Abstract:
A method and system for determining a location of a first device that emits a signal: provide at least three sensors separated and spaced apart from each other; determine estimated location data for the first device for each sensor or unique sensor pair; determine an estimated location of the first device using the estimated location data for each sensor or unique sensor pair; determine residual values for the estimated location data for each sensor or sensor pair; convert the residual values into corresponding weights for the estimated location data for each sensor or sensor pair; weight the estimated location data for each sensor or sensor pair by its corresponding weight; and update the estimated location of the first device using the weighted estimated location data for each sensor or sensor pair.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation application of application Ser. No. 12/402,835 filed on 12 Mar. 2009, which is hereby incorporated for all purposes. 
    
    
     BACKGROUND 
     There are a number of applications where it is desirable to be able to identify an unknown location of an object which emits a signal. One example occurs when planning an indoor wireless local area network (LAN) having one or more RF or microwave emitters. 
     Of course precisely defining an object&#39;s location requires specifying coordinates in three dimensions (e.g., longitude, latitude, and altitude). In the discussion to follow, for simplicity of explanation it is assumed that the third coordinate (i.e., altitude) is either known or is otherwise easily determined once the other two coordinates (e.g., latitude and longitude) are identified. Those skilled in the art will be able to extrapolate the discussion to follow to the case where all three coordinates are to be determined. 
     There are a few known methods to locate signal emitters using a plurality of distributed sensors, or receivers, which are spaced apart from each other. Among these methods are: Angle of Arrival (AOA), Time of Arrival (TOA), Time Difference of Arrival (TDOA), and Received Signal Strength (RSS). 
     In the AOA method, the angle of arrival of the signal is measured with special directional antennas at each receiver. This information is combined to help locate the signal emitter using lines of bearing. 
     In the TOA method, a signal emitter transmits a signal at a predetermined or known time. Three or more sensors each measure the arrival time of the signal at that sensor. The absolute propagation time between emitter and sensor defines a distance or range. The range is computed using the well-known relation, r=vt, where r is the range, v is the propagation velocity, and t is the time of propagation between emitter and sensor. The known time of arrival at each sensor leads to circles of constant received time, centered at that sensor. 
       FIG. 1  illustrates some principles of a TOA method of locating an emitter  105  using three sensors  110 ,  120  and  130 . Shown in  FIG. 1  are three range-defined circles  102 ,  104  and  106  for the three sensors  110 ,  120  and  130 , having respective radii r 1 , r 2  and r 3 . The location where the circles  102 ,  104  and  106  from the three sensors  110 ,  120  and  130  intersect as shown in  FIG. 1  is the most likely location of the signal emitter  105 . In general, at least three sensors are required for the TOA method, but more than three sensors can be employed. 
     A chief limitation of the TOA method is that the emitter(s) to be located and the sensors must be synchronized. 
     The TDOA method, also known sometimes as multilateration or hyperbolic positioning, is a process of locating an emitter by accurately computing the time difference of arrival at three or more sensors of a signal emitted from an emitter to be located. In particular, if a signal is emitted from a signal emitter, it will arrive at slightly different times at two spatially separated sensor sites, the TDOA being due to the different distances to each sensor from the emitter. For given locations of the two sensors, there is a set of emitter locations that would give the same measurement of TDOA. Given two known sensor locations and a known TDOA between them, the locus of possible locations of the signal emitter lies on a hyperbola. As shown in  FIG. 2A , the hyperbola is defined as the locations where the difference between distances to the two sensors is a constant, or, in this case:
 
 r   1   −r   2   =v ( t   1   −t   2 ).
 
     With three or more sensors, multiple hyperbolas can be constructed from the TDOAs of different pairs of sensors. The location where the hyperbolas generated from the different sensor pairs intersect is the most likely location of the signal emitter. In practice, the sensors are time synchronized and the difference in the time of arrival of a signal from a signal emitter at a pair of sensors is measured. 
       FIG. 2B  illustrates some principles of a TDOA method of locating an emitter  105  using three sensors  110 ,  120  and  130 . Shown in  FIG. 2  are three range-defined hyperbolas  202 ,  204  and  206  for the three sensor pairs  110 / 120 ,  110 / 130  and  120 / 130 . The location where the hyperbolas  202 ,  204  and  206  from the three sensor pairs intersect, as shown in  FIG. 2B , is the most likely location of the signal emitter  105 . In general, at least three sensors are required for the TDOA method, but more than three sensors can be employed. 
     In many cases, the time-difference of arrival of a signal at two sensors is difficult to measure since the timing and signal characteristics of the emitter are unknown. In those cases, cross-correlation is a common method for determining the delay τ.  FIG. 3  shows an example cross-correlation curve  310 . The time-difference of arrival between the two sensors is defined as the location  312  where the curve  310  has its maximum. 
     In the RSS method, the power of the received signal at each sensor is measured, and the signal strength information is processed to help locate the signal emitter. There are a few different emitter location procedures that employ RSS. 
     In a basic RSS procedure, the power of the signal received at each sensor is measured. By knowing the broadcast power of the emitter, P 0 , one can convert the received power level, P 1 , to a range using the idealized expression: P 1 =P 0 *r 1   −2 . Other variants of this equation use statistical approaches to account for varieties in terrain. The range from each sensor defines a circle of probable locations for the emitter, centered at that receiver, similar to what is shown in  FIG. 1 . 
     Another form of RSS is a relative power measurement, used when the power level of the signal transmitted at the emitter is not known. In this approach the relative signal power is measured at a pair of two sensors, and the received power levels at the sensors are processed to determine a circle of probable locations for the emitter. 
     A more detailed explanation of principles employed in such an RSS method of locating a signal emitter will now be provided with respect to  FIG. 4 . 
       FIG. 4  illustrates a general case of an emitter  105  and two sensors  110  and  120  which each receives a signal from emitter  105  wherein a circle  402  of probable locations for emitter  105  is determined from a ratio the received signal powers at sensors  110  and  120 . 
     In free space, the received power of a signal transmitted by emitter  105  decreases with the square of the distance from emitter  105 . 
                       P   1     =         P   0     ⁡     (       r   0       r   1       )       2       ,           (   1   )               
where r 1  is the distance between emitter  105  and first sensor  110 , and  2  is the exponential rate at which the power decreases with distance.
 
     Likewise the received power P 2  at second sensor  120  is: 
                       P   2     =         P   0     ⁡     (       r   0       r   2       )       2       ,           (   2   )               
where r 2  is the distance between emitter  105  and second sensor  120 .
 
     This leads to: 
     
       
         
           
             
               
                 
                   
                     
                       P 
                       1 
                     
                     
                       P 
                       2 
                     
                   
                   = 
                   
                     
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                           r 
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                           r 
                           1 
                         
                       
                       ) 
                     
                     2 
                   
                 
               
               
                 
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     With a bit of manipulation this yields: 
     
       
         
           
             
               
                 
                   
                     
                       
                         log 
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                           ( 
                           
                             P 
                             1 
                           
                           ) 
                         
                       
                       - 
                       
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                             P 
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                     2 
                   
                   = 
                   
                     
                       
                         r 
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                         1 
                       
                     
                     = 
                     
                       const 
                       = 
                       α 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     This method is sometimes referred to as Signal Attenuation Difference of Arrival (SADOA). It can be shown that this leads to the circle  402  (the so-called circle of Apollonius) of a given radius R and centered on a point X 0 , Y 0  located on the line  401  defined by the two sensors  110  and  120 . This relationship is illustrated in  FIG. 4 . 
     With at least three sensors (e.g., A, B &amp; C), three such circles are generated from the corresponding three unique pairs of sensors (e.g., A/B, A/C &amp; B/C), and the location of emitter  100  can be found where the three circles intercept. 
     However, the addition of measurement uncertainty and noise makes it difficult to locate a sensor analytically with a high degree of accuracy using the AOA, TOA, TDOA, and RSS techniques as described above. Several error factors affect the accuracy of measurements made by the sensors. These error factors may include:
         Noise. In low Signal-to-noise ratio (SNR) situations, emitter location is more difficult to determine with a high degree of accuracy because measurements of signal power, time-of-arrival, etc. are affected.   Timing and calibration errors. Although these errors are typically small compared to other errors described here, there is nevertheless a need for algorithms that are robust in instances where these errors are significant.   Competing emitters. Signals from multiple emitters can lead to ambiguous results.   Multipath propagation. Reflections from multipath propagation can distort or obscure the true time of arrival, angle of arrival, or strength of a signal received at a sensor.   Blocked line-of-sight, or un-detected direct path (UDP), is a condition in which the main propagation path between the emitter and receiver is blocked.       

     Some or all of these errors can affect the graphical depictions in  FIGS. 1 &amp; 2 , causing the circles or hyperbolas to move so that they do not all intersect at a single point. 
     The effect of all of these errors is illustrated in the example shown in  FIG. 5 . 
       FIG. 5  illustrates a TOA method of locating an emitter  105  using three sensors  110 ,  120  and  130  in the presence of one or more of the factors listed above. Shown in  FIG. 5  are three range-defined circles  502 ,  504  and  506  for the three sensors  110 ,  120  and  130 , having respective radii r 1 , r 2  and r 3 . Because of measurement uncertainty due to one or more of the error-generating factors described above, the three circles  502 ,  504  and  506  do not intersect at one point. Instead, the three circles define an overlap region  505  which may be considered a most likely region for the location of emitter  105 . It can be understood that as the measurement uncertainty increases due to various factors described above, the size of the overlap region  505  may increase to such a degree that the emitter&#39;s location cannot be determined to a desired level of accuracy. 
     Thus, more robust methods of locating an emitter are required to obtain a more accurate solution. 
     What is needed, therefore, is a method and system for locating signal emitters that addresses one or more of these shortcomings. 
     SUMMARY 
     In an example embodiment, a method is provided for determining the location of a first device that emits a signal. The method includes: (a) providing at least three sensors separated and spaced apart from each other; (b) determining estimated location data for the first device for each sensor or unique sensor pair; (c) determining an estimated location of the first device using the estimated location data for each sensor or unique sensor pair; (d) determining residual values for the estimated location data for each sensor or sensor pair; (e) converting the residual values into corresponding weights for the estimated location data for each sensor or sensor pair; (f) weighting the estimated location data for each sensor or sensor pair by its corresponding weight; and (g) updating the estimated location of the first device using the weighted estimated location data for each sensor or sensor pair. 
     In another example embodiment, a system determines a location of a first device that emits a signal. The system comprises: at least three sensors separated and spaced apart from each other, each of the sensors including a receiver adapted to receive the signal emitted by the first device and to acquire the received signals for each of the sensors; a network connecting the sensors and adapted to communicate data from the sensors; and a processor programmed to execute an algorithm comprising: (a) determining estimated location data for the first device for each sensor or unique sensor pair; (b) determining an estimated location of the first device using the estimated location data for each sensor or unique sensor pair; (c) determining residual values for the estimated location data for each sensor or sensor pair; (d) converting the residual values into corresponding weights for the estimated location data for each sensor or sensor pair; (e) weighting the estimated location data for each sensor or sensor pair by its corresponding weight; and (f) updating the estimated location of the first device using the weighted estimated location data for each sensor or sensor pair. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawings will be provided by the Office upon request and payment of the necessary fee. 
       The example embodiments are best understood from the following detailed description when read with the accompanying drawing figures. It is emphasized that the various features are not necessarily drawn to scale. In fact, the dimensions may be arbitrarily increased or decreased for clarity of discussion. Wherever applicable and practical, like reference numerals refer to like elements. 
         FIG. 1  illustrates a time of arrival (TOA) algorithm for determining the location of a signal emitter. 
         FIGS. 2A-B  illustrate a time difference of arrival (TDOA) algorithm for determining the location of a signal emitter. 
         FIG. 3  shows an example of a cross-correlation curve. 
         FIG. 4  illustrates a received signal strength (RSS) algorithm for determining the location of a signal emitter. 
         FIG. 5  illustrates a time of arrival (TOA) algorithm for determining the location of a signal emitter in an environment where one or more error-generating factors are present. 
         FIG. 6  illustrates shows a functional block diagram of one embodiment of a sensor that may be employed in a system for locating a signal emitter. 
         FIG. 7A  illustrates a residual value for estimated location data in the case of a system that generates hyperbolic likelihood curves. 
         FIG. 7B  illustrates a residual value for estimated location data in the case of a system that generates circular likelihood curves. 
         FIG. 8A  illustrates a graphical plot of estimated location data (a likelihood plot) for an emitter calculated for one sensor pair. 
         FIG. 8B  illustrates a graphical plot of combined estimated location data (a likelihood plot) for an emitter calculated for ten sensor pairs. 
         FIG. 9  is a flowchart illustrating one embodiment of a method of locating an emitter using signals received at multiple sensors. 
         FIG. 10  illustrates an exemplary building floor-plan and sensor layout. 
     
    
    
     DETAILED DESCRIPTION 
     In the following detailed description, for purposes of explanation and not limitation, example embodiments disclosing specific details are set forth in order to provide a thorough understanding of an embodiment according to the present teachings. However, it will be apparent to one having ordinary skill in the art having had the benefit of the present disclosure that other embodiments according to the present teachings that depart from the specific details disclosed herein remain within the scope of the appended claims. Moreover, descriptions of well-known apparati and methods may be omitted so as to not obscure the description of the example embodiments. Such methods and apparati are clearly within the scope of the present teachings. 
       FIG. 6  shows a functional block diagram of one embodiment of a sensor  600  that may be employed in a system  10  for locating signal emitters. As will be appreciated by those skilled in the art, one or more of the various “parts” shown in  FIG. 6  may be physically implemented using a software-controlled microprocessor, hard-wired logic circuits, or a combination thereof. Also, while the parts are functionally segregated in  FIG. 6  for explanation purposes, they may be combined variously in any physical implementation. 
     Sensor  600  includes a receiver  610 , a processor  620 , a memory  630 , a network interface  640 , and a timing controller  650 . In some embodiments, receiver  610  includes, or is connected to, an antenna system  612 . In some embodiments, antenna system  612  may comprise a directional antenna system. 
     Receiver  610  provides functionality for sensor  600  to receive and process a signal (e.g., an RF signal, a microwave signal, an acoustic signal, etc.) received from a signal emitter. In some embodiments, receiver  610  is able to simultaneously receive signals from a plurality of different signal emitters. 
     Processor  620  is configured to execute one or more software algorithms in conjunction with memory  630  to provide functionality for sensor  600 . Beneficially, processor  620  includes its own memory (e.g., nonvolatile memory) for storing executable software programming code that allows it to perform the various functions of sensor  300 . Alternatively, or additionally, executable code may be stored in designated memory locations within memory  630 . 
     Memory  630  stores data and/or software programming code used in operations of sensor  600 . 
     Network interface  640  interfaces sensor  600  to a network  30  that includes a plurality of other sensors  600 . By means of network  30 , sensors  600  may share or communicate information with each other, and/or to a central controller or processor  40  and/or associated memory  45  that may be connected via network  30 . 
     Timing controller  650  controls the timing of signal processing operations in sensor  600 . In a beneficial arrangement, sensor  600  shares timing information with other sensors (not shown in  FIG. 6 ) in network  30  via network interface  640 . In one embodiment, timing controllers  650  of sensors  600  in network  30  are synchronized with each other to have a common sense of time. In one embodiment, timing controllers  650  in sensors  600  may obtain a common sense of time via a precision timing protocol (PTP) of IEEE-1588. In such a case, central controller or processor  40  may include a master clock for sensors  600  in network  30 , or a separate dedicated master clock may be provided in network  30 . In another embodiment, one of the timing controllers  650  in one of the sensors  600  may operate as a master clock for sensors  600  in network  30 . 
     In an alternative embodiment, a sensor that may be employed in a system for locating signal emitters could be a simple probe at the end of a wire or fiber that remotely connects to a central receiver and/or processor. 
     Now a method and system of locating signal emitters using received signals at three or more sensors such as sensor  600  of  FIG. 6  will be explained. In various embodiments, the calculations and other steps described below may be performed by processor  40 , by one or more of the processors  620  of sensors  600 , or by a combination of processor  40  and processors  620  programmed to execute predetermined instructions which may be, for example, stored in a corresponding memory or memories  45  and/or  630 . 
     Referring back to  FIG. 5 , statistical methods such as least-squares fitting and maximum likelihood estimates, or more robust graphical methods may be employed to obtain a unique solution for the location of emitter  105 . 
     Robust graphical methods have the advantage of being easy to compute, and easy to interpret. They are performed by converting the hyperbolas to likelihood functions. These functions have maximum likelihood along the defined circle or hyperbola curve (depending on the location method being employed), and gradually declining likelihood away from the curve. 
     An exemplary embodiment of a robust graphical emitter location method employing likelihood functions will now be explained. 
     A first step is to define a grid of points (xi, yj) i=1 . . . N, j=1 . . . M, at which estimated location data in the form of a likelihood function will be computed. The next step is to generate a likelihood function representing the likelihood of the signal emitter being located at a particular location. 
     In one embodiment, the approach is based on computing a residual. In location systems which generate hyperbolas of probable locations for the emitter (e.g., in TDOA systems), a metric is computed which converts the cross-correlation data into a likelihood function. In that case, the residual with respect to first and second sensors  110  and  120  at a point (xi, yj) is defined as:
 
 R   1,2 =|( r   1   −r   2 )− vτ   1,2 |,  (5)
 
where v represents the speed of propagation of the signal from the emitter (e.g., the speed of light), where r 1  and r 2  are the distances between the point (xi, yj) and the first and second sensors  110  and  120  respectively, of the sensor pair, and where τ 1,2  is the time-difference of arrival for the two sensors as determined by the location of the peak in the cross-correlation data (see  FIG. 3 ). Graphically, the TDOA residual value for a sensor pair at point (xi, yj) may be seen as the shortest distance between the hyperbola generated by the sensor pairs&#39; measurements (as in  FIG. 2 ) and the hyperbola that goes through (xi, yj), as illustrated in  FIG. 7A .
 
     In location systems which generate circles of probable locations for the emitter (e.g., in TOA systems and RSS systems employing power ratios), the residual at location (xi, yj) is defined as:
 
 R   1   =|d   1   −r   1 |  (6)
 
where d 1  is the distance between the circle center and the point (xi, yj), and r 1  is the radius of the circle, as illustrated in  FIG. 7B .
 
     Formally, in the case of hyperbola systems (e.g., TDOA systems) the likelihood function for any sensor pair may be computed as: 
                       l     p   ,   q       ⁡     (     x   ,   y     )       =     ⅇ     -       sR     p   ,   q       ⁡     (     x   ,   y     )                   (   7   )               
where s is a constant. Note that there are other possible likelihood functions. Another exemplary likelihood function is:
 
     
       
         
           
             
               
                 
                   
                     
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     The total likelihood function is the sum over all unique sensor pairs: 
     
       
         
           
             
               
                 
                   
                     L 
                     ⁡ 
                     
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                         x 
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                         y 
                       
                       ) 
                     
                   
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                         p 
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     An estimated location of the emitter may be determined as the location where the peak or maximum value of equation (9) is found. 
       FIG. 8A  illustrates an example of a graphical plot of a likelihood function for one pair of sensors  140  and  150  among a plurality of sensors  110 ,  120 ,  130 ,  140  and  150  employing a TDOA location algorithm. The original hyperbola  810  lies along the peak of a surface defined by the likelihood function, and denotes the locations having the maximum likelihood of being the actual location for emitter  105 . In  FIG. 8A , the hyperbola is “spread out” to denote non-zero probability away from the original hyperbola  810 . In the example illustrated in  FIG. 8A , the hyperbola  810  from the sensor pair  140  &amp;  150  has a significant error with respect to the actual location of emitter  105 . In general, this error may be reduced by generating likelihood functions for a large number of unique sensor pairs, and then determining a total likelihood function based on all of the likelihood functions, for example using equation (9) above. 
       FIG. 8B  illustrates a graphical plot of a total likelihood function generated from combining likelihood functions from ten (10) sensor pairs:  110 / 120 ,  110 / 130 ,  110 / 140 ,  110 / 150 ,  120 / 130 ,  120 / 140 ,  120 / 150 ,  130 / 140 ,  130 / 150  and  140 / 150 . The estimated location of emitter  105  (e.g., the location where the peak or maximum value of equation (9) is found) is illustrated in  FIG. 8B  as  820 . As can be seen in  FIG. 8B , the location  820  has a significant error with respect to the actual location of emitter  105 , which may be a result of one or more of the various error factors described above (noise, multipath, blocked signals, timing errors, etc.). 
     As described above, a function (e.g., equation (7)) based on residual values (e.g., equations (5) and (6)) is employed to construct and graph likelihood functions for the location of the emitter over a set of grid points, and the likelihood functions from a plurality of sensors or sensor pairs may then be combined to determine an estimated location of the emitter. 
     Beneficially, residual values may also be employed to improve the accuracy of algorithms for determining the location of a signal emitter, as described below. 
     Given an estimate of the emitter location (xi, yj), the residual describes the difference between that estimate, and the estimated location data from a single sensor or sensor pair. In this context, the residual provides a backward looking metric which illustrates how well each of the individual sets of estimated likelihood data (e.g., equation (7)) match the overall likelihood data (e.g., equation (9)). 
     This information is useful in helping to identify which sensor(s) or sensor pair(s) may be corrupted by bad data. If a particular sensor has a blocked direct path to the emitter, for example, it may be expected that the timing and/or power information from that sensor is compromised. In such cases, the data from that sensor may exhibit large residual values, and thus be identified as inconsistent with the estimated location data from other sensors or sensor pairs. 
     Once an estimate is made of the consistency among the different sensors or sensor pairs, a next step is to recalculate the combined likelihood function (e.g., in equation (9)) by first weighting the estimated location data set from each sensor or sensor pair according to its consistency as measured by the residual values for the sensor or sensor pair. In the above example, the data from a sensor with a blocked direct path would be only lightly weighted, thus minimizing its contribution. In one embodiment, a weighted version of equation (9) is calculated as: 
                     L   ⁡     (     x   ,   y     )       =       ∑     p   ,   q               ⁢       w     p   ,   q       ⁢       l     p   ,   q       ⁡     (     x   ,   y     )                   (   10   )               
where w is a weighting function related to the residual, and the individual likelihood functions are as they were calculated before.
 
     In one embodiment, the weighting function may be chosen as:
 
w=e −kR   (11)
 
where k is a constant. In another embodiment, the weighting function may be:
 
     
       
         
           
             
               
                 
                   w 
                   = 
                   
                     1 
                     kR 
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     Other weighting functions may be employed but, beneficially, the weighting function is inversely proportional to residual value. In another embodiment, the weighting function may include the geometric dilution of precision (GDOP). 
     Once a new estimated location is determined with respect to equation (10), beneficially the process may be iterated by: (1) recalculating the residual values for all sensors or sensor pairs with respect to new estimated location; (2) calculating new weighting function based on the residuals; and (3) recalculating a new estimated location using equation (10). 
       FIG. 9  shows a flowchart of one embodiment of a method  900  of locating a signal emitter. 
     In a step  910  a system provides a plurality of sensors (e.g., sensor  600 ). 
     In a step  920  a processor (e.g., processor  40  and/or processor(s)  620 ) determines emitter location likelihood data for each sensor or sensor pair. 
     In a step  930  a processor (e.g., processor  40  and/or processor(s)  620 ) determines an estimated emitter location using the likelihood data from each sensor or sensor pair. 
     In a step  940  a processor (e.g., processor  40  and/or processor(s)  620 ) determines residual values for each sensor or sensor pair. 
     In a step  950  a processor (e.g., processor  40  and/or processor(s)  620 ) transforms the residual values into corresponding weights. 
     In a step  960  a processor (e.g., processor  40  and/or processor(s)  620 ) determines a new estimated emitter location using the weighted likelihood data from each sensor or sensor pair. 
     In a step  970  a processor (e.g., processor  40  and/or processor(s)  620 ) determines whether or not the weighted likelihood data has converged. Beneficially, convergence may be determined to have occurred when the difference between a previous estimated location of the emitter and an updated estimated location of the emitter is less than a predetermined convergence threshold value. If the data is determined to have converged, then the process  900  ends at step  980 . 
     Otherwise, if the data has not converged, then in a step  990  a processor (e.g., processor  40  and/or processor(s)  620 ) determines whether a maximum number of iterations have been performed. Beneficially, when the number of iterations equals a predetermined maximum permitted number of iterations, then the process  900  ends at step  980 . 
     Otherwise, the process returns to step  940  and another iteration is performed. 
       FIG. 10  illustrates an exemplary building floor-plan and sensor layout that was employed to test the effectiveness of an exemplary embodiment of an iterative emitter location algorithm that employs weighting based on residual values. Approximately 300 measurements were made while varying the following parameters: emitter location, transmitted power, and transmitted signal bandwidth. For the measurements, the weighting function of equation 11 were employed, with k=5. Both RSS and time-based algorithms were employed. Table 1 show that, in this particular example, the disclosed algorithm performed better than either the power or time-based measurements alone. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Measurement Algorithm 
                 Mean Error 
               
               
                   
                   
               
             
             
               
                   
                 Iterative Residual Weighting 
                 10.5 m 
               
               
                   
                 RSS 
                 12.2 m 
               
               
                   
                 TDOA 
                 20.0 m 
               
               
                   
                   
               
             
          
         
       
     
     While example embodiments are disclosed herein, one of ordinary skill in the art appreciates that many variations that are in accordance with the present teachings are possible and remain within the scope of the appended claims. In particular, some exemplary embodiments were described above with respect to RF or microwave emitters and sensors. However, the principles set forth above can be applied to a variety of different signals other than RF or microwave signals, including other electromagnetic signals, and acoustic signals. Also, the propagation models used need not be free-space. Ideally path loss models that are employed match the environment in which the sensor system is deployed. In addition, the description above describes things in two dimensions, but the principles could be generalized to three dimensions. For example, in a case employing TOA, a solution in three dimensions is the volume of intersection of several spherical surfaces. The invention therefore is not to be restricted except within the scope of the appended claims.