Proximity detection

The IoT is becoming an important part in human machine interaction. Its applicability varies from healthcare [171] to mass-market applications [172]. A vital feature that will help enable such applications is indoor localisation. Particularly, IoT indoor localisation- based services are expected to operate without human intervention [173]. Localisation techniques can be divided into two groups: database-matching methods and geometri- cal methods [174]. Database-dependent methods rely on pre-stored location information, which is treated as a fingerprint map of the area. The localisation process is based on a real-time comparison between the collected information to the pre-stored one. This type of methods determines the fingerprint, within the map, in which the user belongs. Geometrical methods are based on real-time computation of the user’s location. The location is determined by measuring distances or angles. Some of the widely used geo- metrical methods are: time-of-flight, multilateration, multiangulation and proximity de- tection [173, 174].

While time-of-flight, multilateration and multiangulation are capable of accurate lo- calisation they usually require high complexity operations or high cost equipment. On the other hand, proximity detection has the lowest computational complexity, and could be easily implemented with the equipment already present in smartphones today. Proximity detection is a distance based method which does not provide exact location, instead it

Beacon

User

Figure 3.2: Proximity detection

can be used to estimate the distance to a transmitting beacon [175]. As illustrated in Fig. 3.2 by using this method one could measure the distance to a nearby beacon but cannot determine the direction to it.

Due to its simplicity and ease of implementation proximity detection is used for the purpose of the study within this chapter as a soft authentication mechanism along with PUFs. A widely adopted technique to obtain the distance to a user (the radius in Fig. 3.2) is by using the RSS. However, numerous factors could negatively impact the wireless communication in an indoor scenario. Such are reflection, diffraction, scattering, slow and fast fading. All of the above have direct impact on the RSS. To overcome these issues one must use a filtration algorithm to treat noisy measurements. A popular filter applied for localisation is the, so called Kalman filter [176]. It works by the assumption that the current state xi has relation to the previous one xi−1, and this relation is expressed as follows:

xi = Axi−1+ Bui−1+ wi−1, (3.2)

where A is a transition matrix which links the current state with the previous one, B is a control matrix which relates the control vector u to the state and w is an i.i.d. normally distributed process noise such that w ∼ N (0, IσQ), which represents factors such as velocity change, wind etc. Following that, the measurements of the current state are given

by:

zi = Gxi+ vi, (3.3)

where G is the observation matrix used to translate each state into a measurement and v is an i.i.d. normally distributed measurement noise such that v ∼ N (0, IσR), which denotes the noise present in the measurements, due to fading, path-loss etc. Given the above, the recursive process of the filter is presented on Fig. 3.3. It is based on two main steps: prediction and correction (time and measurement update, respectively). During the time update step: i) the next state is updated based on the previous one; and, ii) the error covariance matrix Pe is updated based on the previous one. In the above ˆxi¯ and Pei¯ are a priori estimated state and a priori error covariance matrix, i.e., predictions, which are estimated based on the previous instant. In fact the error covariance matrix is a measure of uncertainty of the estimated state ˆxi¯, due to process noise. Next, during the measurement update step the filter uses the a priori estimates calculated in the prediction step and updates them to find their a posteriori values: i) the so called Kalman gain KG is computed such that it minimizes the a posteriori error covariance, i.e., it determines the weight of the measurement zi and the a priori estimate ˆxi¯, such that if the measurement noise is low the measurement will contribute more for the calculation of the a posteriori state, while if the the error in the a priori estimate is low it will be trusted more during the measurement update step; ii) using the Kalman gain estimates ˆxiand Pe,iare updated following the equations from the measurement update step given in Figure 3.3.

Finally, it has been shown that the characteristics of a fading channel follow a log- normal distribution and a commonly used path loss model demonstrated through mea- surements is [177–180]:

RSSI(d) = RSSI0− 10n log

Ç

d d0

å

+ Xσ, (3.4)

where RSSI(d) is the path-loss (average received signal strength) at distance d, RSSI0 represents the average received signal strength at some reference distance d0, n is an attenuation factor that gives the relation between distance and received power, its values

Pe,i¯= APei−1AT + σQ ˆ

xi¯= Aˆxi−1+ Bui−1 Time update Pe,i = (I − KGiG)Pei¯ ˆ xi = ˆxi¯+ KGi(zi− Gˆxi¯) KGi= ¯Pe,iGT(G ¯Pe,iGT + σR)−1 Measurement update

Figure 3.3: Kalman filter steps

ranges from 2 to 6, Xσ is a zero mean Gaussian random variable which captures the variations in the received power with standard deviation (smaller the deviation higher the precision of the model). Typical values of n and and the standard deviation of Xσ for different indoor environment are summarised in [87]. To simplify the model, typically, the reference distance d0 is chosen to be 1m, hence Eq. (3.4) becomes:

RSSI(d) = RSSI0− 10n log(d) + Xσ. (3.5)

To conclude, using the Kalman filter presented on Fig. 3.3 and the path-loss model 3.5, one can build a proximity detection mechanism. Such a mechanism later in this chapter as part of an authentication process.