2.2. Positioning 132.1.3 ErrorThe error for a radio propagation result will be determined by comparing the corpusof measurements m with the simulation results x for each AP configured with nfree.1NapsNlocsRP E( nfree)=NapsNlocsa=1l=1|| ma,l, xa,l||where xa,lis the simulation result for AP a and location l. Likewise ma,lis a collectedmeasurement for AP a and location l. Napsis the number of available APs and Nlocsthe size of the training corpus. For|| m, d|| the l1-norm, the absolute delta| m- s| isused. Therefore, the Radio Propagation Error(RPE) is simply the averaged errorover all collected measurements at the different locations in units of dBm.Another variant of this error that is used in literature is the RMS-RPE. This erroruses the rooted averaged euclidian distance, or the l2-norm, as a metric and is givenby:1RM S- RP E( nfree)=NapsNlocsNapsNlocs( ma,l, xa,l)2a=1l=1The unit of this error is also given by dBm.2.2 PositioningThe task of Positioning is defined as determining the physical position of a stationarydevice by using information received by the sensors of that device. This information,extracted from some measured signals, is obviously required to be related to thethat position for relevancy. The measured signals are usually obstructed by noisyeffects that come from various sources. The performance of a positioning systemis defined over the error that is given by the distance between the real positionand the estimated one. A well performing positioning model will therefore have tocompensate these noisy effect for minimizing the position errorThe source of information that is exploited for positioning in this thesis is givenby measuring the Received-Signal-Strength-Indicator(RSSI) values of available APswith Wi-Fi capable devices. The RSSI value is a measure of the magnitude ofthe electromagnetic field at some physical location. The field is emitted by theantennas of an AP with a known location. The RSSI value is expressed in dBmwhich represents the remaining power of the emitted electromagnetic field in relationto the reference unit of one milliwatt. And explicitly by:x= 10 log10(1000 p)if p is the power at the source of the electromagnetic field given in watt and x is themeasured RSSI value.Alternate interesting sources of information that are exploited by positioning systemsand that were analysed in recent research[10] are: