6.2. Localization 85Figure 6.2 Online and offline 2D localization errors over 36 noise steps. The HMM outperforms the PF during the online and offline mode. The averaged online resultleads to lower errors for both algorithms.history. Interestingly, it is even slower than the PF, since all states of the locationspace have to be visited at each time frame. And this is costly for a high resolutionstate space.The HMM algorithm leads to the lowest error rates over all noise conditions. Evenboth online errors are lower than the PF offline error. This comes by the costs ofincreased computational complexity by the factor 10 and an increase in memoryconsumption of around factor 100. It can be concluded that the HMM approachreaches lower error rates: By conducting an exhaustive search over the hypothesesthe HMM approach is guaranteed to find the optimal solution, whereas the PFapproach is not to able to generate this solution by sampling.Furthermore, both algorithms show the behaviour that the averaged variant of theonline error leads to a better prediction of the hidden location sequence but areoutperformed by the offline error in both cases. An interpretation of this result is,that valuable information is distributed over either the particles or the unprunedstates of the HMM . The backtracked solutions in the offline mode can make senseof this information whereas during the online mode it can only partially be accessedby the averaging process.Additionally, it can be observed from the variance plot in figure 6.2, that the PF,compared to the HMM, shows an elevated decrease in accuracy under increasingnoise at the interval 8 dBm< < 14 dBm. By investigating the individual resultsequences it was observed that at these noise levels the effect of sample impoverish-ment(see 4.3.2.3) becomes significant and seems not to be handled optimal. It isonly countered with random re-sampling which induces a new noise component andtherefore leads to a degraded result. A better way to handle the decay of the set ofparticles in the PF algorithm is proposed in the work of Widyawan[29]. The basicidea is to conserve the particle history, manipulate it by using information from the