Wireless Pers Commun (2008) 44:263–282
DOI 10.1007/s11277-007-9375-z
A Survey on Wireless Position Estimation
Sinan Gezici
Published online: 2 October 2007
© Springer Science+Business Media, LLC. 2007
Abstract In this paper, an overview of various algorithms for wireless position estimation
is presented. Although the position of a node in a wireless network can be estimated directly
from the signals traveling between that node and a number of reference nodes, it is more
practical to estimate a set of signal parameters first, and then to obtain the final position
estimation using those estimated parameters. In the first step of such a two-step positioning
algorithm, various signal parameters such as time of arrival, angle of arrival or signal strength
are estimated. In the second step, mapping, geometric or statistical approaches are commonly
employed. In addition to various positioning algorithms, theoretical limits on their estimation
accuracy are also presented in terms of Cramer–Rao lower bounds.
Keywords Position estimation · Cramer–Rao lower bound · Mapping techniques ·
Bayerian estimation · Maximum likelihood estimation
1 Introduction
Recently, the subject of positioning in wireless networks has drawn considerable attention.
With accurate position estimation, a variety of applications and services such as enhanced-
911, improved fraud detection, location sensitive billing, intelligent transport systems, and
improved traffic management can become feasible for cellular networks [1]. For short-range
networks, on the other hand, position estimation facilitates applications such as inventory
tracking, intruder detection, tracking of fire-fighters and miners, home automation and patient
monitoring [2]. These potential applications of wireless positioning have also been recognized
by the IEEE, which set up a standardization group 802.15.4a for designing a new physical
layer for low-data rate communications combined with positioning capabilities [3]. Also, the
Federal Communications Commission (FCC) in the US has required wireless p roviders to
locate mobile users within tens of meters for emergency 911 calls [4].
S. Gezici (
B
)
Department of Electrical and Electronics Engineering, Bilkent University, Bilkent, Ankara 06800, Turkey
e-mail: gezici@ee.bilkent.edu.tr
123
264 S. Gezici
Fig. 1 a Direct positioning, b two-step positioning
In order to realize potential applications of wireless positioning, accurate estimation of
position should be performed even in challenging environments with multipath and non-line-
of-sight (NLOS) propagation [5]. For accurate position estimation, the details of the position
estimation process and its theoretical limits should be well-understood. Position estimation
can be defined as the process of estimating the position of a node,
1
called the “target” node, in
a wireless network by exchanging signals between the target node and a number of reference
nodes.
2
The position of the target node can be estimated by the target node itself, which is
called self-positioning, or it can be estimated by a central unit that obtains information via
the reference nodes, which is called remote-positioning (network-centric positioning)[6].
Also, depending on whether the position is estimated from the signals traveling between the
nodes directly or not, two different position estimation schemes can be considered. Direct
positioning refers to the case in which the position estimation is performed directly from
the signals traveling between the nodes [7]. On the other hand, two-step positioning extracts
certain signal parameters from the signals first, and then estimates the position based on those
signal parameters (Fig. 1). Although the two-step positioning is suboptimal in general, it can
have significantly lower complexity than the direct approach. Also, the performance of the
two approaches are usually very close for sufficiently high signal bandwidths and/or signal-
to-noise ratios (SNRs) [7,8]. Therefore, the two-step positioning is the common technique
in most positioning systems, which is the main focus of this paper.
In the first step of a two-step positioning algorithm, signal parameters, such as time-of-
arrival (TOA) and received signal strength (RSS), are estimated. Then, in the second step,
the position of the target node is estimated based on the signal parameters obtained in the
first step, as shown in Fig. 1b. In the second step of position estimation, mapping (fingerprint-
ing) approaches, geometric or statistical techniques can be used depending on the accuracy
requirements and system constraints.
The remainder of the paper is organized as follows. In Sect. 2, estimation of position related
signal parameters is studied, and RSS, angle-of-arrival (AOA), TOA, time-difference-of-
arrival (TDOA), and other parameter estimation schemes are investigated. Then, in Sect. 3,
position estimation schemes based on mapping, geometric and statistical approaches are
studied, and theoretical limits are presented in terms of Cramer–Rao lower bounds (CRLBs).
Finally, some concluding remarks are made in Sect. 4.
2 Estimation of Position Related Parameters
In the first step of a two-step positioning algorithm, position related parameters of the sig-
nals traveling between the target node and a number of reference nodes are estimated. For
1
A “node” refers to any device involved in the position estimation process, such as a cellular phone, a base
station or a wireless sensor.
2
In this article, radiolocation is considered, which is the process of position estimation through the use of
radio signals. Other techniques for position estimation include dead-reckoning and proximity systems [1].
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A Survey on Wireless Position Estimation 265
Fig. 2 One node measures the RSS and determines the distance d between itself and the other node, which
defines a circle of uncertainty
self-positioning, the signals received by the target node are used by the target node itself
for parameter estimation. On the other hand, for remote-positioning, each reference node
can estimate the parameter(s) of the signal it receives from the target node, and forward its
estimate to a central unit.
3
In other words, the parameter estimation block in Fig. 1b resides
in the target node for self-positioning systems and in the reference nodes, with each node
estimating a subset of the total signal parameters, for remote-positioning systems.
Depending on accuracy requirements and system constraints, various signal parameters
can be estimated in the first-step of a positioning algorithm. Commonly, signal parameters
employed in positioning are related to power, direction and/or timing of a received signal.
2.1 Received Signal Strength (RSS)
The power, or energy, of a signal traveling between two nodes is a signal parameter that
contains information related to the distance (“range”) between those nodes. This parameter,
commonly referred to as RSS, can be used together with a path-loss and shadowing model
to provide a distance estimate. Therefore, in the error-free case, an RSS estimate at a node
determines the position of the other node on a circle for two-dimensional positioning,
4
as
shown in Fig. 2.
A signal traveling from one node to another experiences fast (multipath) fading, shadow-
ing and path-loss [9]. Ideally, averaging RSS over a sufficiently long time interval excludes
the effects of multipath fading and shadowing, which results in the following model:
5
¯
P(d) = P
0
− 10n log
10
(d/d
0
), (1)
where n is the path loss exponent,
¯
P(d) the average received power in dB at a distance d,
and P
0
is the received power in dB at a short reference distance d
0
.
In practice, the observation interval is not long enough to mitigate the effects of shad-
owing. Therefore, the received power is commonly modeled to include both path-loss and
shadowing effects, the latter of which are modeled as a zero mean Gaussian random variable
with a variance of σ
2
sh
in the logarithmic scale. Therefore, the received power P(d) in dB can
be expressed as
P(d) ∼
N
¯
P(d), σ
2
sh
, (2)
3
It is also possible to forward the received signals directly to the central unit, and to perform both parameter
and position estimation there. However, this approach has considerably higher complexity and is not com-
monly preferred for two-step positioning systems. However, for direct-positioning systems, that is the only
way to perform remote positioning.
4
Two-dimensional positioning is considered in this paper for the convenience of illustrations.
5
Note that there is also thermal noise in real systems, which is commonly position-dependent. It is assumed
that the effects of thermal noise are sufficiently mitigated [10].
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266 S. Gezici
Fig. 3 AOA measurement between two nodes
where
¯
P(d) is as given in (1). Note that this model can be used in both line-of-sight (LOS)
and NLOS scenarios with an appropriate choice of channel parameters.
From the received power model in (2), the CRLB for unbiased distance estimators can be
expressed as [10]
Var{
ˆ
d}≥
(ln 10)σ
sh
d
10 n
, (3)
where
ˆ
d represents an unbiased estimate for the distance d.From(3), it is observed that the
RSS estimates get more accurate as the standard deviation of the shadowing decreases, since
RSS estimates vary less around the true average power in that case. Also a larger path-loss
exponent results in a smaller lower bound, as the average power becomes more sensitive to
distance for larger n. Finally, the accuracy deteriorates as the distance between the nodes
increases.
2.2 Angle of Arrival (AOA)
The angle between two nodes can be determined by estimating the AOA parameter of a signal
traveling between the nodes (Fig. 3). Commonly, antenna arrays are employed in order to
estimate the AOA of a signal.
6
The main principle behind the AOA estimation via antenna
arrays is that differences in arrival times of an incoming signal at different antenna elements
include the angle information if the array geometry is known.
For narrowband signals, time differences can be represented as phase shifts. Therefore,
the combinations of the phase shifted versions of received signals at different array elements
can be tested in order to estimate the AOA [1]. However, for wideband systems, time delayed
versions of received signals should be considered, since a time delay cannot be represented
by a unique phase value for a wideband signal.
In order to study the effects of system parameters on the achievable accuracy of an AOA
estimator, consider a uniform linear array (ULA) with N
a
elements and assume the same
fading coefficient α for all signals arriving at the array elements. Then, the CRLB on the
variance of unbiased AOA estimators can be expressed as [12,13]
Var{
ˆ
ψ}≥
√
3 c
√
2 π
√
SNR β
N
a
(N
2
a
− 1) sin ψ
, (4)
where ψ is the AOA, c the speed of light, SNR = α
2
E/N
0
is the signal-to-noise ratio for each
element, with E denoting the signal energy and
N
0
being the spectral density of background
6
Another approach is to use the ratio of RSS estimates between at least two directional antennas located on
a node [11].
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A Survey on Wireless Position Estimation 267
noise,
7
the inter-element spacing, and β is the effective bandwidth defined by
β =
1
E
∞
−∞
f
2
|S( f )|
2
d f
1/2
(5)
with S( f ) representing the Fourier transform of the received signal.
From (4), it is observed that as the SNR, effective bandwidth, inter-element spacing and/or
the number of antenna elements is increased, the accuracy of AOA estimation increases. It is
also noted that a ULA provides the best AOA estimation accuracy when the signal direction
and the ULA line are perpendicular to each other.
2.3 Time of Arrival (TOA)
Similar to the RSS parameter, estimating the flight time of a signal traveling from one node to
another, called TOA, provides information related to the distance between those two nodes.
Therefore, in the absence of any errors, a TOA estimate provides an uncertainty region in the
shape of a circle as shown in Fig. 2.
In order to calculate the TOA parameter for a signal traveling between two nodes, the nodes
must either have a common clock, or exchange timing information by certain protocols such
as a two-way ranging protocol [3,14,15].
Conventionally, TOA estimation is performed via correlator or matched filter (MF) receiv-
ers [16]. Consider a scenario in which s(t) is transmitted from a node to another, and the
received signal is expressed as
r(t) = s(t − τ)+ n(t), (6)
where τ represents the TOA and n(t) is white Gaussian noise with zero mean and a spectral
density of
N
0
/2. Then, the correlator-based approach correlates the received signal with a
local template s(t −ˆτ) for various delays ˆτ , and calculates the delay corresponding to the
correlation peak. Similarly, the MF approach employs a filter that is matched to the transmit-
ted signal and estimates the instant at which the filter output reaches its largest value. Both
approaches are optimal in the maximum likelihood (ML) sense for the signal model in (6).
However, in practical systems, the signal arrives at the receiver via multiple signal paths. In
such multipath e nvironments, the conventional schemes become suboptimal as they use the
transmitted signal to set their template signals or MF impulse responses.
8
In order to obtain
accurate TOA estimation in multipath env ironments, high-resolution time delay estimation
techniques, such as that described in [17], have been studied for narrowband systems, and
first path detection algorithms are proposed for ultra-wideband (UWB) systems [14,18–20].
In order to observe the main relations between the signal bandwidth and the theoretical
limits for TOA estimation, consider the CRLB for the signal model in (6), which is given by
Poor [21], Cook and Bernfeld [22]
9
Var( ˆτ) ≥
1
2
√
2π
√
SNR β
, (7)
where ˆτ represents an unbiased TOA estimate, SNR = E/
N
0
is the SNR, with E denoting
the signal energy, and β is the effective signal bandwidth defined by (5).
7
The same average noise power is assumed at each element.
8
Since the effects of the propagation environment, such as the multipath, are not known at the time of TOA
estimation, the use of a template signal or a MF impulse response that includes the overall effects of the
channel is not usually possible.
9
Refer to [5,23] for the CRLB for TOA estimation in multipath channels.
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