235:
25:
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1544:
121:
66:
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4060:
The design of the sensor array requires optimizing the power allocation as well as minimizing the communication traffic of the entire system. The design suggested in incorporates probabilistic quantization in sensors and a simple optimization program that is solved in the fusion center only once.
209:
Many civilian and military applications require monitoring that can identify objects in a specific area, such as monitoring the front entrance of a private house by a single camera. Monitored areas that are large relative to objects of interest often require multiple sensors (e.g., infra-red
1330:
1004:
1322:
3167:
3280:
2879:{\displaystyle {\hat {\theta }}={\frac {F^{-1}({\hat {q}}_{2})\tau _{1}-F^{-1}({\hat {q}}_{1})\tau _{2}}{F^{-1}({\hat {q}}_{2})-F^{-1}({\hat {q}}_{1})}},\quad F(x)={\frac {1}{\sqrt {2\pi }}}\int \limits _{x}^{\infty }e^{-v^{2}/2}dw}
210:
detectors) at multiple locations. A centralized observer or computer application monitors the sensors. The communication to power and bandwidth requirements call for efficient design of the sensor, transmission, and processing.
2384:
225:
enables online recording of medical information while allowing the patient to move around. Military applications (e.g. locating an intruder into a secured area) are also good candidates for setting a wireless sensor network.
3440:
4030:
4742:
548:
3773:
901:
1539:{\displaystyle {\hat {\theta }}=\tau -F^{-1}\left({\frac {1}{N}}\sum \limits _{n=1}^{N}m_{n}(x_{n})\right),\quad F(x)={\frac {1}{{\sqrt {2\pi }}\sigma }}\int \limits _{x}^{\infty }e^{-w^{2}/2\sigma ^{2}}\,dw}
3971:
3901:
738:
1180:
1067:
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681:
1815:
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38:
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1988:
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2015:
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376:
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2050:
4661:
2575:{\displaystyle {\hat {q}}_{1}={\frac {2}{N}}\sum \limits _{n=1}^{N/2}m_{A}(x_{n}),\quad {\hat {q}}_{2}={\frac {2}{N}}\sum \limits _{n=1+N/2}^{N}m_{B}(x_{n})}
44:
4152:
3356:
4706:
4052:, then this design requires a factor of 4 in the number of sensors to achieve the same variance of the MLE in the unconstrained bandwidth settings.
221:
is an example where a vast number of sensors distributed among hospital facilities allow staff to locate a patient in distress. In addition, the
3976:
4371:
451:
3716:
833:
201:
the location of an object from a set of noisy measurements. These measurements are acquired in a distributed manner by a set of sensors.
4259:(July 2006). "Bandwidth-constrained distributed estimation for wireless sensor networks-part II: unknown probability density function".
3923:-unbiased property while theoretical arguments show that an optimal (and a more complex) design of the decision intervals would require
2937:
The system design of for the case that the structure of the noise PDF is unknown. The following model is considered for this scenario:
4097:
as to meet the energy constraints. Another work employs a similar approach to address distributed detection in wireless sensor arrays.
4061:
The fusion center then broadcasts a set of parameters to the sensors that allows them to finalize their design of messaging functions
3926:
3856:
175:
157:
102:
84:
76:
52:
690:
4770:
4364:
1967:. A coarse estimation can be used to overcome this limitation. However, it requires additional hardware in each of the sensors.
4671:
4127:
4106:
3853:. In fact, this intuitive design of the decision intervals is also optimal in the following sense. The above design requires
1126:
1013:
2943:
4317:
Xiao, Jin-Jun; Zhi-Quan Luo (August 2005). "Universal decentralized detection in a bandwidth-constrained sensor network".
1947:
is a major disadvantage of this method since our model does not assume prior knowledge about the approximated location of
1069:. The next sections suggest alternative designs when the sensors are bandwidth constrained to 1 bit transmission, that is
599:
827:
355:
2134:
A noise model may be sometimes available while the exact PDF parameters are unknown (e.g. a
Gaussian PDF with unknown
999:{\displaystyle \mathbb {E} \|\theta -{\hat {\theta }}\|^{2}={\text{var}}({\hat {\theta }})={\frac {\sigma ^{2}}{N}}}
4775:
1781:
4780:
4681:
4529:
4170:(March 2006). "Bandwidth-constrained distributed estimation for wireless sensor Networks-part I: Gaussian case".
1888:
1317:{\displaystyle m_{n}(x_{n})=I(x_{n}-\tau )={\begin{cases}1&x_{n}>\tau \\0&x_{n}\leq \tau \end{cases}}}
4572:
4504:
4302:
Xiao, Jin-Jun; Andrea J. Goldsmith (June 2005). "Joint estimation in sensor networks under energy constraint".
193:
3162:{\displaystyle w_{n}\in {\mathcal {P}},{\text{ that is }}:w_{n}{\text{ is bounded to }},\mathbb {E} (w_{n})=0}
2055:
1970:
A system design with arbitrary (but known) noise PDF can be found in. In this setting it is assumed that both
3819:
2317:
2225:
4433:
4387:
4220:
Luo, Zhi-Quan (June 2005). "Universal decentralized estimation in a bandwidth constrained sensor network".
553:
4712:
4453:
1639:
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773:
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4326:
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4179:
3216:
1258:
4723:
4064:
3973:, that is: the number of sensors is nearly optimal. It is also argued in that if the targeted MSE
3666:
and so on. It can be shown that these decision intervals and the corresponding set of coefficients
1755:
1007:
1592:
1072:
408:
4342:
4284:
4237:
4195:
3778:
3669:
3475:
3017:
904:
684:
218:
1686:
4109:
Harvard group working on wireless sensor network technology to a range of medical applications.
4035:
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4146:
198:
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1973:
1950:
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1735:
1572:
244:
4728:
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4410:
4395:
4334:
4276:
4229:
4187:
3275:{\displaystyle m_{n}(x_{n})={\begin{cases}1&x\in S_{n}\\0&x\notin S_{n}\end{cases}}}
1820:
3613:
3448:
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2109:
1993:
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2020:
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4288:
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4346:
222:
4131:
1845:
times the variance of MLE without bandwidth constraint. The variance increases as
3435:{\displaystyle {\hat {\theta }}=\sum \limits _{n=1}^{N}\alpha _{n}m_{n}(x_{n})}
4676:
4494:
1927:
the factor in the MSE remains approximately 2. Choosing a suitable value for
1569:
is a parameter leveraging our prior knowledge of the approximate location of
4686:
4600:
4478:
4338:
4280:
4233:
4191:
448:. The application processing the data applies a pre-defined estimation rule
2929:
to have an MSE with a reasonable factor of the unconstrained MLE variance.
4356:
4025:{\displaystyle \mathbb {E} \|\theta -{\hat {\theta }}\|\leq \epsilon ^{2}}
3610:
sensors would encode the second bit by setting their decision interval to
4633:
4620:
4605:
2052:. The estimator of also reaches an MSE which is a constant factor times
4595:
4577:
4514:
4463:
4443:
4428:
4423:
4405:
1683:. The processing center averages the received bits to form an estimate
683:
are designed to minimize estimation error. For example: minimizing the
4743:
International
Conference on Information Processing in Sensor Networks
4643:
4552:
4547:
4438:
4415:
1752:. It can be verified that for the optimal (and infeasible) choice of
358:(PDF). The sensors transmit measurements to a central processor. The
543:{\displaystyle {\hat {\theta }}=f(m_{1}(x_{1}),\cdot ,m_{N}(x_{N}))}
3768:{\displaystyle |\mathbb {E} (\theta -{\hat {\theta }})|<\delta }
2154:). The idea proposed in for this setting is to use two thresholds
896:{\displaystyle {\hat {\theta }}={\frac {1}{N}}\sum _{n=1}^{N}x_{n}}
4638:
4519:
4509:
4489:
233:
2378:. The processing center estimation rule is generated as follows:
4610:
4537:
4499:
3172:
In addition, the message functions are limited to have the form
4360:
3966:{\displaystyle N\geq \lceil \log {\frac {2U}{\delta }}\rceil }
3896:{\displaystyle N\geq \lceil \log {\frac {8U}{\delta }}\rceil }
114:
59:
18:
3353:. The fusion estimator is also restricted to be linear, i.e.
3838:
3080:
1145:
1032:
733:{\displaystyle \mathbb {E} \|\theta -{\hat {\theta }}\|^{2}}
3268:
1310:
2889:
As before, prior knowledge is necessary to set values for
16:
Estimating objects's location in wireless sensor networks
1175:{\displaystyle w_{n}\sim {\mathcal {N}}(0,\sigma ^{2})}
1062:{\displaystyle w_{n}\sim {\mathcal {N}}(0,\sigma ^{2})}
135:
3713:-unbiased estimator, which is an estimator satisfying
3004:{\displaystyle x_{n}=\theta +w_{n},\quad n=1,\dots ,N}
4067:
4038:
3979:
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2023:
1996:
1976:
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333:
287:
267:
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4722:
4695:
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4394:
676:{\displaystyle f(m_{1}(x_{1}),\cdot ,m_{N}(x_{N}))}
130:
may be too technical for most readers to understand
4089:
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2009:
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1316:
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998:
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675:
588:
542:
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397:
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346:
319:
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253:
4749:Conference on Embedded Networked Sensor Systems
4737:European Conference on Wireless Sensor Networks
4372:
3445:The design should set the decision intervals
743:Ideally, sensors transmit their measurements
8:
4006:
3985:
3960:
3936:
3890:
3866:
1810:{\displaystyle {\frac {\pi \sigma ^{2}}{4}}}
1732:, which is then used to find an estimate of
941:
919:
721:
699:
1920:{\displaystyle |\tau -\theta |\sim \sigma }
53:Learn how and when to remove these messages
4379:
4365:
4357:
261:denote the position of interest. A set of
4072:
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4037:
4016:
3995:
3994:
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3945:
3928:
3908:
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3547:by setting their decision interval to be
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3390:
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2111:
2091:
2086:. In this method, the prior knowledge of
2065:
2059:
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2022:
2001:
1995:
1975:
1952:
1932:
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176:Learn how and when to remove this message
158:Learn how and when to remove this message
142:, without removing the technical details.
103:Learn how and when to remove this message
4707:Ad hoc On-Demand Distance Vector Routing
2079:{\displaystyle {\frac {\sigma ^{2}}{N}}}
770:right to the processing center, that is
4222:IEEE Transactions on Information Theory
4119:
3846:{\displaystyle w_{n}\in {\mathcal {P}}}
2371:{\displaystyle m_{B}(x)=I(x-\tau _{2})}
2279:{\displaystyle m_{A}(x)=I(x-\tau _{1})}
4319:IEEE Transactions on Signal Processing
4304:IEEE Transactions on Signal Processing
4261:IEEE Transactions on Signal Processing
4172:IEEE Transactions on Signal Processing
4151:: CS1 maint: archived copy as title (
4144:
1885:, but it can be shown that as long as
1589:. In this design, the random value of
4215:
4213:
4211:
4209:
589:{\displaystyle m_{n},\,1\leq n\leq N}
140:make it understandable to non-experts
7:
2017:are confined to some known interval
1676:{\displaystyle (q=F(\tau -\theta ))}
3527:sensors to encode the first bit of
3376:
2922:{\displaystyle \tau _{1},\tau _{2}}
2512:
2421:
2187:{\displaystyle \tau _{1},\tau _{2}}
1384:
1182:system can be designed as follows:
320:{\displaystyle x_{n}=\theta +w_{n}}
3499:. Intuitively, one would allocate
2837:
1778:the variance of this estimator is
1486:
819:{\displaystyle m_{n}(x_{n})=x_{n}}
327:contaminated by an additive noise
75:tone or style may not reflect the
14:
34:This article has multiple issues.
1865:deviates from the real value of
119:
85:guide to writing better articles
64:
23:
2979:
2796:
2478:
1438:
550:. The set of message functions
42:or discuss these issues on the
4672:Sensor network query processor
4084:
4078:
4000:
3803:
3788:
3755:
3751:
3745:
3730:
3721:
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3638:
3632:
3617:
3569:
3554:
3429:
3416:
3366:
3340:
3319:
3205:
3192:
3150:
3137:
3126:
3111:
3042:
3027:
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2800:
2787:
2775:
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2724:
2696:
2684:
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2633:
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2598:
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934:
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632:
619:
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537:
534:
521:
499:
486:
473:
461:
435:
422:
1:
4090:{\displaystyle m_{n}(\cdot )}
3816:and for every realization of
1771:{\displaystyle \tau =\theta }
281:sensors acquire measurements
3775:for every possible value of
1625:{\displaystyle m_{n}(x_{n})}
1105:{\displaystyle m_{n}(x_{n})}
828:maximum likelihood estimator
441:{\displaystyle m_{n}(x_{n})}
356:probability density function
354:owing some known or unknown
3809:{\displaystyle \theta \in }
3686:{\displaystyle \alpha _{n}}
3492:{\displaystyle \alpha _{n}}
3048:{\displaystyle \theta \in }
4797:
2222:sensors are designed with
2126:of the previous approach.
1705:{\displaystyle {\hat {q}}}
4682:Wireless powerline sensor
4045:{\displaystyle \epsilon }
3903:to satisfy the universal
3108: is bounded to
4505:Near-field communication
2130:Unknown noise parameters
826:. In this settings, the
194:wireless sensor networks
4771:Wireless sensor network
4388:Wireless sensor network
4339:10.1109/TSP.2005.850334
4281:10.1109/TSP.2006.874366
4234:10.1109/TIT.2005.847692
4192:10.1109/TSP.2005.863009
3916:{\displaystyle \delta }
3706:{\displaystyle \delta }
3540:{\displaystyle \theta }
2147:{\displaystyle \sigma }
2106:replaces the parameter
1983:{\displaystyle \theta }
1960:{\displaystyle \theta }
1878:{\displaystyle \theta }
1745:{\displaystyle \theta }
1582:{\displaystyle \theta }
254:{\displaystyle \theta }
4713:Dynamic Source Routing
4091:
4056:Additional information
4046:
4026:
3967:
3917:
3897:
3847:
3810:
3769:
3707:
3687:
3660:
3604:
3576:
3541:
3521:
3493:
3466:
3436:
3395:
3347:
3306:
3276:
3163:
3049:
3005:
2923:
2880:
2841:
2576:
2545:
2448:
2372:
2308:
2280:
2216:
2188:
2148:
2120:
2100:
2080:
2046:
2011:
1984:
1961:
1941:
1921:
1879:
1859:
1839:
1838:{\displaystyle \pi /2}
1811:
1772:
1746:
1726:
1706:
1677:
1626:
1583:
1563:
1540:
1490:
1403:
1318:
1176:
1106:
1063:
1000:
897:
882:
820:
764:
734:
677:
590:
544:
442:
399:
372:
348:
321:
275:
255:
238:
4257:Georgios B. Giannakis
4168:Georgios B. Giannakis
4092:
4047:
4027:
3968:
3918:
3898:
3848:
3811:
3770:
3708:
3688:
3661:
3659:{\displaystyle \cup }
3605:
3577:
3542:
3522:
3494:
3472:and the coefficients
3467:
3465:{\displaystyle S_{n}}
3437:
3375:
3348:
3307:
3305:{\displaystyle S_{n}}
3277:
3164:
3050:
3006:
2924:
2881:
2827:
2577:
2511:
2420:
2373:
2309:
2281:
2217:
2189:
2149:
2121:
2119:{\displaystyle \tau }
2101:
2081:
2047:
2012:
2010:{\displaystyle w_{n}}
1985:
1962:
1942:
1940:{\displaystyle \tau }
1922:
1880:
1860:
1858:{\displaystyle \tau }
1840:
1812:
1773:
1747:
1727:
1707:
1678:
1627:
1584:
1564:
1562:{\displaystyle \tau }
1541:
1476:
1383:
1319:
1177:
1107:
1064:
1001:
898:
862:
821:
765:
763:{\displaystyle x_{n}}
735:
678:
591:
545:
443:
400:
398:{\displaystyle x_{n}}
373:
349:
347:{\displaystyle w_{n}}
322:
276:
256:
237:
4484:Bluetooth Low Energy
4255:Ribeiro, Alejandro;
4166:Ribeiro, Alejandro;
4065:
4036:
4032:uses a small enough
3977:
3927:
3907:
3857:
3820:
3779:
3717:
3697:
3693:produce a universal
3670:
3614:
3586:
3551:
3531:
3503:
3476:
3449:
3357:
3316:
3289:
3179:
3062:
3018:
2944:
2893:
2589:
2385:
2318:
2290:
2226:
2198:
2158:
2138:
2110:
2090:
2056:
2021:
1994:
1974:
1951:
1931:
1889:
1869:
1849:
1821:
1782:
1756:
1736:
1716:
1687:
1640:
1593:
1573:
1553:
1331:
1193:
1127:
1073:
1014:
911:
834:
774:
747:
691:
600:
596:and the fusion rule
554:
452:
409:
382:
362:
331:
285:
265:
245:
4667:Location estimation
4331:2005ITSP...53.2617X
4273:2006ITSP...54.2784R
4184:2006ITSP...54.1131R
3603:{\displaystyle N/4}
3520:{\displaystyle N/2}
3090: that is
2307:{\displaystyle N/2}
2215:{\displaystyle N/2}
189:Location estimation
4087:
4042:
4022:
3963:
3913:
3893:
3843:
3806:
3765:
3703:
3683:
3656:
3600:
3572:
3537:
3517:
3489:
3462:
3432:
3343:
3302:
3272:
3267:
3159:
3045:
3001:
2919:
2876:
2572:
2368:
2304:
2276:
2212:
2184:
2144:
2116:
2096:
2076:
2042:
2007:
1980:
1957:
1937:
1917:
1875:
1855:
1835:
1807:
1768:
1742:
1722:
1702:
1673:
1622:
1579:
1559:
1536:
1314:
1309:
1172:
1102:
1059:
996:
905:unbiased estimator
893:
816:
760:
730:
685:mean squared error
673:
586:
540:
438:
395:
378:th sensor encodes
368:
344:
317:
271:
251:
239:
219:Harvard University
197:is the problem of
4776:Estimation theory
4758:
4757:
4003:
3958:
3888:
3748:
3369:
3109:
3091:
2933:Unknown noise PDF
2825:
2824:
2791:
2778:
2737:
2687:
2636:
2601:
2509:
2489:
2418:
2398:
2099:{\displaystyle U}
2074:
1805:
1725:{\displaystyle q}
1699:
1474:
1468:
1381:
1343:
1006:assuming a white
994:
970:
956:
937:
860:
846:
717:
464:
371:{\displaystyle n}
274:{\displaystyle N}
186:
185:
178:
168:
167:
160:
113:
112:
105:
79:used on Knowledge
77:encyclopedic tone
57:
4788:
4781:Detection theory
4662:Key distribution
4411:ERIKA Enterprise
4381:
4374:
4367:
4358:
4351:
4350:
4314:
4308:
4307:
4299:
4293:
4292:
4252:
4246:
4245:
4228:(6): 2210–2219.
4217:
4204:
4203:
4163:
4157:
4156:
4150:
4142:
4140:
4139:
4130:. Archived from
4124:
4096:
4094:
4093:
4088:
4077:
4076:
4051:
4049:
4048:
4043:
4031:
4029:
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4023:
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4020:
4005:
4004:
3996:
3984:
3972:
3970:
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3959:
3954:
3946:
3922:
3920:
3919:
3914:
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3894:
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3876:
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3766:
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3749:
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3724:
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3682:
3681:
3665:
3663:
3662:
3657:
3609:
3607:
3606:
3601:
3596:
3581:
3579:
3578:
3575:{\displaystyle }
3573:
3546:
3544:
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3498:
3496:
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3487:
3471:
3469:
3468:
3463:
3461:
3460:
3441:
3439:
3438:
3433:
3428:
3427:
3415:
3414:
3405:
3404:
3394:
3389:
3371:
3370:
3362:
3352:
3350:
3349:
3346:{\displaystyle }
3344:
3311:
3309:
3308:
3303:
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3300:
3281:
3279:
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3273:
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3270:
3264:
3263:
3239:
3238:
3204:
3203:
3191:
3190:
3168:
3166:
3165:
3160:
3149:
3148:
3136:
3110:
3107:
3105:
3104:
3092:
3089:
3084:
3083:
3074:
3073:
3054:
3052:
3051:
3046:
3010:
3008:
3007:
3002:
2975:
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2956:
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2928:
2926:
2925:
2920:
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2905:
2904:
2885:
2883:
2882:
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2864:
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2826:
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2792:
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2785:
2780:
2779:
2771:
2764:
2763:
2745:
2744:
2739:
2738:
2730:
2723:
2722:
2709:
2708:
2707:
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2694:
2689:
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2680:
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2657:
2656:
2644:
2643:
2638:
2637:
2629:
2622:
2621:
2608:
2603:
2602:
2594:
2581:
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2578:
2573:
2568:
2567:
2555:
2554:
2544:
2539:
2535:
2510:
2502:
2497:
2496:
2491:
2490:
2482:
2471:
2470:
2458:
2457:
2447:
2443:
2434:
2419:
2411:
2406:
2405:
2400:
2399:
2391:
2377:
2375:
2374:
2369:
2364:
2363:
2330:
2329:
2313:
2311:
2310:
2305:
2300:
2286:, and the other
2285:
2283:
2282:
2277:
2272:
2271:
2238:
2237:
2221:
2219:
2218:
2213:
2208:
2193:
2191:
2190:
2185:
2183:
2182:
2170:
2169:
2153:
2151:
2150:
2145:
2125:
2123:
2122:
2117:
2105:
2103:
2102:
2097:
2085:
2083:
2082:
2077:
2075:
2070:
2069:
2060:
2051:
2049:
2048:
2045:{\displaystyle }
2043:
2016:
2014:
2013:
2008:
2006:
2005:
1989:
1987:
1986:
1981:
1966:
1964:
1963:
1958:
1946:
1944:
1943:
1938:
1926:
1924:
1923:
1918:
1910:
1896:
1884:
1882:
1881:
1876:
1864:
1862:
1861:
1856:
1844:
1842:
1841:
1836:
1831:
1816:
1814:
1813:
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1806:
1801:
1800:
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1769:
1751:
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1748:
1743:
1731:
1729:
1728:
1723:
1711:
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1708:
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1692:
1682:
1680:
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1674:
1631:
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1628:
1623:
1618:
1617:
1605:
1604:
1588:
1586:
1585:
1580:
1568:
1566:
1565:
1560:
1545:
1543:
1542:
1537:
1528:
1527:
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1513:
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1507:
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1475:
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1469:
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1434:
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1426:
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1397:
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1367:
1366:
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1323:
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1315:
1313:
1312:
1300:
1299:
1275:
1274:
1240:
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1205:
1204:
1181:
1179:
1178:
1173:
1168:
1167:
1149:
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1139:
1138:
1111:
1109:
1108:
1103:
1098:
1097:
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1084:
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1060:
1055:
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1005:
1003:
1002:
997:
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989:
980:
972:
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963:
957:
954:
949:
948:
939:
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930:
918:
902:
900:
899:
894:
892:
891:
881:
876:
861:
853:
848:
847:
839:
825:
823:
822:
817:
815:
814:
799:
798:
786:
785:
769:
767:
766:
761:
759:
758:
739:
737:
736:
731:
729:
728:
719:
718:
710:
698:
682:
680:
679:
674:
666:
665:
653:
652:
631:
630:
618:
617:
595:
593:
592:
587:
566:
565:
549:
547:
546:
541:
533:
532:
520:
519:
498:
497:
485:
484:
466:
465:
457:
447:
445:
444:
439:
434:
433:
421:
420:
404:
402:
401:
396:
394:
393:
377:
375:
374:
369:
353:
351:
350:
345:
343:
342:
326:
324:
323:
318:
316:
315:
297:
296:
280:
278:
277:
272:
260:
258:
257:
252:
181:
174:
163:
156:
152:
149:
143:
123:
122:
115:
108:
101:
97:
94:
88:
87:for suggestions.
83:See Knowledge's
68:
67:
60:
49:
27:
26:
19:
4796:
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4787:
4786:
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4761:
4760:
4759:
4754:
4727:
4718:
4698:
4691:
4648:
4615:
4582:
4564:
4557:
4455:
4448:
4397:
4390:
4385:
4355:
4354:
4316:
4315:
4311:
4301:
4300:
4296:
4254:
4253:
4249:
4219:
4218:
4207:
4165:
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4160:
4143:
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4135:
4128:"Archived copy"
4126:
4125:
4121:
4116:
4103:
4068:
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4058:
4034:
4033:
4012:
3975:
3974:
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3924:
3905:
3904:
3877:
3855:
3854:
3823:
3818:
3817:
3777:
3776:
3715:
3714:
3695:
3694:
3673:
3668:
3667:
3612:
3611:
3584:
3583:
3549:
3548:
3529:
3528:
3501:
3500:
3479:
3474:
3473:
3452:
3447:
3446:
3419:
3406:
3396:
3355:
3354:
3314:
3313:
3312:is a subset of
3292:
3287:
3286:
3266:
3265:
3255:
3247:
3241:
3240:
3230:
3222:
3212:
3195:
3182:
3177:
3176:
3140:
3096:
3065:
3060:
3059:
3016:
3015:
2966:
2947:
2942:
2941:
2935:
2909:
2896:
2891:
2890:
2850:
2842:
2768:
2752:
2727:
2711:
2710:
2699:
2677:
2661:
2648:
2626:
2610:
2609:
2587:
2586:
2559:
2546:
2479:
2462:
2449:
2388:
2383:
2382:
2355:
2321:
2316:
2315:
2288:
2287:
2263:
2229:
2224:
2223:
2196:
2195:
2174:
2161:
2156:
2155:
2136:
2135:
2132:
2108:
2107:
2088:
2087:
2061:
2054:
2053:
2019:
2018:
1997:
1992:
1991:
1972:
1971:
1949:
1948:
1929:
1928:
1887:
1886:
1867:
1866:
1847:
1846:
1819:
1818:
1791:
1787:
1780:
1779:
1754:
1753:
1734:
1733:
1714:
1713:
1685:
1684:
1638:
1637:
1632:is distributed
1609:
1596:
1591:
1590:
1571:
1570:
1551:
1550:
1517:
1499:
1491:
1459:
1417:
1404:
1372:
1368:
1355:
1329:
1328:
1308:
1307:
1291:
1289:
1283:
1282:
1266:
1264:
1254:
1231:
1209:
1196:
1191:
1190:
1159:
1130:
1125:
1124:
1118:
1116:Known noise PDF
1089:
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1070:
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609:
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215:CodeBlue system
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136:help improve it
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109:
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73:This article's
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4454:Communications
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4101:External links
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2354:
2351:
2348:
2345:
2342:
2339:
2336:
2333:
2328:
2324:
2303:
2299:
2295:
2275:
2270:
2266:
2262:
2259:
2256:
2253:
2250:
2247:
2244:
2241:
2236:
2232:
2211:
2207:
2203:
2181:
2177:
2173:
2168:
2164:
2143:
2131:
2128:
2115:
2095:
2073:
2068:
2064:
2041:
2038:
2035:
2032:
2029:
2026:
2004:
2000:
1990:and the noise
1979:
1956:
1936:
1916:
1913:
1909:
1905:
1902:
1899:
1895:
1874:
1854:
1834:
1830:
1826:
1817:which is only
1804:
1798:
1794:
1790:
1767:
1764:
1761:
1741:
1721:
1698:
1695:
1672:
1669:
1666:
1663:
1660:
1657:
1654:
1651:
1648:
1645:
1621:
1616:
1612:
1608:
1603:
1599:
1578:
1558:
1547:
1546:
1535:
1532:
1524:
1520:
1516:
1512:
1506:
1502:
1498:
1494:
1488:
1483:
1479:
1472:
1467:
1464:
1458:
1453:
1450:
1447:
1444:
1441:
1437:
1433:
1429:
1424:
1420:
1416:
1411:
1407:
1401:
1396:
1393:
1390:
1386:
1380:
1377:
1371:
1365:
1362:
1358:
1354:
1351:
1348:
1342:
1339:
1325:
1324:
1311:
1306:
1303:
1298:
1294:
1290:
1288:
1285:
1284:
1281:
1278:
1273:
1269:
1265:
1263:
1260:
1259:
1257:
1252:
1249:
1246:
1243:
1238:
1234:
1230:
1227:
1224:
1221:
1216:
1212:
1208:
1203:
1199:
1187:
1186:
1171:
1166:
1162:
1158:
1155:
1152:
1147:
1142:
1137:
1133:
1122:Gaussian noise
1117:
1114:
1101:
1096:
1092:
1088:
1083:
1079:
1058:
1053:
1049:
1045:
1042:
1039:
1034:
1029:
1024:
1020:
993:
988:
984:
978:
975:
969:
966:
960:
952:
947:
943:
936:
933:
927:
924:
921:
917:
890:
886:
880:
875:
872:
869:
865:
859:
856:
851:
845:
842:
813:
809:
805:
802:
797:
793:
789:
784:
780:
757:
753:
727:
723:
716:
713:
707:
704:
701:
697:
672:
669:
664:
660:
656:
651:
647:
643:
640:
637:
634:
629:
625:
621:
616:
612:
608:
605:
585:
582:
579:
576:
573:
569:
564:
560:
539:
536:
531:
527:
523:
518:
514:
510:
507:
504:
501:
496:
492:
488:
483:
479:
475:
472:
469:
463:
460:
437:
432:
428:
424:
419:
415:
405:by a function
392:
388:
367:
341:
337:
314:
310:
306:
303:
300:
295:
291:
270:
250:
231:
228:
206:
203:
184:
183:
166:
165:
127:
125:
118:
111:
110:
72:
70:
63:
58:
32:
31:
29:
22:
15:
13:
10:
9:
6:
4:
3:
2:
4793:
4782:
4779:
4777:
4774:
4772:
4769:
4768:
4766:
4750:
4747:
4744:
4741:
4738:
4735:
4734:
4732:
4730:
4725:
4721:
4714:
4711:
4708:
4705:
4704:
4702:
4700:
4694:
4688:
4685:
4683:
4680:
4678:
4675:
4673:
4670:
4668:
4665:
4663:
4660:
4659:
4657:
4655:
4651:
4645:
4644:TinyDB-TOSSIM
4642:
4640:
4637:
4635:
4632:
4630:
4627:
4626:
4624:
4622:
4618:
4612:
4609:
4607:
4604:
4602:
4599:
4597:
4594:
4593:
4591:
4589:
4585:
4579:
4576:
4574:
4571:
4570:
4568:
4566:
4560:
4554:
4551:
4549:
4546:
4544:
4541:
4539:
4536:
4533:
4531:
4528:
4526:
4523:
4521:
4518:
4516:
4513:
4511:
4508:
4506:
4503:
4501:
4498:
4496:
4493:
4491:
4488:
4485:
4482:
4480:
4477:
4475:
4472:
4470:
4469:IEEE 802.15.4
4467:
4465:
4462:
4461:
4459:
4457:
4451:
4445:
4442:
4440:
4437:
4435:
4432:
4430:
4427:
4425:
4422:
4419:
4417:
4414:
4412:
4409:
4407:
4404:
4403:
4401:
4399:
4393:
4389:
4382:
4377:
4375:
4370:
4368:
4363:
4362:
4359:
4348:
4344:
4340:
4336:
4332:
4328:
4324:
4320:
4313:
4310:
4305:
4298:
4295:
4290:
4286:
4282:
4278:
4274:
4270:
4266:
4262:
4258:
4251:
4248:
4243:
4239:
4235:
4231:
4227:
4223:
4216:
4214:
4212:
4210:
4206:
4201:
4197:
4193:
4189:
4185:
4181:
4177:
4173:
4169:
4162:
4159:
4154:
4148:
4134:on 2008-04-30
4133:
4129:
4123:
4120:
4113:
4108:
4105:
4104:
4100:
4098:
4081:
4073:
4069:
4055:
4053:
4039:
4017:
4013:
4009:
3997:
3991:
3988:
3955:
3951:
3948:
3942:
3939:
3933:
3930:
3910:
3885:
3881:
3878:
3872:
3869:
3863:
3860:
3833:
3828:
3824:
3800:
3797:
3794:
3791:
3785:
3782:
3762:
3759:
3742:
3736:
3733:
3700:
3678:
3674:
3650:
3647:
3644:
3641:
3635:
3629:
3626:
3623:
3620:
3597:
3593:
3589:
3566:
3563:
3560:
3557:
3534:
3514:
3510:
3506:
3484:
3480:
3457:
3453:
3443:
3424:
3420:
3411:
3407:
3401:
3397:
3391:
3386:
3383:
3380:
3372:
3363:
3337:
3334:
3331:
3328:
3325:
3322:
3297:
3293:
3260:
3256:
3252:
3249:
3244:
3235:
3231:
3227:
3224:
3219:
3213:
3208:
3200:
3196:
3187:
3183:
3175:
3174:
3173:
3156:
3153:
3145:
3141:
3129:
3123:
3120:
3117:
3114:
3101:
3097:
3093:
3085:
3075:
3070:
3066:
3058:
3057:
3039:
3036:
3033:
3030:
3024:
3021:
3014:
3013:
2998:
2995:
2992:
2989:
2986:
2983:
2980:
2976:
2971:
2967:
2963:
2960:
2957:
2952:
2948:
2940:
2939:
2938:
2932:
2930:
2914:
2910:
2906:
2901:
2897:
2873:
2870:
2865:
2861:
2855:
2851:
2847:
2843:
2832:
2828:
2821:
2818:
2814:
2809:
2803:
2797:
2793:
2782:
2772:
2760:
2757:
2753:
2749:
2741:
2731:
2719:
2716:
2712:
2704:
2700:
2691:
2681:
2669:
2666:
2662:
2658:
2653:
2649:
2640:
2630:
2618:
2615:
2611:
2604:
2595:
2585:
2584:
2564:
2560:
2551:
2547:
2541:
2536:
2532:
2528:
2525:
2522:
2519:
2516:
2506:
2503:
2498:
2493:
2483:
2475:
2467:
2463:
2454:
2450:
2444:
2440:
2436:
2431:
2428:
2425:
2415:
2412:
2407:
2402:
2392:
2381:
2380:
2379:
2360:
2356:
2352:
2349:
2343:
2340:
2334:
2326:
2322:
2301:
2297:
2293:
2268:
2264:
2260:
2257:
2251:
2248:
2242:
2234:
2230:
2209:
2205:
2201:
2179:
2175:
2171:
2166:
2162:
2141:
2129:
2127:
2113:
2093:
2071:
2066:
2062:
2036:
2033:
2030:
2027:
2002:
1998:
1977:
1968:
1954:
1934:
1914:
1911:
1903:
1900:
1897:
1872:
1852:
1832:
1828:
1824:
1802:
1796:
1792:
1788:
1765:
1762:
1759:
1739:
1719:
1693:
1664:
1661:
1658:
1652:
1649:
1646:
1635:
1614:
1610:
1601:
1597:
1576:
1556:
1533:
1530:
1522:
1518:
1514:
1510:
1504:
1500:
1496:
1492:
1481:
1477:
1470:
1465:
1462:
1456:
1451:
1445:
1439:
1435:
1431:
1422:
1418:
1409:
1405:
1399:
1394:
1391:
1388:
1378:
1375:
1369:
1363:
1360:
1356:
1352:
1349:
1346:
1337:
1327:
1326:
1304:
1301:
1296:
1292:
1286:
1279:
1276:
1271:
1267:
1261:
1255:
1250:
1244:
1241:
1236:
1232:
1225:
1222:
1214:
1210:
1201:
1197:
1189:
1188:
1185:
1184:
1183:
1164:
1160:
1156:
1153:
1140:
1135:
1131:
1123:
1115:
1113:
1094:
1090:
1081:
1077:
1051:
1047:
1043:
1040:
1027:
1022:
1018:
1009:
991:
986:
982:
976:
964:
950:
945:
931:
925:
922:
907:whose MSE is
906:
888:
884:
878:
873:
870:
867:
863:
857:
854:
849:
840:
829:
811:
807:
803:
795:
791:
782:
778:
755:
751:
741:
725:
711:
705:
702:
686:
662:
658:
649:
645:
641:
638:
635:
627:
623:
614:
610:
603:
583:
580:
577:
574:
571:
567:
562:
558:
529:
525:
516:
512:
508:
505:
502:
494:
490:
481:
477:
470:
467:
458:
430:
426:
417:
413:
390:
386:
365:
357:
339:
335:
312:
308:
304:
301:
298:
293:
289:
268:
248:
236:
229:
227:
224:
220:
216:
211:
204:
202:
200:
196:
195:
190:
180:
177:
162:
159:
151:
141:
137:
131:
128:This article
126:
117:
116:
107:
104:
96:
86:
80:
78:
71:
62:
61:
56:
54:
47:
46:
41:
40:
35:
30:
21:
20:
4666:
4654:Applications
4543:WirelessHART
4322:
4318:
4312:
4303:
4297:
4264:
4260:
4250:
4225:
4221:
4175:
4171:
4161:
4136:. Retrieved
4132:the original
4122:
4059:
3444:
3284:
3171:
2936:
2888:
2314:sensors use
2194:, such that
2133:
1969:
1548:
1119:
742:
240:
223:sensor array
214:
212:
208:
192:
188:
187:
172:
154:
145:
129:
99:
90:
74:
50:
43:
37:
36:Please help
33:
4724:Conferences
4563:Programming
4325:(8): 2617.
4267:(7): 2784.
4178:(3): 1131.
3285:where each
4765:Categories
4677:Sensor web
4495:ISA100.11a
4138:2008-04-30
4114:References
199:estimating
39:improve it
4699:protocols
4687:Telemetry
4601:Iris Mote
4565:languages
4479:Bluetooth
4456:protocols
4420:NanoQplus
4396:Operating
4082:⋅
4040:ϵ
4014:ϵ
4010:≤
4007:‖
4001:^
3998:θ
3992:−
3989:θ
3986:‖
3961:⌉
3956:δ
3943:
3937:⌈
3934:≥
3911:δ
3891:⌉
3886:δ
3873:
3867:⌈
3864:≥
3834:∈
3792:−
3786:∈
3783:θ
3763:δ
3746:^
3743:θ
3737:−
3734:θ
3701:δ
3675:α
3636:∪
3621:−
3535:θ
3481:α
3398:α
3377:∑
3367:^
3364:θ
3323:−
3253:∉
3228:∈
3115:−
3076:∈
3031:−
3025:∈
3022:θ
2993:…
2961:θ
2911:τ
2898:τ
2848:−
2838:∞
2829:∫
2822:π
2776:^
2758:−
2750:−
2735:^
2717:−
2701:τ
2685:^
2667:−
2659:−
2650:τ
2634:^
2616:−
2599:^
2596:θ
2513:∑
2487:^
2422:∑
2396:^
2357:τ
2353:−
2265:τ
2261:−
2176:τ
2163:τ
2142:σ
2114:τ
2063:σ
2028:−
1978:θ
1955:θ
1935:τ
1915:σ
1912:∼
1904:θ
1901:−
1898:τ
1873:θ
1853:τ
1825:π
1793:σ
1789:π
1766:θ
1760:τ
1740:θ
1697:^
1665:θ
1662:−
1659:τ
1634:Bernoulli
1577:θ
1557:τ
1519:σ
1497:−
1487:∞
1478:∫
1471:σ
1466:π
1385:∑
1361:−
1353:−
1350:τ
1341:^
1338:θ
1305:τ
1302:≤
1280:τ
1245:τ
1242:−
1161:σ
1141:∼
1112:=0 or 1.
1048:σ
1028:∼
983:σ
968:^
965:θ
942:‖
935:^
932:θ
926:−
923:θ
920:‖
864:∑
844:^
841:θ
722:‖
715:^
712:θ
706:−
703:θ
700:‖
639:⋅
581:≤
575:≤
506:⋅
462:^
459:θ
302:θ
249:θ
148:July 2020
93:July 2020
45:talk page
4751:(SenSys)
4729:journals
4634:LinuxMCE
4621:Software
4606:Sun SPOT
4588:Hardware
4525:Sidewalk
4486:(Wibree)
4289:11410878
4242:11574873
4200:16223482
4147:cite web
4107:CodeBlue
1008:Gaussian
4697:Routing
4596:Arduino
4578:LabVIEW
4534:TIBUMAC
4515:One-Net
4464:6LoWPAN
4444:OpenWSN
4429:OpenTag
4424:Nano-RK
4406:Contiki
4398:systems
4347:8072065
4327:Bibcode
4269:Bibcode
4180:Bibcode
3582:, then
687:(MSE),
230:Setting
134:Please
4745:(IPSN)
4739:(EWSN)
4709:(AODV)
4553:Z-Wave
4548:Zigbee
4530:Thread
4439:TinyOS
4416:LiteOS
4345:
4287:
4240:
4198:
1010:noise
903:is an
830:(MLE)
4715:(DSR)
4639:OPNET
4520:OSIAN
4510:OCARI
4490:DASH7
4343:S2CID
4285:S2CID
4238:S2CID
4196:S2CID
1549:Here
4629:NS-2
4611:XBee
4538:TSMP
4500:MiWi
4434:RIOT
4153:link
3760:<
1277:>
241:Let
213:The
4474:ANT
4335:doi
4277:doi
4230:doi
4188:doi
3940:log
3870:log
1712:of
955:var
217:of
205:Use
191:in
138:to
4767::
4341:.
4333:.
4323:53
4321:.
4283:.
4275:.
4265:54
4263:.
4236:.
4226:51
4224:.
4208:^
4194:.
4186:.
4176:54
4174:.
4149:}}
4145:{{
3442:.
1120:A
740:.
48:.
4726:,
4573:C
4380:e
4373:t
4366:v
4349:.
4337::
4329::
4306:.
4291:.
4279::
4271::
4244:.
4232::
4202:.
4190::
4182::
4155:)
4141:.
4085:)
4079:(
4074:n
4070:m
4018:2
3982:E
3952:U
3949:2
3931:N
3882:U
3879:8
3861:N
3839:P
3829:n
3825:w
3804:]
3801:U
3798:,
3795:U
3789:[
3756:|
3752:)
3731:(
3727:E
3722:|
3679:n
3654:]
3651:U
3648:2
3645:,
3642:U
3639:[
3633:]
3630:0
3627:,
3624:U
3618:[
3598:4
3594:/
3590:N
3570:]
3567:U
3564:2
3561:,
3558:0
3555:[
3515:2
3511:/
3507:N
3485:n
3458:n
3454:S
3430:)
3425:n
3421:x
3417:(
3412:n
3408:m
3402:n
3392:N
3387:1
3384:=
3381:n
3373:=
3341:]
3338:U
3335:2
3332:,
3329:U
3326:2
3320:[
3298:n
3294:S
3261:n
3257:S
3250:x
3245:0
3236:n
3232:S
3225:x
3220:1
3214:{
3209:=
3206:)
3201:n
3197:x
3193:(
3188:n
3184:m
3157:0
3154:=
3151:)
3146:n
3142:w
3138:(
3134:E
3130:,
3127:]
3124:U
3121:,
3118:U
3112:[
3102:n
3098:w
3094::
3086:,
3081:P
3071:n
3067:w
3043:]
3040:U
3037:,
3034:U
3028:[
2999:N
2996:,
2990:,
2987:1
2984:=
2981:n
2977:,
2972:n
2968:w
2964:+
2958:=
2953:n
2949:x
2915:2
2907:,
2902:1
2874:w
2871:d
2866:2
2862:/
2856:2
2852:v
2844:e
2833:x
2819:2
2815:1
2810:=
2807:)
2804:x
2801:(
2798:F
2794:,
2788:)
2783:1
2773:q
2766:(
2761:1
2754:F
2747:)
2742:2
2732:q
2725:(
2720:1
2713:F
2705:2
2697:)
2692:1
2682:q
2675:(
2670:1
2663:F
2654:1
2646:)
2641:2
2631:q
2624:(
2619:1
2612:F
2605:=
2570:)
2565:n
2561:x
2557:(
2552:B
2548:m
2542:N
2537:2
2533:/
2529:N
2526:+
2523:1
2520:=
2517:n
2507:N
2504:2
2499:=
2494:2
2484:q
2476:,
2473:)
2468:n
2464:x
2460:(
2455:A
2451:m
2445:2
2441:/
2437:N
2432:1
2429:=
2426:n
2416:N
2413:2
2408:=
2403:1
2393:q
2366:)
2361:2
2350:x
2347:(
2344:I
2341:=
2338:)
2335:x
2332:(
2327:B
2323:m
2302:2
2298:/
2294:N
2274:)
2269:1
2258:x
2255:(
2252:I
2249:=
2246:)
2243:x
2240:(
2235:A
2231:m
2210:2
2206:/
2202:N
2180:2
2172:,
2167:1
2094:U
2072:N
2067:2
2040:]
2037:U
2034:,
2031:U
2025:[
2003:n
1999:w
1908:|
1894:|
1833:2
1829:/
1803:4
1797:2
1763:=
1720:q
1694:q
1671:)
1668:)
1656:(
1653:F
1650:=
1647:q
1644:(
1636:~
1620:)
1615:n
1611:x
1607:(
1602:n
1598:m
1534:w
1531:d
1523:2
1515:2
1511:/
1505:2
1501:w
1493:e
1482:x
1463:2
1457:1
1452:=
1449:)
1446:x
1443:(
1440:F
1436:,
1432:)
1428:)
1423:n
1419:x
1415:(
1410:n
1406:m
1400:N
1395:1
1392:=
1389:n
1379:N
1376:1
1370:(
1364:1
1357:F
1347:=
1297:n
1293:x
1287:0
1272:n
1268:x
1262:1
1256:{
1251:=
1248:)
1237:n
1233:x
1229:(
1226:I
1223:=
1220:)
1215:n
1211:x
1207:(
1202:n
1198:m
1170:)
1165:2
1157:,
1154:0
1151:(
1146:N
1136:n
1132:w
1100:)
1095:n
1091:x
1087:(
1082:n
1078:m
1057:)
1052:2
1044:,
1041:0
1038:(
1033:N
1023:n
1019:w
992:N
987:2
977:=
974:)
959:(
951:=
946:2
916:E
889:n
885:x
879:N
874:1
871:=
868:n
858:N
855:1
850:=
812:n
808:x
804:=
801:)
796:n
792:x
788:(
783:n
779:m
756:n
752:x
726:2
696:E
671:)
668:)
663:N
659:x
655:(
650:N
646:m
642:,
636:,
633:)
628:1
624:x
620:(
615:1
611:m
607:(
604:f
584:N
578:n
572:1
568:,
563:n
559:m
538:)
535:)
530:N
526:x
522:(
517:N
513:m
509:,
503:,
500:)
495:1
491:x
487:(
482:1
478:m
474:(
471:f
468:=
436:)
431:n
427:x
423:(
418:n
414:m
391:n
387:x
366:n
340:n
336:w
313:n
309:w
305:+
299:=
294:n
290:x
269:N
179:)
173:(
161:)
155:(
150:)
146:(
132:.
106:)
100:(
95:)
91:(
81:.
55:)
51:(
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