4.3. Positioning and Tracking 51Figure 4.4 Signal preprocessing recovers missing signal components(marked asgreen circles) by using information from adjacent signals and injects the neededadditional interpolated signal vectors(grey) to allow a maximum walking speed of3 ms- 1under the constraints of the(5, 5, 3) model.as described in 2.5.4, the task of the Viterbi Decoder to evaluate p( s| x) becomes asimple euclidean distance5calculation between the stored mean vector and an inputRSSI vector.Special attention is given to the problem of missing signals in the input vector.Although signal preprocessing mitigates this problem by interpolation of missing APcomponents in the sequence of measurement vectors(see figure 4.4), there can still bemissing AP components at the head or the tail of the sequence. If missing signals aresimply adjusted to a value of- 100 dbm this leads to undesirable high deltas duringthe distance calculation for the neighbouring states of the correct location. There, inthe case of a missing signal, the corresponding AP values are larger than- 100 dbm.With larger simulated RSSI values for such an AP at these states, the effect becomesstronger. The states near the correct location get an artificially elevated distanceand are in a sense"pushed away". Empirical investigations have lead to the bestresults by fully skipping the component, although assigning a distance of zero seemsto be a form of inappropriate reward for this case.4.3.1.3 Transition ProbabilitiesThe transition probabilities p( s| s) are the key instruments for modelling the sequen-tial nature of the input signal. They have a discrete probability distribution that isstored in a large table containing number of states times the number of transitionsentries. The model ensures that the normalization constraints of the discrete PDFgiven bys Sp( s)= 1 ands S(5, 5, 3)p( s| s)= p( s) are satisfied. Furthermore, theprobability mass of p( s) is divided evenly over the three jump widths. One third isreserved for the 0-jump and the other two thirds are given to the 1- and 2-jump.every material intersection. Overlapping signal information of different recursion depths could thenbe interpreted as a result of multipath radio propagation.5The Viterbi Decoder can also be configured to use other distance functions. Pretty muchequivalent results in terms of errors were archived with the computational less expensive manhat-tan distance( l1-norm) restricted to the max 3 signal deltas. The restriction to the top 3 deltasanticipates the greater weight of component distances of lp-norms with p> 1