentary WSN Representation

_{t}’ locations. Y

_{t}= (x

_{j}, y

_{j}), where j = 1...m. These ‘m’ sensors are responsible for detecting the target within the sensing range R. The future position is estimated using Equation (1).

#### 3.2. Sensor Representation for Detecting Targets

#### 3.3. Strategies in Target Tracking

#### 3.3.1. Naive Activation

#### 3.3.2. Random Activation

#### 3.3.3. Selective Activation

_{p}’. Let X

_{b}be the original location of the target. X

_{a}= X

_{s}denotes prior location of the target. X

_{f}denotes future location of the target. This strategy uses past history of target’s location to arrive at the future position of the target. In other words, X

_{f}is estimated using X

_{a}. Sensors that are enclosed within a circular area of radius ‘r’ and those that lie around X

_{f}(t + 1) are signaled to toggle to sensing mode. Only sensors that are within sensing range R of the original location X

_{b}(t + 1) are toggled to sense the target. In tracking area, two circular sections may overlap with each other. This causes the sensors that lie within the overlapping area to detect the target. The new future position X

_{a}(t + 1) is estimated by finding out the centroid of locations of all sensors that lie in the overlapping area as shown in Figure 5. The sensors that lie in the covering region with radius ‘r

_{p}’ around the estimated location of target X

_{f}alone need to be switched on and should be in sensing mode at any instant. To model this strategy, Equations (13) and (14) are used.

#### 3.3.4. Periodic Activation

#### 3.4. Representation of Energy in WSN

_{i}is considered to be sensing in tracking area and cost of energy that is expended by s

_{i}at each time step is E

_{rx}.

_{i}is communicating with another sensor node s

_{j}is given in Equation (17).

_{j}.

#### 3.5. Representation of Target in Motion

_{m}’. (${v}_{x}\left(m\right){v}_{y}\left(m\right))$ are the target velocities along x direction and y direction at time ‘t

_{m}’, respectively. The model that is used to describe target in motion in x-y plane is of stable velocity and is characterized by Equation (20).

_{m}

_{+1}and t

_{m}is given by Equation (21).

_{w}. Therefore, noise across x and y axis is modeled using w

_{x}and w

_{y}. Covariance matrix C

_{w}is given by Equation (23).

- w
_{x}is not correlated to w_{y}. - Covariance and mean of multiplicative noise is given.
- Covariance and mean of additive noise is also given.
- Another crucial assumption is that if noises are absent, then it is fairly straightforward to determine position of the target.

## 4. Materials and Methods

#### 4.1. Proposed TDTT Model

#### 4.2. Pre-Localization

_{m}’ and noises that are measured by different sensors are exclusive and independent of other sensors defined by N = {N

_{i}}; i = 1,..., n and $P\left(N|(x,y\right)$) denotes conditional probability density function of N. The idea behind using Maximum Likelihood Estimation (MLE) to predict unidentified target locations (x,y) is that if $p(N|\left(x,y\right))$ is maximized, the location of the target can be identified. The mathematical model for the above explained concept is given in Equation (24), assuming measurement noises of sensor are independent and exclusive.

_{i}is very small, probability density function can be rewritten as given in Equation (25). The minor approximation done is negligible in probability density function and it is a well-known fact that KF is very resistant towards small variations in measurement noise.

^{(i+1)}and y

^{(i+1)}using Equation (28) where h is step size.

#### 4.3. Position Estimation Using KF

_{m}denotes measurement noise that is converted after prelocalization. This N

_{m}value is to be used in KF. Equation (31) shows Baye’s rule for posterior probability distribution.

_{b}(x,y). However, p

_{b}(x,y) does not include any information on the previous position of the target under consideration. p

_{b}(x,y) is uniform, always in sensing region. Considering this, $P\left(x,y|N\right)$ is shown in Equation (32).

#### 4.4. Choosing Sampling Period

#### 4.5. Choosing Sensors to Be in Sensing Mode

#### 4.6. Identification of Successive Cliques

_{1}’ is assumed to have unpredictable velocity such that ‘t

_{1}’ is assumed to move in a complex way and it is difficult to represent the complexity. The sequence of steps that is required to identify the clique in which the target ‘t

_{1}’ is travelling is:

- t
_{1}is detected by s_{3}. - s
_{3}exchanges this information with the neighbors. - s
_{3}receives the information from all other neighbors and conducts the comparison between its own information and the neighbors’ information. - All the neighboring sensor nodes are in sensing mode and t
_{1}is tracked within the sensing region and the immediate neighbor closest to t_{1}maintains the required information. - The clique in which t
_{1}moves is constructed.

_{1}’s movement from F

_{1}to any other clique F

_{j}is tracked using monitor and backup operation. This operation is based on all locations of t

_{1}, considering the current motion trajectory. The next step to be carried out is calculating the direction of target’s motion. The clique that is constructed in the previous step is represented by set M

_{n},

_{1}’s center of gravity position is used to find t

_{1}’s position. t

_{1}may follow any dynamic path such as travelling in a linear fashion, turning towards right or left, and performing U turn.

_{1}, S

_{2}... In each S

_{i}, the duration is set to 1. The direction of movement and target is denoted by $\theta $. The state of motion of target t

_{1}at time S is denoted by

_{1}can be calculated by each node in the following ways:

_{1}in ${\theta}_{h}$ direction.

_{1}is p, then

_{1}and h, the estimated location of l

_{j}

_{+1}with approximate coordinates $\left({x}_{j+1},{y}_{j+1}\right)$ of t

_{1}at j + 1 is

_{1}can be calculated by changing ${\theta}_{h}$ between −π and π.

_{j}, where t

_{1}is in motion currently, the sequence of positions is obtained by the previous step. An alert message is issued to the neighbors of F

_{i}. If the node that receives the alert is the requested node, then all those nodes are grouped in F

_{j}

_{+1}and other cliques. If it does not receive the signal, then the node is in awakening state. If t

_{1}is detected and signal is received, then exchange communication with new backup and proceed with calculating the new maneuver of t

_{1}. Finally, if target t

_{1}is detected in F

_{j}

_{+1}then l

_{j}is the new location. F

_{j}= F

_{j}

_{+1}is the new clique.

Algorithm 1 TDTT Model |

1. Activate sensor at regular interval. |

2. Apply prelocalization on the set of activated sensors. |

3. Apply Kalman filter. |

4. If no target detected then go to step 1. |

5. Select neighboring set of sensors. |

6. Recalculate sampling period. |

7. Exchange information about target with its neighbor. |

8. Track target’s clique using monitor and backup operation. |

9. Compute direction of target’s motion. |

## 5. Results

^{2}field with around 950 sensors in a 40 × 40 grid and a sensing range of 100 m per sensor. The monitored area of this simulation was set to 1000 m and parameters were captured by playing the simulation until 2500 s.

#### 5.1. Scenario 1

#### 5.2. Scenario 2

#### 5.3. Scenario 3

#### 5.4. Comparison of TDTT with Other Existing Approaches in Terms of Accuracy

#### 5.5. Assessment of Energy Consumption and Accuracy

^{2}. The motion of the target was set to linear and around 1000 steps were taken by the target. The velocity was set between 0 m/s and 30 m/s randomly.

## 6. Conclusions and Future Works

## Author Contributions

## Funding

## Institutional Review Board Statement

## Conflicts of Interest

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**MDPI and ACS Style**

Leela Rani, P.; Sathish Kumar, G.A.
Detecting Anonymous Target and Predicting Target Trajectories in Wireless Sensor Networks. *Symmetry* **2021**, *13*, 719.
https://doi.org/10.3390/sym13040719

**AMA Style**

Leela Rani P, Sathish Kumar GA.
Detecting Anonymous Target and Predicting Target Trajectories in Wireless Sensor Networks. *Symmetry*. 2021; 13(4):719.
https://doi.org/10.3390/sym13040719

**Chicago/Turabian Style**

Leela Rani, P., and G. A. Sathish Kumar.
2021. "Detecting Anonymous Target and Predicting Target Trajectories in Wireless Sensor Networks" *Symmetry* 13, no. 4: 719.
https://doi.org/10.3390/sym13040719