Abstract:
A method of identifying a position of a user equipment within a wireless communication network includes: a) providing expected radio signal strengths produced by at least one radio communication station on each of plural elementary area elements in which a geographic area is subdivided; b) defining an initial attenuation experienced by the radio signals to the user equipment whose position is to be identified; c) obtaining measured radio signal strength measurements of the radio signals provided to the user equipment whose position is to be identified; d) determining an estimated elementary area element corresponding to the position of the user equipment whose position is to be identified based on the expected radio signal strengths, the initial attenuation and the radio signal strength measurements, and e) computing a final attenuation based on the estimated elementary area element. The operations b)-e) are iterated at least twice.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    Field of the Invention 
         [0002]    The present invention refers to communication systems. More particularly, the present invention relates to the field of wireless or mobile telecommunication networks. Even more particularly, the present invention relates to a positioning method and system for identifying a position of mobile communication devices (e.g., mobile telephones, smartphones and tablets)—generally referred to as User Equipment, or UE in brief—in a wireless communication network. 
         [0003]    Overview of the Related Art 
         [0004]    In the art, a common approach for estimating UE position within an area covered by the wireless communication network is based on a matching between Radio Frequency (RF) signals strength maps (e.g., a database comprising expected RF signal strengths each associated with a respective portion or pixel of a geographic area of interest—coverage area—of the wireless communication network) and the signal strength measurements that are generally performed by UE to be located during their operation. This positioning technology is often referred to as “RF fingerprint positioning”, because the expected RF signal strengths in an area of interest are also referred to as “RF fingerprints”. 
         [0005]    For example in the case the wireless communication network is a mobile telephony network, RF signal strength measurements are periodically sent by UE to the wireless communication network for call management by the wireless communication network. Such RF signal strength measurements may be used for locating and tracking the UE that sent them to the wireless communication network. RF signal strength measurements may also be requested by the wireless communication network to the UE even when no radio link (i.e., an active connection for performing communication) between the UE and the wireless communication network is set up. 
         [0006]    RF signals strength maps are provided by means of radio signal propagation simulation tools and are generally generated and used for the planning/deployment of the wireless communication network. Such kind of radio signal propagation simulation tools are based on Radio Access Network (RAN) configuration information, including positions of radio communication stations and parameters of their antennas (which radio communication stations manages communication over respective portions of the coverage area of the wireless communication network). Furthermore, the radio signal propagation simulation tools may take into account ground morphology information (i.e., building profiles, ground profile, areas with dense forests etc.). A RF signals strength map provides one or more expected RF signal strengths for each pixel of the coverage area, particularly the expected strengths perceivable in such pixel of the RF signals by some radio communication stations located in the neighborhood of such pixel. 
         [0007]    The quality of RF fingerprints estimated with radio signal propagation simulation tools may also be improved by on-site measurements (e.g., collected by means of a field measurement campaign performed on the whole coverage area by means of radio signal strength detectors) allowing an on-field tuning of the RF signals strength maps. 
         [0008]    Several positioning methods based on RF fingerprint have been proposed in the art for locating UE inside the coverage area of the wireless communication network. 
         [0009]    For example, Laitinen H., Lahteenmaki J , Nordstrom T., “Database correlation method for GSM location”, Vehicular Technology Conference, 2001, VTC 2001 Spring, IEEE VTS 53rd, discloses a set of algorithms that can be used for locating UE in a wireless communication network. 
         [0010]    D. Zimmermann, J. Baumann, M. Layh, F. Landstorfer, “Database Correlation for Positioning of Mobile Terminals in Cellular Networks using Wave Propagation Models”, Vehicular Technology Conference, VTC 2004 Fall, discloses an algorithm for the estimation of the position of UE with RF fingerprint approach. The document does not address the problem of locating a UE indoor or inside vehicles. 
         [0011]    U.S. Pat. No. 7,725,111 discloses a method for determining the location of a mobile unit in a wireless communication system and presenting it to a remote party. The location of a remote mobile unit is determined by comparing a snapshot of a predefined portion of the radio-frequency spectrum taken by the mobile unit to a reference database containing multiple snapshots taken at various locations. The result of the comparison is used to determine if the mobile unit is at a specific location. The comparison may be made in the mobile unit, or at some other location situated remotely from the mobile unit. In the latter case, sufficient information regarding the captured fingerprint is transmitted from the mobile unit to the remote location. The database may be pre-compiled or generated on-line. 
         [0012]    Jian Zhu and Gregory D. Durgin, “Indoor/Outdoor Location of Cellular Handsets Based on Received Signal Strength”, IEE Electronics Letters, 6 Jan. 2005, and Jian Zhu, School of Electrical and Computer Engineering Georgia Institute of Technology PhD thesis Indoor/Outdoor Location of Cellular Handsets Based on Received Signal Strength, (available, at the date of filing of the present application, at http://www.propagation.gatech.edu/Archive/PG_TR_060515_JZ/PG_TR_060515_JZ.pdf) describe a method to handle an attenuation associated with a position of the UE with single set of measurement or a sequence of signal strength measurements. 
       SUMMARY OF THE INVENTION 
       [0013]    The Applicant has found that the known solutions mentioned above fail in providing a satisfactory positioning and tracking system capable of considering an estimation of signal losses due to obstacles that cannot be included in models used by radio signal propagation simulation tools for generating the RF signals strength map. As a result, RF signal strength maps calculated by radio signal propagation simulation tools substantially may provide accurate RF signal strengths referred to an outdoor environment of the coverage area, while an (actual) measured radio signal strength through signal strength measurements performed by the UE may be affected by attenuations caused by additional obstacles such as bodies of vehicles (i.e., when the UE is within a vehicle), walls of building (when the UE is within a building, whose walls losses are not known), or the elevation of the position of the user handling the UE inside a building with respect to the ground level (which in a first approximation may cause an increase of the signal strength). The field measurement campaigns mentioned above are not able to provide useful data regarding the attenuation introduced by such obstacles like vehicles or wall of buildings for an indoor environment within the coverage area. 
         [0014]    Therefore, the Applicant has coped with the problem of devising a UE positioning and tracking method and system able to take into account signal strength attenuations (such as attenuations due to vehicles and buildings) not considered in signal strength prediction or measurement, thus allowing to identify with an improved accuracy UE positions. 
         [0015]    The Applicant has found that, in order to take into account signal strength attenuations (such as attenuations due to vehicles and buildings) not considered in signal strength prediction or measurement, it is useful to identify an uncertainty area around an estimated UE position, and calculate an average expected signal strength in respect of the uncertainty area (e.g., an average of the expected signal strengths for neighboring pixels around the pixel corresponding to the estimated UE position). Such average of the expected signal strengths for neighboring pixels around the pixel corresponding to the estimated UE position can be used to refine the estimation of the signal strength attenuation. 
         [0016]    Particularly, one aspect of the present invention proposes a method of identifying a position of a user equipment within a wireless communication network comprising at least one radio communication station transmitting radio signals over a geographic area. The method comprising the following steps: a) providing expected radio signal strengths produced by the at least one radio communication station on each of a plurality of elementary area elements in which the geographic area is subdivided; b) defining an initial attenuation experienced by the radio signals provided by the at least one radio communication station to the user equipment whose position is to be identified; c) obtaining measured radio signal strength measurements of the radio signals provided to the user equipment whose position is to be identified; d) determining an estimated elementary area element corresponding to the position of the user equipment whose position is to be identified on the basis of said expected radio signal strengths, said initial attenuation and said radio signal strength measurements, and e) computing a final attenuation on the basis of said estimated elementary area element. The steps b)-e) are iterated at least twice, with each further iteration of the step b) which comprises defining the respective initial attenuation for said each further iteration on the basis of at least one final attenuation previously computed in step e) of at least one previous iteration. 
         [0017]    Preferred features of the present invention are set forth in the dependent claims. 
         [0018]    In an embodiment of the present invention, a second iteration of the step b) comprises defining as the initial attenuation the final attenuation computed during the first iteration of step e). 
         [0019]    In an embodiment of the present invention, each further iteration of the step b) comprises defining as initial attenuation an average of the final attenuations previously computed. 
         [0020]    In an embodiment of the present invention, each further iteration of the step b) comprises defining as initial attenuation an average of at least part of the final attenuations previously computed. 
         [0021]    In an embodiment of the present invention, said average is a weighted average. 
         [0022]    In an embodiment of the present invention, said weighted average comprises weights based on an exponential decreasing function. 
         [0023]    In an embodiment of the present invention, the step d) comprises determining the estimated elementary area element on the basis of a probability distribution of the position of the user equipment in the plurality of elementary area elements in which the geographic area is subdivided. 
         [0024]    In an embodiment of the present invention, the step d) comprises determining a standard deviation of said probability distribution and the method further comprises the step of f) defining an uncertainty area centered on the estimated elementary area element and having a radius substantially corresponding to said standard deviation. 
         [0025]    In an embodiment of the present invention, the step d) comprises determining the estimated elementary area element as a maximum of said probability distribution. 
         [0026]    In an embodiment of the present invention, the step d) comprises determining the estimated elementary area element as a center of mass of an uncertainty area computed during a previous iteration of steps b)-e) or an initial search space in a first iteration of steps b)-e). 
         [0027]    In an embodiment of the present invention, said probability distribution is based on a set of probabilities that the user equipment is within each one of the plurality of elementary area elements in which the geographic area is subdivided, the set of probabilities comprising a probability in respect of each radio communication station of the at least one radio communication station. 
         [0028]    In an embodiment of the present invention, each probability of the set of probabilities is computed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     p 
                      
                     
                       ( 
                       
                         x 
                         
                           i 
                           , 
                           j 
                         
                       
                       ) 
                     
                   
                    
                 
                 
                   a 
                   - 
                   h 
                 
               
               = 
               
                 
                   1 
                   
                     
                       
                         2 
                          
                         
                             
                         
                          
                         π 
                          
                         
                           
                             σ 
                             
                               i 
                               , 
                               j 
                             
                           
                         
                       
                        
                     
                     
                       a 
                       - 
                       h 
                     
                   
                 
                 × 
                 
                   e 
                   
                     - 
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         m 
                                          
                                         
                                             
                                         
                                          
                                         s 
                                       
                                        
                                     
                                     
                                       a 
                                       - 
                                       h 
                                     
                                   
                                   - 
                                   
                                     es 
                                     
                                       i 
                                       , 
                                       j 
                                     
                                   
                                 
                                  
                               
                               
                                 a 
                                 - 
                                 h 
                               
                             
                             - 
                             
                               μ 
                               ni 
                             
                           
                           ) 
                         
                         2 
                       
                       
                         
                           
                             2 
                              
                             
                                 
                             
                              
                             
                               σ 
                               
                                 i 
                                 , 
                                 j 
                               
                             
                           
                            
                         
                         
                           a 
                           - 
                           h 
                         
                         2 
                       
                     
                   
                 
               
             
             , 
           
         
       
     
         [0029]    wherein es i,j\a-h  is the expected radio signal strength in the respective one of the elementary area elements of the plurality of elementary area elements, σ i,j\a-h  is the standard deviation of a statistical error associated with said expected radio signal strength in the respective one of the plurality of elementary area elements, ms \a-h  is the measured radio signal strength measurement and μ ni  initial attenuation of the n-th iteration. 
         [0030]    In an embodiment of the present invention, each probability of the set of probabilities is normalized into a corresponding normalized probability before being used as a basis for said probability distribution. 
         [0031]    In an embodiment of the present invention, said probability distribution is defined by a set of total probabilities each of which is computed as a product of the normalized probabilities associated with a same elementary area element of the plurality of elementary area elements. 
         [0032]    In an embodiment of the present invention, the method further comprises the step of g) computing average expected radio signal strengths as an average of the expected radio signal strengths of each elementary area element comprised in the uncertainty area, and wherein the step e) comprises computing the final attenuation as an average of the differences between the average expected radio signal strengths and the measured radio signal strengths. 
         [0033]    Another aspect of the present invention proposes a wireless communication network comprising a plurality of radio communication stations transmitting radio signals over a geographic area adapted to implement the method of above. 
         [0034]    In an embodiment of the present invention, the wireless communication network is a mobile telephony network. 
         [0035]    In an embodiment of the present invention, the wireless communication network is a Global Navigation Satellite System network. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0036]    These and others features and advantages of the solution according to the present invention will be better understood by reading the following detailed description of an embodiment thereof, provided merely by way of non-limitative example, to be read in conjunction with the attached drawings, wherein: 
           [0037]      FIG. 1  is a schematic view of a portion of a wireless communication network in which a solution according to an embodiment of the present invention can be implemented; 
           [0038]      FIGS. 2A-2C  is a schematic flowchart of a positioning and tracking method according to an embodiment of the present invention, and 
           [0039]      FIGS. 3A-3C  are schematic views of search spaces showing an uncertainty area in which the user equipment to be positioned is located according to an embodiment of the present invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0040]    With reference to the drawings,  FIG. 1  is a schematic view of a portion of a wireless communication network in which an embodiment of the present invention can be implemented. 
         [0041]    A generic wireless communication network  100  allows and manages communications over a coverage area (not shown) of user equipments or UE (e.g., mobile telephones, smartphones and tablets). Such a (geographic) coverage area is generally subdivided in a plurality of portions, such as the cell  105  in which communication is managed by a radio communication station. For example, in a wireless communication network  100  for mobile telephony, one or more radio transceivers (not shown) of a radio communication station  110   a , such as an evolved Node B, or eNodeB in 3GPP Long Term Evolution (LTE)/LTE Advanced (LTE-A) systems, manage communications (i.e., transmission and/or reception of information, such as binary data packets) of the UE within the radio communication station coverage area or cell  105 . A plurality of neighboring radio communication stations  110   b - h  (of which only seven are shown in the example of  FIG. 1 ) manage the communication within respective cells (not shown) which are neighbor of the cell  105 . 
         [0042]    The coverage area is ideally subdivided into relatively small, elementary area elements or pixels x i,j  (where 1≦i≦l and 1≦j≦J, with l and J positive integer numbers), each pixel being an elementary, unit (in the shown example, the pixel are squares in shape) area of predefined width, e.g. 1″ of latitude by 1″ of longitude (even though different pixels not necessarily have the same size or shape). Therefore each cell, such as the cell  105 , of the wireless communication network  100  is subdivided into a plurality of pixels x i,j . 
         [0043]    The levels of the electromagnetic field, i.e. the expected signal strengths es i,j\a-h , produced by the radio communication stations  110   a - h  on the generic pixel x i,j  are measured or calculated, e.g. by means of known radio signal propagation simulation tools or through an estimation taking into account the path loss model in each pixel and radio communication parameters (i.e. emitted power, antenna gain, antenna position) of the radio communication stations, and they are compared one another. Each pixel x i,j  is then associated with the respective radio communication station  110   a - h  which, compared to all the other radio communication stations  110   a - h , produces in the pixel x i,j  the best expected signal strengths es i,j\a-h . The set of pixels x i,j  associated with a same radio communication station, such as the radio communication station  110   a , define the cell, such as the cell  105 , of the respective radio communication station. 
         [0044]    At the same time, the expected signal strengths es i,j\a-h  measured or calculated by the radio signal propagation simulation tools or based on the above cited path loss estimation generate a RF signals strength map, which is a database that, for each pixel x i,j , comprises the expected signal strengths es i,j\a-h  related to the radio communication stations  110   a - h  of the wireless communication network  100 . The RF signals strength map, for each expected signal strength es i,j\a-h , further comprises an indication of a statistical error, such as a standard deviation σ i,j\a-h  that affects such expected signal strength es i,j\a-h . 
         [0045]    It should be noted that the RF signals strength map of the wireless communication network  100  may have been already generated during a network planning phase of the wireless communication network  100  and therefore such a RF signals strength map may be used for positioning and tracking purposes, without the need of generating a new RF signals strength map. 
         [0046]    In addition, the wireless communication network  100  has a certain positioning capability, i.e. the wireless communication network  100  may provide a rough estimation of the position, within its coverage area, of UE (not shown). 
         [0047]    For example, by considering the case in which the wireless communication network  100  is a mobile telephony network, the wireless communication network  100  knows in which cell, e.g. the cell  105 , the UE is located, since the wireless communication network  100  is aware of the radio communication station, e.g. the radio communication station  110   a , associated with (i.e., serving) such UE. Furthermore, the wireless communication network may identify in which portion of cell or sector of the cell  105  the UE is located by identifying with which radio transceivers of the radio communication station  110   a  the UE is associated. 
         [0048]    In addition, the wireless communication network  100  may identify a distance between the UE and the radio communication station  110   a  by means of a timing advance value corresponding to the length of time a signal takes to reach the communication station from the UE. Therefore, the wireless communication network may identify a portion of the sector of the cell  105  in which the UE is located. Such sector portion can be used as an initial search space  120  for accurately locating the UE in a method according to an embodiment of the present invention. 
         [0049]    Turning now to  FIGS. 2A-2C , they are a schematic flowchart of a positioning method according to an embodiment of the present invention. 
         [0050]    Initially, a initialization phase comprising a first and a second UE position estimation cycles is performed. 
         [0051]    The first UE position estimation cycle determines a first UE estimated position of a UE inside the search space  120 . A first initial attenuation value, or simply first initial attenuation μ 1i , is assigned to each pixel x i,j  of the search space  120  (step  202 ) for taking into account a probable signal attenuation experienced by signals transmitted by the serving radio communication station taking into account losses not considered in the expected signal strengths for each pixel in the RF signals strength map. 
         [0052]    In an embodiment of the invention, the first initial attenuation μ 1i  is a constant value comprised in a predetermined range of values, for example the first initial attenuation μ 1i  is comprised between 0 dB and 10 dB, such as for example μ 1i =5 dB. 
         [0053]    In another embodiment of the invention, the first initial attenuation μ 1i  is a constant value selected from a table of attenuation values that lists a plurality of attenuation values for not modeled obstacle(s) (for example, 8 dB if an in-vehicle scenario should be considered). 
         [0054]    Then (step  204 ), measured RF signal strengths ms \a-h  measured by the UE with respect to each one of the radio communication stations  110   a - h  (which provide a signal strength above a minimum threshold) are obtained. Such measured RF signal strengths ms \a-h  are periodically sent by UE to the wireless communication network  100  for call management and, moreover, the measurements may also be requested by the wireless communication network  100  to the UE even when no radio link is set up (i.e., an active connection for performing communication). 
         [0055]    Afterwards (step  206 ), a set of probabilities that the UE is within the generic pixel x i,j  of the search space  120  is determined for each pixel of the search space  120 . The set of probabilities preferably comprises a probability p(x i,j )\ a-h  in respect of each radio communication station  110   a - h  (eight in the example of  FIG. 1 ) for which a respective expected signal strength es i,j\a-h  is comprised in the RF signals strength map. 
         [0056]    In an embodiment of the invention, for each pixel x i,j  of the search space  120  a plurality of (eight in the considered example) respective probabilities p(x i,j )l a-h  can be computed (one for each of the—eight in the considered example—radio communication stations  110   a - h ) according to the following formula: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           p 
                            
                           
                             ( 
                             
                               x 
                               
                                 i 
                                 , 
                                 j 
                               
                             
                             ) 
                           
                         
                          
                       
                       
                         a 
                         - 
                         h 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               2 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                 
                                   σ 
                                   
                                     i 
                                     , 
                                     j 
                                   
                                 
                               
                             
                              
                           
                           
                             a 
                             - 
                             h 
                           
                         
                       
                       × 
                       
                         e 
                         
                           - 
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             ( 
                                             
                                               m 
                                                
                                               
                                                   
                                               
                                                
                                               s 
                                             
                                              
                                           
                                           
                                             a 
                                             - 
                                             h 
                                           
                                         
                                         - 
                                         
                                           es 
                                           
                                             i 
                                             , 
                                             j 
                                           
                                         
                                       
                                        
                                     
                                     
                                       a 
                                       - 
                                       h 
                                     
                                   
                                   - 
                                   
                                     μ 
                                     
                                       1 
                                        
                                       i 
                                     
                                   
                                 
                                 ) 
                               
                               2 
                             
                             
                               
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   
                                     σ 
                                     
                                       i 
                                       , 
                                       j 
                                     
                                   
                                 
                                  
                               
                               
                                 a 
                                 - 
                                 h 
                               
                               2 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    wherein σ i,j\a-h  is the standard deviation of the statistical error that affects such expected signal strength es i,j\a-h  associated with the pixel x i,j  of the search space  120 . 
         [0057]    Preferably, albeit not strictly necessarily, normalized probabilities p norm (x i,j )\ a-h  are used in the subsequent calculations, where the normalized probabilities p norm (x i,j )\ a-h  are calculated as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             p 
                             norm 
                           
                            
                           
                             ( 
                             
                               x 
                               
                                 i 
                                 , 
                                 j 
                               
                             
                             ) 
                           
                         
                          
                       
                       
                         a 
                         - 
                         h 
                       
                     
                     = 
                     
                       
                         
                           
                             
                               p 
                                
                               
                                 ( 
                                 
                                   x 
                                   
                                     i 
                                     , 
                                     j 
                                   
                                 
                                 ) 
                               
                             
                              
                           
                           
                             a 
                             - 
                             h 
                           
                         
                         
                           
                             
                               
                                 ∑ 
                                 
                                   x 
                                   
                                     i 
                                     , 
                                     j 
                                   
                                 
                               
                                
                               
                                 p 
                                  
                                 
                                   ( 
                                   
                                     x 
                                     
                                       i 
                                       , 
                                       j 
                                     
                                   
                                   ) 
                                 
                               
                             
                              
                           
                           
                             a 
                             - 
                             h 
                           
                         
                       
                       = 
                       
                         
                           
                             1 
                             
                               
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                    
                                   
                                     
                                       σ 
                                       
                                         i 
                                         , 
                                         j 
                                       
                                     
                                   
                                 
                                  
                               
                               
                                 a 
                                 - 
                                 h 
                               
                             
                           
                           × 
                           
                             e 
                             
                               - 
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 ( 
                                                 
                                                   m 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   s 
                                                 
                                                  
                                               
                                               
                                                 a 
                                                 - 
                                                 h 
                                               
                                             
                                             - 
                                             
                                               es 
                                               
                                                 i 
                                                 , 
                                                 j 
                                               
                                             
                                           
                                            
                                         
                                         
                                           a 
                                           - 
                                           h 
                                         
                                       
                                       - 
                                       
                                         μ 
                                         
                                           1 
                                            
                                           i 
                                         
                                       
                                     
                                     ) 
                                   
                                   2 
                                 
                                 
                                   
                                     
                                       2 
                                        
                                       
                                           
                                       
                                        
                                       
                                         σ 
                                         
                                           i 
                                           , 
                                           j 
                                         
                                       
                                     
                                      
                                   
                                   
                                     a 
                                     - 
                                     h 
                                   
                                   2 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 ∑ 
                                 
                                   x 
                                   
                                     i 
                                     , 
                                     j 
                                   
                                 
                               
                                
                               
                                 p 
                                  
                                 
                                   ( 
                                   
                                     x 
                                     
                                       i 
                                       , 
                                       j 
                                     
                                   
                                   ) 
                                 
                               
                             
                              
                           
                           
                             a 
                             - 
                             h 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    whereby: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           ∑ 
                           
                             x 
                             
                               i 
                               , 
                               j 
                             
                           
                         
                          
                         
                           
                             p 
                             norm 
                           
                            
                           
                             ( 
                             
                               x 
                               
                                 i 
                                 , 
                                 j 
                               
                             
                             ) 
                           
                         
                       
                        
                     
                     
                       a 
                       - 
                       h 
                     
                   
                   = 
                   1. 
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0058]    For each pixel x i,j  of the search space  120  the (eight in the considered example) calculated (normalized) probabilities p norm (x i,j )\ a-h  are then combined (step  208 ) in such a way to obtain a total probability p(x i,j )\ tot  that the UE is located within that pixel x i,j . In an embodiment of the invention, since the radio signal propagation behavior (radio signal attenuation) of each radio signal is independent from the others, the total probability p(x i,j )\ tot  for the pixel x i,j  can for example be computed as a product of the (eight in the considered example) probabilities p norm (x i,j )\ a-h ,i.e.: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               p 
                                
                               
                                 ( 
                                 
                                   x 
                                   
                                     i 
                                     , 
                                     j 
                                   
                                 
                                 ) 
                               
                             
                              
                           
                           tot 
                         
                         = 
                         
                           
                             ∏ 
                             
                               k 
                               = 
                               a 
                             
                             h 
                           
                            
                           
                             
                               p 
                               norm 
                             
                              
                             
                               ( 
                               
                                 x 
                                 
                                   i 
                                   , 
                                   j 
                                 
                               
                               ) 
                             
                           
                         
                       
                        
                     
                     k 
                   
                   . 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0059]    This is not the case when common residual attenuations are based on the same measurements. 
         [0060]    It should be noted that the total probabilities p(x i,j )\ tot  of all the pixels x i,j  of the search space  120  define a first position probability distribution d 1 (x i,j ) of the (possible) position of the UE in the search space  120  that has generally a Gaussian shape. 
         [0061]    By using the total probabilities p(x i,j )\ tot  calculated for all the pixels x i,j  of the search space  120 , a first location pixel x i,j\1  is identified (step  210 ). In an embodiment of the present invention, a first center of mass, or first centroid C 1d , of the search space  120  is determined based on the total probabilities p(x i,j )\ tot  calculated for all the pixels x i,j  of the search space  120 , that is on the basis of the first position probability distribution d 1 (x i,j ), and such a centroid is selected as the first location pixel x i,j\1 . 
         [0062]    Next (step  212 ), a first uncertainty area  305  is defined. As shown in  FIG. 3A , which is a schematic view of the search space  120  showing the first uncertainty area  305  in which the UE whose position is to be determined is located according to an embodiment of the present invention, the first uncertainty area  305  is defined as a circular area of the search space  120  centered on the first location pixel x i,j\1 , i.e. the first centroid C 1d . A radius of the first uncertainty area  305  is defined as substantially corresponding to a first standard deviation Σ 1d  of the first position probability distribution d 1 (x i,j ) computed centered in the first location pixel x i,j\1 , i.e. the first centroid C 1d . 
         [0063]    In an alternative embodiment of the invention, the generic pixel x i,j  of the search space  120  being associated with a first maximum M 1d  of the first position probability distribution d 1 (x i,j ) is selected as the first location pixel x i,j\1 , and the radius of the first uncertainty area  305  is defined as the first standard deviation Σ 1d  of the first position probability distribution d 1 (x i,j ) computed centered at the first location pixel x i,j\1 , i.e. the first maximum M 1d . 
         [0064]    In order to refine the estimation of the UE position, a first final attenuation μ 1f  is computed at the end of the first position estimation cycle (steps  214  and  216 ). Since the estimation of the UE position is affected by an error, the calculation of the expected signal strength should take into account an average expected signal strength estimated over the uncertainty area, by using a plurality of pixels around the estimated position. Thus, firstly (step  214 ) average expected signal strengths  ES   \a-h  are calculated for the whole uncertainty area  305 , i.e.: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ES 
                         
                           
                              
                             a 
                           
                           - 
                           h 
                         
                       
                       _ 
                     
                     = 
                     
                       
                         
                           ∑ 
                           
                             i 
                             , 
                             
                               j 
                               = 
                               1 
                             
                           
                           
                             Iu 
                             , 
                             Ju 
                           
                         
                          
                         
                           es 
                           
                             
                               
                                 
                                   i 
                                   , 
                                   j 
                                 
                                  
                               
                                
                               a 
                             
                             - 
                             h 
                           
                         
                       
                       
                         # 
                          
                         
                             
                         
                          
                         pixels 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where 1≦i≦Iu and 1≦j≦Ju (with Iu≦I and Ju≦J) indicate the coordinates of pixels x i,j  comprised within the uncertainty area  305 , and #pixels indicates the number of pixel x i,j  comprised within the first uncertainty area  305 . 
         [0065]    Then (step  216 ), the first final attenuation μ 1f  is computed as the average of the (eight, in the considered example) differences between the average expected signal strengths  ES   \a-h  and the (eight, in the considered example) measured signal strengths ms \a-h , i.e.: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       μ 
                       
                         1 
                          
                         
                             
                         
                          
                         f 
                       
                     
                     = 
                     
                       
                         
                           
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   a 
                                 
                                 h 
                               
                                
                               
                                 
                                   ES 
                                   
                                      
                                     k 
                                   
                                 
                                 _ 
                               
                             
                             - 
                             
                               m 
                                
                               
                                   
                               
                                
                               s 
                             
                           
                            
                         
                         k 
                       
                       
                         # 
                          
                         
                             
                         
                          
                         rcs 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where #rcs is the number (eight, in the considered example) of radio communication stations for which the UE has measured useful (i.e. above the minimum threshold) measured signal strengths ms a-h , i.e. eight radio communication station  110   a - h  in the example of  FIG. 1 . With the computation of the first final attenuation μ 1f  the first position estimation cycle ends. 
         [0066]    At the end of the first position estimation cycle the method provides a first position estimation for the UE whose position is to be identified, i.e. the first location pixel x i,j\1 , and also defines the first uncertainty area  305  that takes into account statistical errors associated with such estimation. 
         [0067]    Subsequently, the estimation of the UE position can be re-calculated by replacing the first initial attenuation μ 1i  with the first final attenuation μ 1f  resulting at the end of the first position estimation. Thus, the second position estimation cycle starts. The second position estimation cycle performs substantially the same steps as the first position estimation cycle but uses the first final attenuation μ 1f  calculated at the end of the first position estimation cycle as second initial attenuation μ 2i  (step  218 ). As in the previous cycle, measured RF signal strengths ms \a-h  are obtained (or, alternatively, the same measured RF signal strengths ms \a-h  used in the first position estimation cycle are recovered) (step  220 ) and the measured RF signal strengths are used for computing a set of probabilities that the UE is within the generic pixel x i,j  of the first uncertainty area  305  (in the considered example, eight probabilities are calculated for each pixel of the first uncertainty area  305 ) (step  222 ). The (in the considered example, eight) probabilities p(x i,j )\ a-h  calculated for the generic pixel x i,j  of the first uncertainty area  305  (possibly normalized as described above in connection with the first position estimation cycle) are then combined (step  224 ) in such a way to obtain, for that generic pixel x i,j  of the first uncertainty area  305 , a total probability p(x i,j )\ tot  that the UE is located within the generic pixel x i,j  of the first uncertainty area  305 . By using the total probabilities p(x i,j )\ tot  (or, a corresponding second position probability distribution d 2 (x i,j )) that the UE is located within the generic pixel x i,j  of the first uncertainty area  305  a second centroid C 2d , of the first uncertainty area  305  is determined, and a second location pixel x i,j\2  is identified as corresponding to the second centroid C 2d  (or, alternatively, to a second maximum M 2d  of the second position probability distribution d 2 (x i,j )) (step  226 ). 
         [0068]    Next (step  228 ), a second uncertainty area  310  is defined, as shown in  FIG. 3B , which is a schematic view of the search space  120  showing the second uncertainty area  310  in which the UE whose position is to be determined is located according to an embodiment of the present invention. Similarly to the first position estimation cycle, a radius of second uncertainty area  310  is defined as substantially corresponding to a second standard deviation Σ 2d  of the second position probability distribution d 2 (x i,j ) computed centered at the second location pixel x i,j\1 , i.e. the second centroid C 2d  (or alternatively as a second standard deviation Σ 2d  centered at the second maximum M 2d  of the second position probability distribution d 2 (x i,j )). 
         [0069]    In order to refine the position estimation, a second final attenuation μ 2f  is computed at the end of the second position estimation cycle (steps  230  and  232 ) analogously to the first position estimation cycles, i.e. average expected signal strengths  ES   \a-h  are calculated for the whole second uncertainty area  310  and the second final attenuation μ 2f  is computed as the average of the (eight, in the considered example) differences between the average expected signal strengths  ES   \a-h  and the (eight, in the considered example) measured signal strengths ms \a-h . 
         [0070]    At the end of the second position estimation cycle the method provides a second position estimation for the UE whose position is to be identified, i.e. the second location pixel x i,j\2 , and also in this case the second uncertainty area  310  (that is smaller than the first uncertainty area  305 ) takes into account statistical errors associated with such second position estimation. 
         [0071]    It should be noted that, generally, the first centroid C 1d  (or the first maximum M 1d ) used as the center of the first uncertainty area  305  and the second centroid C 2d  (or the second maximum M 2d ) used as the center of the second uncertainty area  310  do not necessarily correspond. Therefore, the first uncertainty area  305  and the second uncertainty area  310  are generally eccentric areas. 
         [0072]    With the end of the second position estimation cycle the positioning initialization phase ends and subsequent position estimation cycles are preferably performed in the following manner. 
         [0073]    Substantially, the generic n-th position estimation cycle performs the same steps of the first position estimation cycle but uses a n-th initial attenuation μ ni  based on a combination of two or more of the previously calculated final attenuations μ 1f  to μ n-1f  (step  234 ). 
         [0074]    The n-th initial attenuation μ ni  may be computed in a plurality of different manner; for example, the n-th initial attenuation μ ni  may be computed depending on whether the UE whose position is to be estimated is moving or has a substantially static position in order to obtain a better estimation of the position of the UE. 
         [0075]    In case the UE whose position is to be estimated has a substantially static position, the n-th initial attenuation μ ni  may be advantageously computed as the average of the all the previously calculated final attenuations μ 1f  to μ n-1f , i.e.: 
         [0000]    
       
         
           
             
               
                 
                   
                     μ 
                     ni 
                   
                   = 
                   
                     
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             1 
                           
                           
                             n 
                             - 
                             1 
                           
                         
                          
                         
                           μ 
                           kf 
                         
                       
                       
                         n 
                         - 
                         1 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0076]    For example, the third initial attenuation μ 3i  may be computed as the average of the first final attenuation μ 1f  and second final attenuation μ 2f , i.e.: 
         [0000]    
       
         
           
             
               
                 
                   
                     μ 
                     
                       3 
                        
                       i 
                     
                   
                   = 
                   
                     
                       
                         
                           μ 
                           
                             1 
                              
                             f 
                           
                         
                         + 
                         
                           μ 
                           
                             2 
                              
                             f 
                           
                         
                       
                       2 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0077]    Alternatively, either in case the UE is moving or has a substantially static position, the n-th initial attenuation μ ni  may be computed by averaging only a subset of the previously calculated final attenuations μ 1f  to μ n-1f , for example by calculating a moving average calculated by taking a moving “averaging window” that may be defined for computing the n-th initial attenuation μ ni  and which comprises a certain number k of previously calculated final attenuations μ n-kf  to μ n-1f . 
         [0078]    The use of a moving averaging window may be particularly advantageous in case the not modeled environment conditions introduce signal attenuations change over time (e.g., in case the UE moved from inside a building to the outdoor environment). Indeed, during UE movements in the area of coverage of the wireless communication network  100 , the not modeled attenuation affecting radio signals may vary; therefore, taking into account the whole set of attenuations already computed in the past may be misleading if a movement of the UE to be positioned is detected. 
         [0079]    In addition, the n-th initial attenuation μ ni  may be computed as a weighted average of some or more, possibly all the previously calculated final attenuations μ 1f  to μ n-1f . This is particularly advantageous in the case of a UE that is moving, i.e. in case of a UE tracking within the wireless communication network  100  during which the not modeled attenuation may vary. For example, the weights may be defined on the basis of an exponential decreasing function. 
         [0080]    In the generic n-th position estimation cycle new measured RF signal strengths ms \a-h  are obtained (or alternatively the same measured signal strengths ms \a-h  used in the previous position estimation cycle(s) are recovered) (step  236 ) and the measured RF signal strengths are used for computing a set of probabilities p(x i,j )\ a-h  that the UE is within the generic pixel x i,j  of the (n−1)-th uncertainty area  315   n-1 , as shown in as shown in  FIG. 3C , which is a schematic view of the search space  120  showing the (n−1)-th uncertainty area  315   n-1  in which the UE to be positioned is located, (in the considered example, eight probabilities are calculated for each pixel of the (n−1)-th uncertainty area  315   n-1 ) (step  238 ). The (in the considered example, eight) probabilities p(x i,j )\ a-h  calculated for the generic pixel x i,j  of the (n−1)-th uncertainty area  315   n-1  (possibly normalized as described in connection with the first position estimation cycle) are then combined (step  240 ) in such a way to obtain, for that generic pixel x i,j  of the (n−1)-th uncertainty area  315   n-1 , a total probability p(x i,j )\ tot  that the UE is located within the generic pixel x i,j . By using the total probabilities p(x i,j )\ tot  (that is, the corresponding position probability distribution d n (x i,j )) that the UE is located within the generic pixel x i,j  of the (n−1)-th uncertainty area  315   n-1 , a n-th center of mass C nd  for the n-th uncertainty area  315   n  is determined, and a n-th location pixel x i,j\n  is identified as corresponding to the n-th center of mass C nd  (or, alternatively, to the n-th maximum M nd  of the corresponding position probability distribution d n (x i,j )) (step  242 ). 
         [0081]    Next (step  244 ), a n-th uncertainty area  315   n  is defined—as shown in  FIG. 3D , which is a schematic view of the search space  120  showing the n-th uncertainty area  315   n  in which the UE whose position is to be determined is located. Similarly to the previous position estimation cycles, a radius of the n-th uncertainty area  315   n  is defined as substantially corresponding to a n-th standard deviation Σ nd  of the n-th position probability distribution d n (x i,j ) computed centered at the n-th location pixel x i,j\1 , i.e. the n-th centroid C 2d  (or alternatively as a n-th standard deviation Σ nd  centered in the n-th maximum M nd  of the n-th position probability distribution d n (x i,j )). 
         [0082]    Finally, a n-th final attenuation μ nf  is computed (steps  246  and  248 ). Similarly to the previous position estimation cycles, average expected signal strengths  ES   \a-h  are calculated (steps  246 ) for the whole n-th uncertainty area  315   n , i.e.: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ES 
                         
                           
                              
                             a 
                           
                           - 
                           h 
                         
                       
                       _ 
                     
                     = 
                     
                       
                         
                           ∑ 
                           
                             i 
                             , 
                             
                               j 
                               = 
                               1 
                             
                           
                           
                             
                               Iu 
                               ′ 
                             
                             , 
                             
                               Ju 
                               ′ 
                             
                           
                         
                          
                         
                           es 
                           
                             
                               
                                 
                                   i 
                                   , 
                                   j 
                                 
                                  
                               
                                
                               a 
                             
                             - 
                             h 
                           
                         
                       
                       
                         # 
                          
                         
                             
                         
                          
                         pixels 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where 1≦i≦Iu′ and 1≦j≦Ju′ (with Iu′≦I and Ju′≦J) indicate the coordinates of pixels x i,j  comprised within the n-th uncertainty area  315   n , and #pixels indicates the number of pixel x i,j  comprised within the n-th uncertainty area  315   n . 
         [0083]    Then (step  248 ), the n-th final attenuation μ nf  is computed as the average of the (eight, in the considered example) differences between the average expected signal strengths  ES   \a-h  and the (eight, in the considered example) measured signal strengths ms \a-h , i.e.: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       μ 
                       nf 
                     
                     = 
                     
                       
                         
                           
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   a 
                                 
                                 h 
                               
                                
                               
                                 
                                   ES 
                                   
                                      
                                     k 
                                   
                                 
                                 _ 
                               
                             
                             - 
                             
                               m 
                                
                               
                                   
                               
                                
                               s 
                             
                           
                            
                         
                         k 
                       
                       
                         # 
                          
                         
                             
                         
                          
                         rcs 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where #rcs is the number (eight, in the considered example) of radio communication stations for which the UE has measured useful (i.e. above the minimum threshold) measured signal strengths ms a-h , i.e. eight radio communication station  110   a - h  in the example of  FIG. 1 . 
         [0084]    At the end of the n-th position estimation cycle the method provides a n-th estimation of the position estimation for the UE whose position is to be determined, i.e. the n-th location pixel x i,j\n  and also defines the n-th uncertainty area  315   n  (smaller than the previous uncertainty area  305  to  315   n-1 ) that takes into account statistical errors associated with such estimation. 
         [0085]    Then operation returns to step  234  for refining further the position estimation by performing a further position estimation cycle (i.e., the steps  234  to  248  are reiterated). 
         [0086]    If there is no outstanding correlation between the measured signal strengths ms \a-h  associated with the (eight in the considered example) radio communication stations  110   a - h  and the expected signal strengths es i,j\a-h  of pixels x i,j  around (i.e., within the n-th uncertainty area  315   n ) the estimated position, i.e. the n-th location pixel x i,jn , the n-th final attenuation μ nf  may be excluded and not used in determining the next (n+1)-th initial attenuation. In this case, the (n+1)-th initial attenuation is not based on the immediately previous n-th final attenuation μ nf  (but only based on final attenuations comprised in a set going from the first final attenuation μ 1f  to the (n−1)-th final attenuation) the error affecting the measured signal strengths ms \a-h  at the (n+1)-th step are independent one another and the total probabilities p(x i,j )\ tot  can be again calculated through equation (4). 
         [0087]    Thanks to the method according to an embodiment of the invention, it is possible to perform a continuous and self-refining positioning and a tracking of UE within the wireless communication network that take into account estimation of losses due to obstacles that cannot be included in models used by RF signal strength prediction tools or path loss estimation for generating the RF signals strength map; thus an improved accuracy in the positioning of UE within the wireless communication network is attained. 
         [0088]    The method according to an embodiment of the invention is adapted to refine at each cycle the attenuation value starting from a selected value to a final value substantially corresponding to a real attenuation term affecting the signal to/from the UE; therefore the method according to an embodiment of the invention is particularly adapted for positioning and tracking purposes even when measured signal strengths are affected by attenuations caused by additional obstacles such as vehicles (i.e., when the UE is within a vehicle), the foliage that varies according to the season, walls of building (when the UE is within a building, whose walls losses are not known), or the elevation of the position of the user handling the UE in a building with respect to the ground level (which in a first approximation may cause an increase of the signal strength) which vary in time and/or that cannot be successfully modeled in radio propagation tools. 
         [0089]    It should be apparent to those skilled in the art that embodiments of the present invention are not limited to terrestrial wireless communication networks. In an embodiment of the invention, the wireless communication network is a satellite communication or navigation system such as the Global Navigation Satellite System (GNSS), such as GPS, Glonass or Galileo. 
         [0090]    In this case, UE signal strength measurements are obtained in respect of signals provided by GNSS satellites in view and/or ground repeater antennas in range and expected signal strength are obtained from a corresponding GNSS signal strength map. In other words, the positioning method described above with respect to the wireless communication network  100  for mobile telephony, may be substantially straightforwardly applied to a Global Navigation Satellite System, by using, as expected signal strengths es i,j\a-h , signal strength values taken from the GNSS signal strength map, instead of the expected signal strengths of the radio signals irradiated by the radio communication stations  110   a - h . Referring back to equation (1), in such a case the terms ms \a-h  represent measures, performed by the UEs, of the received GNSS signals. 
         [0091]    It should be noted that, since an initial GNSS positioning is more accurate that an initial positioning (i.e., the search area  120 ) provided by the mobile telephony network, the loss (i.e. the attenuation) estimation is more accurate and the positioning and tracking achievable through the proposed invention provides an even better accuracy than in the case of mobile telephony networks. 
         [0092]    In particular, the accuracy of correction of the estimation of the position of UE exploiting GNSS signal strength maps may be improved by implementing the method end system according to the present invention in scenarios where the accuracy of the GNSS positioning may be degraded, such as for example in urban canyons scenario where the shadowing and the diffraction of RF signals caused by buildings may reduce an number of GNSS satellites actually in view and/or cause electromagnetic fields propagation delays (i.e., delays that affect the RF signals).