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Localizing a jammer in an indoor environment in wireless sensor networks becomes a significant research problem due to the ease of blocking the communication between legitimate nodes. An adversary may emit radio frequency to prevent the transmission between nodes. In this paper, we propose detecting the position of the jammer indoor by using the received signal strength and Kalman filter (KF) to reduce the noise due to the multipath signal caused by obstacles in the indoor environment. We compare our work to the Linear Prediction Algorithm (LP) and Centroid Localization Algorithm (CL). We observed that the Kalman filter has better results when estimating the distance compared to other algorithms.

Wireless sensor networks (WSNs) are utilized in different fields including healthcare monitoring, industrials, military, air pollution, water quality monitoring, security monitoring, wearable devices, internet of things, and more [

Locating a jammer in WSNs is very important to support the improvement of existing countermeasures. In an indoor environment, applications using the wireless communication are rapidly increased, such as health monitoring, internet of things applications, and monitoring secured place inside the building. Because the WSNs are designed as multi-hop networks, the sensor forwards its information to the next hop node until it is received by the destination. Therefore, routing protocol is designed to find the shortest path between the sender and the sink node before the transmitter starts transmitting its collected data. By detecting the jammer location, the routing protocol is forced to avoid the jamming region which causes repeated messages due to delivery failure [

Jamming attacks in WSNs have been intensively studied and defined as a stranger transmitting signal with high power to inject a false signal, override the legitimate node’s message, or isolate nodes from the network [

Several algorithms have been proposed as anti-jamming attacks in wireless communication, such as the Frequency Hopping Spread Spectrum (FHSS) and the Direct Sequence Spread Spectrum (DSSS) [

Indoor localization is challenging due to multipath signals caused by surrounding objects. When the signal propagates between two transceivers, it may have reflected, diffracted, or scattered before being received by the next hop node. The Non-Line-of-Sight (NLOS) [

Existing location detecting technology, such as a Global Position System (GPS), may not work correctly due to the weakness of the signal inside the building [

This paper is organized as follows: the network model and types of nodes in general model and jammed launch is discussed in section 2. In section 3, the path loss model, NLOS, and Sight-of-Line (SOL) are presented. The Linear Prediction, Centroid Localization, and Kalman filter are discussed in sections 5, 6 and 7 respectively. Section 8 includes the analysis and simulation results. Section 9 concludes this paper.

We considered the sensors deployed randomly over a small area in an indoor environment. All sensors in our proposal are classified as having the following characteristics:

Multi-hop. Each node must pass the data collected to its neighbor to the sink node.

Stationary. All nodes have fixed position and remain not change after node deployed.

Neighbor-Aware. Each node knows its neighbor position by exchanging the location information.

Location-Award. A node can detect its location coordinate after sensors are deployed.

Homogenous. The sensor has an omnidirectional antenna and transmits with the same power level.

Unaffected node: All nodes that are outside the jammer’s transmission range, and they can receive a packet from all their neighbors.

Jammed nodes: Any sensors within the jammer’s transmission range. A node cannot receive a message from its neighbor.

Boundary node: A node can receive a packet from part of its neighbor. A boundary node can also measure the jammer Received Signal Strength from oncoming messages. We estimate the jammer position using the boundary nodes, where they can receive the jammer’s received signal strength.

Wireless communication is susceptible to several challenges as signals travel from the transmitter to the receiver. Not only can the signal suffer from noise and interference, but also from the reflection, diffraction, and scattering [

P r ( d ) = P t G t G r λ 2 ( 4 π d ) 2 (1)

where P r ( d ) is received signal power at distance d, P t is the transmission’s signal power, G r and G t tare the system gain, λ is the wavelength and d is the distance between sender and receiver. The Log-normal model can be presented in the following forms:

P j ( d ) i = P j ( d 0 ) − 10 ∗ n log d i d 0 + X σ (2)

where n is the path loss exponential where there is a change from one environment to another. In an indoor place, the path loss exponential is between 2-3. X σ is zero-mean Gaussian distributed random variable.

P j ( d 0 ) = 10 ∗ n log 10 d 0 (3)

P j ( d ) i = P j ( d 0 ) − 10 ∗ n log d i d 0 (4)

where d i is the estimated distance from filtered JRSS.

Linear prediction is one way to predict a future value from a series of data [

J R S S ^ L P = ∑ i = 1 p a i ∗ J R S S ( n − i ) + e [ n ] (5)

a p J R S S ( n − p ) + a p − 1 J R S S ( n − ( p − 1 ) ) + a p − 2 J R S S ( n − ( p − 2 ) ) + a p − 3 J R S S ( n − ( p − 3 ) ) + a 0 J R S S ( n ) = J R S S ( n + 1 ) (6)

where n = p is the system order. e is the error from the estimated JRSS, also called a residual signal.

e = ‖ J R S S − J R S S ^ ‖ (7)

Each boundary node is set to capture a series of JRSS at time N, so our data set contains N number of JRSS. By solving linear algebra for (6), we obtained the order coefficient a as follows.

a = ( X T X ) − 1 X T Y (8)

X = [ J R S S 1 J R S S 2 ⋯ J R S S p J R S S 2 J R S S 3 ⋯ J R S S P + 1 ⋮ ⋮ ⋱ ⋮ J R S S N − p − 1 J R S S N − p ⋯ J R S S N − 1 ] , a = [ a p ⋮ a 1 a 0 ] , Y = [ J R S S p + 1 J R S S P + 2 ⋮ J R S S N ] (9)

where X denotes the J R S S L P at time instant N, and Y is the value we want to predict.

Centroid Localization (CL) is used to localize a sensor by averaging all nodes around the target node. The localization error using CL is based on the density and location of jammed nodes [

( X j , Y j ) = ∑ i = 1 n X i N , ∑ i = 1 n Y i N (10)

where N is the number of jammed nodes.

The Kalman filter was developed by Rudolf Kalman in 1960. The Kalman filter is

a recursive estimation filter based on the linear dynamical system. It uses the past, and current estimate to predict and update current value. It has two steps to estimate the current state, prediction, and correction state [

X ^ k | k − 1 = ( H k Z k − 1 | k − 1 ) − 1 (11)

P k | k − 1 = ( H k R k ) − 1 ( H T ) − 1 (12)

Prediction

X ^ k | k − 1 = A k X ^ k − 1 | k − 1 + B k u k (13)

P k | k − 1 = A k P k − 1 | k − 1 ∗ A k T + Q k (14)

Computing Kalman gain

K k = P k | k − 1 H k T ( H k P k | k − 1 H k T + R k ) − 1 (15)

Updating filter

X ^ k = X ^ k | k − 1 + K k ( Z k − H k X k | k − 1 ) (16)

P k = P k | k − 1 − K k H k P k | k − 1 (17)

where Z k is the jammer’s received signal strength received by a boundary node at time k, and X ^ k is the Kalman filter output after k times during the process. In our case, the observed JRSS at each boundary node is X ^ k . A k is the state transition model, H k is the observation model, Q k is the covariance of the process noise, R k is the covariance of observation noise,#Math_37# and u k are the control input, and K is the Kalman filter gain. Because we measure the JRSS of the fixed position jammer, A k become an identity matrix and B and u were set to zero.

Computing jammer coordinates directly using captured JRSS resulted in the wrong position. In this section, we localize a jammer in three different methods: the Kalman filter, linear prediction, and centroid localization algorithm. To eliminate noise from the JRSS effected by surrounding environment and obstacles in an indoor place, the Kalman filter, and linear prediction come in to play. Moreover, centroid localization performs a position estimation by averaging all jammed nodes, so the noisy distance is not considered in the computation. However, CL is sensitive to the jammed nodes positions and a number of jammed nodes. In the following, we estimate the jammer distance by converting the JRSS captured by each node to distance using the Log-Normal Shadowing model (4) as follows:

d ^ i = d 0 10 P j ( d 0 ) − P j ( d ) i 10 n (18)

where d ^ i is the estimated distance computed at each boundary node i. The Euclidean distance formula (19) is used to find the distance between the anchor and target, as shown in

d ^ i = ( x i − x j ) 2 + ( y i − y j ) 2 , i = 1 , 2 , 3 , ⋯ , n (19)

{ d ^ 1 2 = ( x 1 − x j ) 2 + ( y 1 − y j ) 2 d ^ 1 2 = ( x 1 − x j ) 2 + ( y 1 − y j ) 2 ⋮ d ^ n 2 = ( x n − x j ) 2 + ( y n − y j ) 2 (20)

x ^ = ( A T A ) − 1 A T B (21)

where

x ^ = [ x j y j ] , A = 2 [ x 2 − x 1 y 2 − y 1 ⋮ ⋮ x 2 − x 1 y 2 − y 1 x n − x 1 y n − y 1 ] , B = [ d ^ 1 2 − d ^ 2 2 − ( x 1 2 + y 1 2 ) + ( x 2 2 − y 2 2 ) d ^ 1 2 − d ^ 3 2 − ( x 1 2 + y 3 2 ) + ( x 3 2 − y 3 2 ) ⋮ d ^ 1 2 − d ^ n 2 − ( x 1 2 + y n 2 ) + ( x n 2 − y n 2 ) ] (22)

where the ( x i , y i ) the boundary node location and ( x j , y j ) is the jammer location

In our network model, we simulate the effect of the jamming attack in an indoor environment to evaluate the reliability of localizing a jammer in an area of 100 m × 100 m using MATLAB. The network nodes were randomly distributed with a transmission range of 25 m and sensing a range of 15 m. The jammer location was evaluated in a different situation with a transmission range of 30m and randomly placed. We studied and evaluated three different algorithms including the Kalman filter, linear prediction, and centroid localization, and analyze the performance of each model to estimate the jammer location. To investigate the impact of JRSS samples acquired by boundary nodes, we compared KF to LP. LP is a method to predict future values and to eliminate the signal fluctuation caused by surrounding noise and multipath signals in our case. It estimates next value from a combination of past p samples, where p is system order. The main aim of LP is to compute LP coefficients to reduce the prediction error [

The mean square error (MSE) was used to evaluate the efficiency of the Kalman filter to locate the jammer in an indoor environment compared to linear prediction and centroid localization algorithms. During the experiment run time, we generated different samples of jammer received signal strength (JRSS) captured by the boundary nodes. The jammer and the nodes are randomly placed in the network. The density of the network nodes differed for each runtime to evaluate the efficiency of localizing the jammer. For the first experiment we analyzed, the network density was set to 50 nodes, the nodes and jammer were deployed randomly, and the jammer’s transmission range was 35m. We studied the Kalman filter and linear prediction by increasing the number of input to 50, 100, and 200 samples as shown in

computed 50 JRSSs and 200 JRSSs. The distance error between boundary node 13 and the jammer was 0.4 at 50 samples input and 0.02 at 200 JRSSs. We can see that KF has a better performance to reduce the distance error compared to LP. However, using LP and CL, the X and Y jammer coordinate error remained steady, as shown in

Finally, we analyzed the impact of the jammer localization performance of the algorithms.

Boundary node ID | Original JRSS | Noisy JRSS | KF JRSS | LP JRSS | Original Dist. (m) | Est. Dist. KF (m) | Est. Dist. LP (m) | MSE KF (m) | MSE LP (m) |
---|---|---|---|---|---|---|---|---|---|

4 | −70.90 | −70.69 | −70.93 | −70.53 | 35.09 | 35.21 | 33.64 | 0.08 | 1.02 |

5 | −70.16 | −68.93 | −70.21 | −70.30 | 32.21 | 32.42 | 32.73 | 0.14 | 0.37 |

16 | −69.60 | −68.62 | −69.53 | −68.96 | 30.20 | 29.99 | 28.07 | 0.15 | 1.50 |

34 | −71.14 | −70.57 | −71.25 | −71.12 | 36.06 | 36.54 | 35.97 | 0.33 | 0.06 |

38 | −69.87 | −68.63 | −69.82 | −69.67 | 31.16 | 30.98 | 30.45 | 0.12 | 0.50 |

44 | −70.84 | −70.86 | −70.90 | −70.96 | 34.84 | 35.09 | 35.35 | 0.17 | 0.35 |

45 | −70.36 | −69.58 | −70.24 | −70.46 | 32.99 | 32.52 | 33.37 | 0.33 | 0.26 |

49 | −71.45 | −71.38 | −71.40 | −72.02 | 37.40 | 37.18 | 39.92 | 0.15 | 1.78 |

Algorithm | x | y | x ^ | y ^ | x-axis MSE (m) | y-axis MSE (m) |
---|---|---|---|---|---|---|

KF | 63.34 | 18.47 | 63.61 | 18.64 | 0.19 | 0.11 |

LP | 54.72 | 27.18 | 6.09 | 6.15 | ||

CL | 67.19 | 19.62 | 2.72 | 0.81 |

In this paper, we estimate the jammer position using KF, and we compared its performance with similar algorithms, such as LP and CL. The mean distance error is very small in KF compared to LP. The CL shows better performance than LP when the jammed nodes distributed around the jammer. LP remained steady over the changes in the samples of JRSS, the density of the networks, and the location of the jammer. The KF performed better when the vast samples were taken to KF as an input and can detect the target with high accuracy compared to LP and CL.

Aldosari, W. and Zohdy, M. (2018) Localizing Jammer in an Indoor Environment by Estimating Signal Strength and Kalman Filter. Wireless Engineering and Technology, 9, 20-33. https://doi.org/10.4236/wet.2018.92003