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===== Conclusion =====

Through the values shown in the tables TAB.1.A and TAB. 2, the bayesian method looks  that roughly works like the tomographic method. Instead the tomographic methods is better than the bayesian, because the first one does not requir any a-priori informaiton on the target's movements. In our simulation the transiction probability function, about  the target's movements, is well-known.

The results show that the Kalman filter does not give significant advantages, in fact, all the error parameters in both cases, “with and without” Kalman, are the same.

The tomographic approach suffers the parameters calibration of the weights of the regularization matrix, as show the values in the TAB.1 with label no noise.

===== New Scenario =====

This video shows the PATH1 followed by the target, for a scenario with 24 anchors and the VRTI algorithm{{:postuloca:misure_path1_s24_multi_qtv.avi|}}\\
This video shows the PATH2 followed by the target, for a scenario with 24 anchors and the VRTI algorithm{{:postuloca:misure_path1_s24_multi_qtv.avi|}}\\
This video shows the PATH3 followed by the target, for a scenario with 24 anchors and the VRTI algorithm{{:postuloca:misure_path1_s24_multi_qtv.avi|}}

===== Tomographic approach =====

The results in TAB.1 are drawn from [[postuloca:tomographic]] show that the accurancy of the measures (number of channels, samples per second collected, quantization level) is instrumental for the accurancy of the localizzation estimation.

^ SCENARIO               ^ RMSE    ^ Percentile (75°) ^ Percentile (90°) ^                                                                ^
^ C_40 VRTI              | 1.595 m | 1.946 m          | 2.668  m         |Area 6.4 m X 4.5 m, 25 sensors, Data Collection on 1 Radio Channel|
^ C_40 KALMAN            | 1.588 m | 1.933 m          | 2.624  m         |:::                                                               |
^ C_40 VRTI no noise     | 2.548 m | 3.278 m          | 3.776  m         |:::                                                               |
^ C_40 KALMAN no noise   | 2.545 m | 3.275 m          | 3.772  m         |:::                                                               |
^ PAT_1 VRTI             | 0.615 m | 0.683 m          | 1.04 m           |Area 8.4 m X 6.5 m, 33 sensors, Data Collection on 5 Radio Channel|     
^ PAT_1 KALMAN           | 0.623 m | 0.675 m          | 1.02 m           |:::                                                               |
^ PAT_1 VRTI no noise    | 1.641 m | 1.809 m          | 2.232 m           |:::                                                              |                                                              
^ PAT_1 KALMAN no noise  | 1.625 m | 1.803 m          | 2.226 m           |:::                                                               |
^ PAT_2 VRTI             | 1.259 m | 1.554 m          | 1.998m           |Area 6.5 m X 4.5 m, 28 sensors, Data Collection on 1 Radio Channel    |
^ PAT_2 KALMAN           | 1.258 m | 1.550 m          | 1.974 m          |:::                                                               |
^ PAT_2 VRTI no noise    | 1.673 m | 1.846 m          | 2.531m           |:::                                                               |
^ PAT_2 KALMAN no noise  | 1.662 m | 1.826 m          | 2.534 m          |:::                                                               |
^ Runner VRTI             | 3.06 m | 4.24 m          | 5.60 m           |Area 6.5 m X 4.5 m, 28 sensors, Data Collection on 1 Radio Channel    |
^ Runner KALMAN           | 3.05 m | 4.23 m          | 5.59 m          |:::                                                               |
^ Runner VRTI no noise    | 3.52 m | 5.09 m          | 5.78m           |:::                                                               |
^ Runner KALMAN no noise  | 3.51 m | 5.07 m          | 5.78 m          |:::                                                               |

==== Table 1.A ====

In the videos {{:postuloca:mio_25sen_1p_2sec.avi|scenario_c40}}, {{:postuloca:pat1_33sen_1p_2sec.avi|scenario_pat_1}} and {{:postuloca:pat2_28sen_1p_1sec.avi|scenario_pat_2}} the performance of the radio tomographic algoritm are shown. In the videos the magenta tag "X" is the position of the target, the white tag "o" is the estimed position by VRTI and the cyan tag "[]" is the estimed position by Kalman filter. The 'colored area' in the video shows how the VRTI changes in the time, when the target move along the path.

^ SCENARIO               ^ RMSE    ^ Percentile (75°) ^ Percentile (90°) ^                                                                ^
^ C_40 VRTI              | 1.595 m | 1.946 m          | 2.668  m         |Area 6.4 m X 4.5 m, 25 sensors, Data Collection on 1 Radio Channel|
^ C_40 KALMAN            | 1.588 m | 1.933 m          | 2.624  m         |:::                                                               |
^ C_40 VRTI no noise     | 2.548 m | 3.278 m          | 3.776  m         |:::                                                               |
^ C_40 KALMAN no noise   | 2.545 m | 3.275 m          | 3.772  m         |:::                                                               |
^ PAT_1 VRTI             | 0.615 m | 0.683 m          | 1.04 m           |Area 8.4 m X 6.5 m, 33 sensors, Data Collection on 5 Radio Channel|     
^ PAT_1 KALMAN           | 0.623 m | 0.675 m          | 1.02 m           |:::                                                               |
^ PAT_1 VRTI no noise    | 1.641 m | 1.809 m          | 2.232 m           |:::                                                              |                                                              
^ PAT_1 KALMAN no noise  | 1.625 m | 1.803 m          | 2.226 m           |:::                                                               |
^ PAT_2 VRTI             | 1.259 m | 1.554 m          | 1.998m           |Area 6.5 m X 4.5 m, 28 sensors, Data Collection on 1 Radio Channel    |
^ PAT_2 KALMAN           | 1.258 m | 1.550 m          | 1.974 m          |:::                                                               |
^ PAT_2 VRTI no noise    | 1.673 m | 1.846 m          | 2.531m           |:::                                                               |
^ PAT_2 KALMAN no noise  | 1.662 m | 1.826 m          | 2.534 m          |:::                                                               |
^ Runner VRTI             | 3.06 m | 4.24 m          | 5.60 m           |Area 6.5 m X 4.5 m, 28 sensors, Data Collection on 1 Radio Channel    |
^ Runner KALMAN           | 3.05 m | 4.23 m          | 5.59 m          |:::                                                               |
^ Runner VRTI no noise    | 3.52 m | 5.09 m          | 5.78m           |:::                                                               |
^ Runner KALMAN no noise  | 3.51 m | 5.07 m          | 5.78 m          |:::                                                               |

The values shown in the tables TAB.1.B suggest that the number of channels as well as the "quality of channel" used are fundamental for the performance of the 
algorithm. In fact, specially by the percentile values wew can obvserve that the multi-channel measure is more efficient than single-channel, and the measures with no AP's interference are more efficient that one with AP's interference. So we can assert that the Tomographic approach is not so resilient to the interference.
Hence, the choice of the channel can compromize the localizzation estimation. 

==== Table 1.B ====


^ SCENARIO               ^ RMSE    ^ Percentile (75°) ^ Percentile (90°) ^                                                                   ^
^ c14_s20_diag           | 0.69  m | 0.89   m         | 1   m            |Area 3.6 m X 4.8 m, 20 sensors, Data Collection on 1 Radio Channel|
^ c14_s20_diag_noap      | 0.69  m | 0.85  m          | 0.94   m         |:::                                                               |
^ c17_s20_diag           | 0.74 m  | 0.87  m          | 1  m             |:::                                                               |
^ c17_s20_diag_noap      | 0.92  m | 1  m             | 1.17   m          |:::                                                               |
^ c21_s20_diag           | 1.3  m  | 1.53 m           | 1.67 m           |:::                                                               |     
^ c21_s20_diag_noap      | 0.53  m | 0.61  m          | 0.67 m           |:::                                                               |
^ c24_s20_diag           | 1.22  m | 1.34 m           | 1.62 m           |:::                                                               |     
^ c24_s20_diag_noap      | 0.65 m  | 0.85  m          | 0.98 m           |:::                                                               |
^ c17-25_s20_diag_       | 0.53  m | 0.65 m           | 0.79 m           |Area 3.6 m X 4.8 m, 20 sensors, Data Collection on 2 Radio Channel|     
^ c17-25_s20_diag_noap   | 0.56 m  | 0.72 m           | 0.86 m           |:::                                                               |
^ m12-16-20-24_diag_noap | 0.44  m | 0.53 m           | 0.61 m           |Area 3.6 m X 4.8 m, 20 sensors, Data Collection on 4 Radio Channel|     


===== Characterization of excess path length =====


The figures below show how the excess path length values (named lambda) affect the localization estimation. The figures show the results for both values RMSE and 75-th Percentile estimation over the excess path length. The results show that lambda value, for which we have the minimum of the estimation, does not change significantly for given scenario and for different channels used for the RSSI acquisition. Notable change in the value of labda arise in the case of RSSI acquisition over four channels. 

^ SCENARIO          ^ Min RMSE^ Min Prc (75°)    ^ Figure^ 
^ c14_s20           | 0.95  m | 1.15   m        |{{:postuloca:excess_path_length_characterization_c14.png?200|}}|
^ c17_s20           | 1.05  m | 1.1  m          |{{:postuloca:excess_path_length_characterization_c17.png?200|}}|
^ c21_s20           | 1.2  m  | 1.9 m           |{{:postuloca:excess_path_length_characterization_c21.png?200|}}| 
^ c24_s20           | 1.3  m  | 1.55 m          |{{:postuloca:excess_path_length_characterization_c24.png?200|}}|    
^ m17-25_s20        | 1.6     | 1.55            |{{:postuloca:excess_path_length_characterization_m17-25.png?200|}}|
^ m12-16-20-24      | 0.85  m | 0.1 m           |{{:postuloca:excess_path_length_characterization_m12-16-20-24.png?200|}}|

===== Bayesian approach ===== 

The results in TAB.2 are drawn from [[postuloca:bayesian]] show that the accurancy of the measures (number of channels, samples per second collected, quantization level) is instrumental for the accurancy of the localizzation estimation.
Moreover, also the a-priori information is fundamental for the estimation error, in fact, the error falls into the parameters shown below because the motion of the target is known a-priori.
In fact the results about the scenario C_40 show in the the first row show the results assuming that also the cells in the middle in the room, where the sensors are placed, can be crossed. The results in the the second row show the results about the scenario where we assume that the cells can not be crossed. Note that the advantage due to the a-priori information become much more clear looking at the error distribution figure, in the BAYESIAN APPROACH  section.

^ SCENARIO     ^ RMSE     ^ Percentile (75°) ^ Percentile (90°)    ^                                                                   ^
^ C_40         | 0.867 m  | 0.881 m          | 1.225m             | Area 6.4 m X 4.5 m, 25 sensors, Data Collection on 1 Radio Channel|
^ :::          | 0.77 m   | 0.904 m          | 1.1 m              | :::                                                               | 
^ PAT_2        | 3.88 m   | 4.7 m            | 5.8 m              | Area 6.5 m X 4.5 m, 28 sensors, Data Collection on 1 Radio Channel    |  
^ :::          | :::      |:::               | :::                | :::                                                               | 
^ Runner        | 1.62 m   | 0.47 m            | 3.55 m              | Area 6.5 m X 4.5 m, 28 sensors, Data Collection on 1 Radio Channel    |  

==== Table 2 ====
 
In the videos {{:postuloca:c40_25sen_1p_1sec.avi|}}, {{:postuloca:pat_2_28sen_1p_1sec.avi|}} the performance of the bayesian algoritm is shown. In the videos the magenta tag "X" is the position of the target, the white tag "o" is the estimed position . The 'colored area' in the video shows the probability distribution of the target cross the cell in the time, when the target move along the path.

====IPIN 2013 SIMULATIONS ====

^ SCENARIO                     ^ Comparison^    Simulation Set-Up                                                               ^
^ comparison_ch14_mo2mu        |{{:postuloca:comparison_ch14_mo2mu.png?200|}}|Area 3.6 m X 4.8 m, 20 sensors, Data Collection on 1 Radio Channel \\ Data elaboration on 4 Radio Channels, variance sampling window 3 and 5 seconds |
^ comparison_ch17_mo2mu        |{{:postuloca:comparison_ch17_mo2mu.png?200|}}|:::                                                               |
^ comparison_ch21_mo2mu        |{{:postuloca:comparison_ch21_mo2mu.png?200|}}|:::                                                               |
^ comparison_ch24_mo2mu        |{{:postuloca:comparison_ch24_mo2mu.png?200|}}|:::                                                               |
^ comparison_m12-16-20-24_mu2mo|{{:postuloca:comparison_m12-16-20-24_mu2mo.png?200|}}|Area 3.6 m X 4.8 m, 20 sensors, Data Collection on 4 Radio Channel \\ Data elaboration on 1 Radio Channel, variance sampling window 3 and 5 seconds|     
^ comparison_m17-25_mu2mo      |{{:postuloca:comparison_m17-25_mu2mo.png?200|}}|Area 3.6 m X 4.8 m, 20 sensors, Data Collection on 2 Radio Channel \\ Data elaboration on 1 Radio Channel, variance sampling window 3 and 5 seconds|
^ comparison_mono_multi       |{{:postuloca:comparison_mono_multi.png?200|}}|Area 3.6 m X 4.8 m, 20 sensors, Data Collection on 1,2 and 4 Radio Channel \\ Data elaboration on 1, 2 and 4 Radio Channel, respectively, variance sampling window 3, 5 and 10 seconds| 
^ comparison mono-channel to multi-channel, with mono-channel filtered out from multi-channel|{{:postuloca:comparison_ch12_filtered.png?200|}}|Area 3.6 m X 4.8 m, 20 sensors, Data Collection on 4 Radio Channel (12,16,20,24) \\ Data elaboration on 1 Radio Channel filtered out from multi-channel, variance sampling window 3 and 5 seconds|  
^ :::|{{:postuloca:comparison_ch16_filtered.png?200|}}|:::|
^ :::|{{:postuloca:comparison_ch20_filtered.png?200|}}|:::|
^ :::|{{:postuloca:comparison_ch24_filtered.png?200|}}|:::|
^ comparison mono-channel to multi-channel, with mono-channel filtered out from multi-channel|{{:postuloca:comparison_ch17_filtered.png?200|}}|Area 3.6 m X 4.8 m, 20 sensors, Data Collection on 2 Radio Channel (17,25) \\ Data elaboration on 1 Radio Channel filtered out from multi-channel, variance sampling window 3 and 5 seconds|  
^ :::|{{:postuloca:comparison_ch25_filtered.png?200|}}|:::|