## 2 Synchronization Protocols in WSN
### Temperature-Based Synchronization Protocols in WSNs  
The use of temperature in WSN synchronization protocols is a field of study with high relevance [5, 6, 12]. Since the publication of RBS, TPSN and FTSP, several temperature-based synchronization protocols have been proposed to improve the performance of the synchronization process. Among these works, two approaches can be highlighted: Temperature Compensated Time Synchronization (TCTS) and the Environment-Aware Clock Skew Estimation and Synchronization for WSNs (EACS).  
[PERSON] _et al._[12] propose TCTS. It takes into account the temperature sensor built in the motes, and it calibrates the local oscillator by removing the effects due to temperature changes. This approach has a process known as _frequency error estimation_, which determines the clock skew of the localoscillator related to the reference node of the network for every given measured temperature. The authors assume that temperature remains constant for every clock skew estimation. After obtaining the clock skew for a pair of nodes in a given temperature, a new clock skew with a new temperature value is then computed. When the complete range of temperatures has been explored, TCTS begins with the synchronization phase. If a certain temperature is not computed, the calibration process restarts again to include that new skew information. Thus, the node carries out a realistic adjustment of the frequency. Once the relationship between the frequency error and the obtained temperature is learned, the node increases the time between synchronization intervals. This allows an improvement of the synchronization period, minimizing the number of synchronization periods and, thus, optimizing the energy consumption. [PERSON] _et al._ provide simulation results during a \(96\) h period. For the first \(24\) h, TCTS is in the calibration mode. At the end of the simulation, 95% of the errors lie within \(\pm 4\) tics of a \(32\) khz oscillator. Results show a clock stability of \(<\)0.07 ppm for a \(16\) h test with no resynchronization.  
EACS was proposed by [PERSON] _et al._[6]. Taking into account temperature variations, [PERSON] _et al._ describe a highly accurate clock skew estimation. The authors propose an additional information-aided multi-model Kalman filter (AMKF) algorithm to dynamically compensate for the clock skew. The great benefit of EACS is the possibility of using it as a component of any conventional WSN synchronization protocol based on the clock skew estimation. This allows the update of the local clock with local information before the clock resynchronization is carried out, which improves the lifetime of the more by increasing the synchronization period. The EACS algorithm builds up an initial table of each node of the network based on the correlation between temperature and clock skew. A Kalman filtering is applied to obtain the theoretical relationship between those components. This procedure has very large computational requirements, which does not make it a suitable method for low cost WSN. Simulation results show that the error is always below \(2\) ms for the whole \(8,000\)-s simulation. Experimental results with a Mica2 testbed provide an error of \(8\) ms for a \(7,200\)-s test duration. The authors do not provide any measure of frequency stability.  
The above mentioned proposals improve the behavior of protocols as, for example, FTSP, under temperature variations. However, both approaches (i) have high computational costs and energy consumption, (ii) require a large amount of memory per node to store the relationship between temperature and clock skew, (iii) cannot manage new temperatures without a recalibration process and (iv) are constrained to always use the same reference node. Any change in these restrictions triggers the need for a new calibration.