In less-weights to) the NLOS range information.

In most cited applications, awareness of location
information is fundament1al
since collected data are meaningless without any geographical context. For
example, if a ?re forest is detected, we need to know where the detection
occurred in order to intervene.

Therefore, sensor localization has become a fundamental
issue, especially in wireless sensor networks, where sensors lack for a ?xed
infrastructure and are able to move in an uncontrollable manner. However, there
are unresolved problems that impede the progress of accurate position
estimation using time-of-arrivals (TOAs) or time-differences- of-arrivals
(TDOAs). One of the key issues is the nonexistence of the line-of-sight (LOS)
ray in many indoor and outdoor environments. None-line-of-sight (NLOS)
propagation takes place when there are obstructions (e.g., walls, vegetation,
buildings, mountains, etc.) between the transmitter (TX) and receiver (RX).
Under such conditions, performances of the conventional TOA- or TDOA-based
localization schemes that depend heavily on the LOS assumption are highly
deteriorated. One typical example is the GPS (Global Position System) 4 that
cannot function properly in indoor environments 5.


Some non TOA- or TDOA-based localization schemes have
been proposed to mitigate the NLOS propagation (e.g., see 12-16). In order to
deal with the fact that detailed information of the environment is generally
not available, the main idea of these approaches is based on a pattern-matching
localization technique (called fingerprinting) using the received signal
strength indicator (RSSI). For example, the Weighted K- Nearest Neighbor (WKNN)
scheme in 14 computes the Euclidean distances between RSSIs of an unknown
node and RSSIs of the reference nodes. Then the K-nearest reference nodes are
found and used to estimate the position of the unknown node. A more accurate
fingerprinting scheme is proposed in 15-16 where the powerful kernel methods
17-18 are employed to improve the sensitivity

and accuracy in pattern matching. However, due to the fading


nature of RSSIs, the reference nodes need to be uniformly and
densely distributed in the area of interests so as to achieve a better accuracy


Some TOA- and TDOA-based localization schemes have also
been proposed to mitigate the NLOS propagation (e.g., see 6-11). In 6-9,
the main idea of the proposed approaches is to firstly distinguish NLOS from
LOS and secondly discard (or give less-weights to) the NLOS range information.
But in practice there is a high possibility of false-alarms (mistaking a LOS
measurement as NLOS) and missed-detections (mistaking a NLOS measurement as
LOS) because most propagation environments are very complex and the information
of the environments are usually not fully available. To overcome this
shortcoming, a semidefinite programming method has been proposed in 10. It
does not need to distinguish the NLOS from the LOS range estimates, but it
still needs to know the distribution of NLOS errors. A further improvement is
proposed in 11 where a semidefinite relaxation is considered. But it is a
centralized approach which requires greater processing time and cannot scale
with the size of the network.


Recently, a TDOA fingerprinting method is introduced in
19. It uses the spatial sparsity of a transmitter and apply compressed
sensing to estimate the transmitter’s position. As the approach uses a simple pattern
matching procedure (where the best estimation error is of the order of the grid
size), it suffers several drawbacks. Firstly, the region of interests needs to
be divided into very fine uniform grids in order to acquire a better
localization accuracy. Secondly, the localization accuracy is very sensitive to
TDOA measurement errors. Thirdly, it requires a huge fingerprint database as
its size is proportional to the number of grids. Fourthly, the approach can
essentially localize accurately only one transmitter at a time. To mitigate
these drawbacks, we adopt the Kernel-based machine learning scheme in 15 and
propose in this paper a robust TOA localization approach. Like 19, whether
the first arrivals at the receivers are from LOS or not is irrelevant because
what is important in a fingerprinting approach is the similarity of TOAs among
neighboring nodes. In addition, the proposed approach can use TDOAs (instead of
TOAs) because a constant timing bias on all measured TOAs does not change our
similarity measure of any two nodes. However, unlike 19, the proposed
approach can use coarsely and randomly distributed reference nodes (grids) to
give good localization results. Moreover, the proposed approach is insensitive to
random synchronization and measurement timing errors. Comparing to the RSSI
machine learning localization approach in 15, it is shown that the
localization accuracy obtained by using TOAs or TDOAs is much better than that
using RSSI.