Unified Fingerprinting/Ranging Localization in Harsh Environments

Abstract

Context-awareness in wireless sensor networks (WSNs) relies mainly on the position of objects and humans. The provision of this positional information becomes challenging in the harsh environmental conditions where WSNs are commonly deployed. With an antagonistic philosophy of design, fingerprinting and ranging have emerged as the key technologies underpinning wireless localization in harsh environments. Fingerprinting primarily focuses on accurate estimation at the expense of exhaustive calibration. Ranging mainly pursues an easy-to-deploy solution at the expense of moderate performance. In this paper, we present a resilient framework for sustained localization based on accurate fingerprinting in critical areas and light ranging in noncritical spaces. Such framework is conceived from the Bayesian perspective that facilitates the specification of recursive algorithms for real-time operation. In comparison to conventional implementations, we assessed the proposed framework in an indoor scenario with measurements gathered by commercial devices. The presented techniques noticeably outperform current approaches, enabling a flexible adaptation to the fluctuating conditions of harsh environments.

1. Introduction

The burgeoning demand for context-aware services and smarter environments has been largely motivated by the proliferation of the increasingly dense wireless sensor networks (WSNs) and intelligent embedded devices [1–5]. These services and environments accommodate applications in diverse fields such as healthcare [6–8], emergency [9–11], or industry [12–14]. In order to satisfy such a demand, the positional information plays a crucial role and has inevitably put indoor localization in the forefront of research [15–21]. Current positioning techniques that rely on global navigation satellite systems (GNSS) operate robustly in open areas and sparse environments [16, 22]. However, there is no alternative technique with analogous performance and affordable complexity in indoor areas or harsh environments [23, 24]. The proposed alternatives can be coarsely classified into fingerprinting and ranging localization techniques [25–35].

Fingerprinting techniques determine the location of a mobile target from position-related information provided by offline and online measurements [25–28]. In the offline phase, different features from the transmitted signals in the wireless network are stored at several positions to form a database of location fingerprints. In the online phase, the position is estimated by comparison of the new received values with the database (i.e., with their fingerprint). Fingerprinting techniques involve two major drawbacks: they require an arduous offline phase of calibration and are very sensitive to fast environmental changes [25].

Ranging techniques determine the location of a mobile target from range-related information provided by time-of-arrival (TOA) [29–31] or received signal-strength (RSS) [32–34] measurements. In a first stage, the distance to a set of anchors with known positions is estimated from the signals transmitted to the target. In a second stage, the position is estimated by a process known as trilateration (i.e., intersection of circles). Ranging techniques suffer from two dominant limitations: their accuracy is far from fingerprinting methods and falls down under multipath and non-line-of-sight (NLOS) conditions [35].

Strengths and weaknesses of fingerprinting and ranging localization have inevitably focused the challenge in developing unifying systems without substantially increasing complexity and cost. Such solutions will enable fine localization via fingerprinting in places where the accuracy is critical or when the database can be frequently updated and coarse localization via ranging in areas where there is no database or when it has become obsolete. In [36], fingerprint- and TOA-based methods are coupled to localize UWB devices from a maximum-likelihood (ML) perspective; in [37], fingerprint- and RSS-based techniques are fused by using RFID tags/readers and particle filtering; in [38], fingerprint-based localization and channel-estimation tracking are combined to localize UWB devices via extended Kalman filter (EKF); in [39], fingerprinting positioning and pyroelectric infrared sensors are joined to overcome error induced by RSS variation.

In this paper, we propose framework and algorithms for unified fingerprinting/ranging in harsh environments based on Bayesian filtering. Such framework integrates position-related measurements from the first and range-related measurements from the second. Moreover, it further considers the dynamic nature of the wireless channel entailing more accurate ranging localization. Specifically, the main contributions of the paper are as follows: (i)

We define a unifying framework for target localization that accommodates fine estimates via fingerprinting and coarse estimates via ranging.

(ii)

We provide realistic likelihood functions to model fingerprints and path-loss exponents based on kernel mixtures.

(iii)

We derive algorithms to implement such framework by means of the unscented transformation that allows for efficient computation.

(iv)

We assess the performance of the developed framework and algorithms in a real scenario over conventional light devices.

The rest of the paper is organized as follows: Section 2 outlines the multiagent architecture proposed in previous works for information fusion; Section 3 presents the framework for unified data fusion of fingerprinting/ranging measurements; Section 4 offers efficient algorithms to enable real-time operation under the proposed framework; Section 5 assesses the provided algorithms under an experimental case study with light devices; and Section 6 summarizes the conclusions drawn from the research.

Notations. $x_{1 : k}$ denotes the sequence of random vectors ${x_{1}, \dots, x_{k}}$ ; ${[\cdot]}^{T}$ denotes the transpose of its argument; $I_{n} \in R^{n \times n}$ denotes the $n \times n$ identity matrix; $f (x)$ denotes the probability density function of a continuous random variable x; and $φ (x; μ, Σ)$ denotes the probability density function of a Gaussian random vector $x ~ N (μ, Σ)$ .

2. Previous Work

This section provides a general overview of the multiagent architecture based on virtual organizations that we presented recently to accomplish the information fusion problem [40]. The virtual organization of agents manages the resources of the Cloud system in which it is deployed. It was created with the PANGEA platform that facilitates the development of agents in light devices and the integration of different hardware [41, 42]. The architecture is organized in $4$ layers as can be seen in Figure 1 and that is what we briefly describe here for completeness [40].

Figure 1

The architecture presented in previous works consists of a multiagent architecture based on virtual organizations that integrates with an information fusion model [40].

Layer 0. It defines communication with sensor networks of different nature and gets the raw (encapsulated) data from them.

Layer 1. It processes the contextual information obtained from layer 0 and provides a set of low-level services for this purpose.

Layer 2. It incorporates agents specifically designed to interact with layer 1 and brings others specialized in information fusion.

Layer 3. It allows the management and customization of services to end users and facilitates decision-making by the user.

In the presented architecture, the fusion of different information flows is accomplished in layer 2. However, the low-level services that extract information from row data are implemented in layer 1. The greater the information extracted regarding a parameter in layer 1 the better the performance of the fusion model in layer 2 [43, 44]. In our previous work, we focused on layer 2, specifically on workflow and fusion organizations [40]. In this paper, we focus on layer 1 and layer 2, specifically on the processing of RSS data to extract position-related information.

3. Localization Framework

In this section, we formulate the problem of localization in harsh environments and provide a general framework for its solution based on optimal recursive Bayesian filtering [45, 46].

3.1. Problem Statement

In the following, we are going to assume a two-dimensional scenario where we estimate the position of a mobile target by fusing information provided by RSS measurements. In order to do that, we first accomplish an offline phase in which we collect RSS measurements at a set of M fingerprint points, ${f_{m}}_{m = 1}^{M}$ , covering only a selected area. In the online phase, we collect again RSS measurements, ${y_{k}}_{k \in N}$ , at discrete time instants, $t_{k \in N}$ , inside or outside the selected area (hereinafter, “fingerprinting area” or “ranging area,” resp.). From these measurements, we estimate the state vector, ${x_{k}}_{k \in N}$ . Next, we determine the entries to state and measurement vectors.

The state vector contains the position and its first derivatives so that ${x_{k}}_{k \in N}$ is a Markov chain (i.e., the current state only depends on the previous one) [35, 45]. In this paper, such a vector is augmented to include the path-loss exponent with respect to every anchor used in the ranging area (see Section 3.2). Therefore, the state vector is $x_{k} = [p_{k}, v_{k}, a_{k}, β_{k}] \in R^{6 + L}$ , where $p_{k} \in R^{2}$ is the target's position, $v_{k} \in R^{2}$ its velocity, $a_{k} \in R^{2}$ its acceleration, $β_{k} \in R^{L}$ the vector of path-loss exponents, and $L \in R$ the total number of anchors used for ranging.

The measurement vector conveys any state-related information received at time instant $t_{k}$ (i.e., its dimension may be different from the previous one). We have to use different measurements vector depending on whether we are within the fingerprinting or the ranging area. In the former case, the state vector is $y_{k} = y_{k}^{f} \in R^{L_{k}}$ , where $y_{k}^{f} \in R^{L_{k}}$ are the RSS measurements received at time $t_{k}$ . In the latter case, the state vector is $y_{k} = [y_{k}^{s}, y_{k}^{β}] \in R^{2 L_{k}}$ , where $y_{k}^{s} \in R^{L_{k}}$ are the RSS measurements received at time $t_{k}$ and $y_{k}^{β} \in R^{L_{k}}$ the path-loss exponents measured with respect to the visible anchors. In both cases, $L_{k} \in R$ is the number of visible anchors at that particular moment.

In addition to the information conveyed by the measurements, the fact that the sequence of positions is highly correlated in time can also be used as another source of information. With the defined measurements and state vectors, it can be assumed that, given the current state vector, $x_{k}$ , the measurement vector, $y_{k}$ , is independent of all previous and future states and measurements [35, 45]. Therefore, we can build the hidden Markov model (HMM) shown in Figure 2 that leads to two kinds of dependence between the random variables: the relationship between the state vector in time $t_{k}$ and the state vector in time $t_{k - 1}$ , that is, $f (x_{k} | x_{k - 1})$ , called dynamic model; and the relationship between the measurements and the state vector in each time, that is, $f (y_{k} | x_{k})$ , called measurements model [35, 45]. (Note that, in addition to different measurements vectors, we have to use different measurements models for fingerprinting and ranging areas since the unknown dependencies between them prevent us from utilizing a joint model.) Next subsection defines both models for fingerprinting/ranging localization in harsh environments. (The proposed framework accommodates other position-related information given by diverse devices such as GPS receivers or foot-mounted inertial measurement units [47].)

Figure 2

HMM for states and measurements evolution. The relationship between $x_{k}$ and $x_{k - 1}$ and the relationship between $y_{k}$ and $x_{k}$ are the only two kinds of dependence.

3.2. Involved Models

In the following, we define realistic models for the fusion of time-evolution and measuring information.

3.2.1. Dynamic Model

The dynamic model is characterized by the conditional density $f (x_{k} | x_{k - 1})$ .

Given the position, velocity, and acceleration at time $t_{k - 1}$ , $p_{k - 1}$ , $v_{k - 1}$ , and $a_{k - 1}$ , we can approximate their values in time $t_{k}$ , $p_{k}$ , $v_{k}$ , and $a_{k}$ , by means of their Taylor series expansion as [45]

\begin{matrix} [\begin{bmatrix} p_{k} \\ v_{k} \\ a_{k} \end{bmatrix}] = (\begin{pmatrix} I_{2} & Δ_{k} I_{2} & \frac{Δ_{k}^{2}}{2} I_{2} \\ 0 & I_{2} & Δ_{k} I_{2} \\ 0 & 0 & I_{2} \end{pmatrix}) [\begin{bmatrix} p_{k - 1} \\ v_{k - 1} \\ a_{k - 1} \end{bmatrix}] + n_{k}^{d, 1}, \end{matrix}

(1)

where

Δ_{k} = (t_{k} - t_{k - 1}) \in R

is the sampling interval and

n_{k}^{d, 1} \in R^{6}

is the error term. To model this error term as white Gaussian noise (i.e., as a discrete Wiener process) is the most common.

The characteristics of the wireless channel are highly related in time [48–50]. However, this fact is rarely considered in the design of positioning filtering algorithms [51]. In this paper, given the vector of path-loss exponents at time $t_{k - 1}$ , $β_{k - 1}$ , the vector of path-loss exponents at time $t_{k}$ , $β_{k}$ , is modeled as

\begin{matrix} β_{k} = β_{k - 1} + n_{k}^{d, 2}, \end{matrix}

(2)

where the term

n_{k}^{d, 2} \in R^{L}

is white Gaussian noise.

Therefore, the dynamic model, $f (x_{k} | x_{k - 1})$ , is given by

\begin{matrix} f (x_{k} | x_{k - 1}) = φ (x_{k}; F_{k} x_{k - 1}, Σ_{k}^{d}), \end{matrix}

(3)

where the transition matrix

\begin{matrix} F_{k} = (\begin{pmatrix} I_{2} & Δ_{k} I_{2} & \frac{Δ_{k}^{2}}{2} I_{2} & 0 \\ 0 & I_{2} & Δ_{k} I_{2} & 0 \\ 0 & 0 & I_{2} & 0 \\ 0 & 0 & 0 & I_{L} \end{pmatrix}) \end{matrix}

(4)

and

Σ_{k}^{d} \in R^{(6 + L) \times (6 + L)}

is the covariance matrix corresponding to the noise vector

[n_{k}^{d, 1}, n_{k}^{d, 2}]

3.2.2. Ranging Likelihood

The measurements model in ranging areas is characterized by the likelihood $f (y_{k}^{s} | x_{k})$ .

The RSS values are attenuated, among other factors, by the distance between target and anchors. This attenuation is proportional to the inverse of the distance raised to a path-loss exponent [34, 35]. In logarithmic units, we have that, for the lth anchor, with position $p^{(l)} \in R^{2}$ ,

\begin{matrix} y_{k}^{s} = α - 10 β_{k} \log_{10} ‖p^{(l)} - p_{k}‖ + n_{k}^{s}, \end{matrix}

(5)

where

α \in R

is a constant that depends on several factors such as fast and slow fading, gains in transmitter and receiver antennas, and the transmitted power and

β_{k} \in R

is the path-loss exponent that characterizes the wireless channel [49]. Finally,

n_{k}^{s}

is a Gaussian noise term caused by shadowing [34, 35]. The value of α can be previously known, for example, by averaging measured values at the reference distance (in this case,

1

meter away from the anchor) or by self-calibration with measurements shared among anchors (with known positions) [18]. The path-loss exponent,

β_{k}

, in turn, can be dynamically obtained or trained in each scenario [27, 34].

Then, the RSS measurements in ranging areas are governed by the likelihood,

\begin{matrix} f (y_{k}^{s} | p_{k}) = φ (y_{k}^{s}; α - 10 β_{k} \log_{10} ‖p^{(l)} - p_{k}‖, σ_{k}^{s}), \end{matrix}

(6)

where

σ_{k}^{s} \in R

is the standard deviation corresponding to

n_{k}^{s}

Figure 3 represents the performance of the likelihood function defined in (6). Figure 3(a) depicts the position of the anchors with known positions (in orange) as well as the position of the target (in red). Figure 3(b) shows the likelihood values obtained in the area by means of (6) after receiving one RSS measurement from every anchor. Figure 3(c) shows the likelihood values in the fixed axis (indicated in Figure 3(b)) obtained by means of (6) for different numbers of RSS measurements received from anchor $A P 1$ . From Figure 3 we can point out that the greater the number of measurements the narrower the likelihood in the direction joining target and anchor. This result is in concordance with the known fact that each range measurement only provides information about the position in the direction joining target and anchor [17].

Figure 3

The defined likelihood for ranging areas provides a continuous function that facilitates the information fusion under the Bayesian framework.

In order to generalize the localization framework, we here consider the most general case where path-loss exponents are dynamically estimated, for which a variety of algorithms can be found in the literature [34, 52–56]. Specifically, we adhere to the technique proposed in [34] based on maximizing the compatibility of the distances between the target and the anchors given a set of received RSS values and subject to a set of feasible solutions, Λ. (The set of constrains can come, e.g., from feasible distances between the target and the anchors based on transmission power and antenna gains [34].) That is,

\begin{matrix} {\hat{β}}_{k} = \underset{β_{k}}{argmax} C (y_{k}^{s}, α, β_{k}, p_{k}, {\{p^{(l)}\}}_{l = 1, \dots, L_{k}}) s.t. β_{k} \in Λ, \end{matrix}

(7)

where

C (\cdot)

is the compatibility function as defined in [34].

Given the actual state, we can treat estimates of path-loss exponents as independent additional measurements, $y_{k}^{β}$ , related with the state by the model

\begin{matrix} y_{k}^{β} = β_{k} + n_{k}^{β}, \end{matrix}

(8)

where

n_{k}^{β} \in R^{L}

is white Gaussian noise. (Note that this is a mild assumption since the main relationship between RSS measurements and path-loss exponents is given by the distance between target and anchor, and the remaining possible dependencies are unknown).

Then, the measured path-loss exponents in ranging areas are governed by the likelihood

\begin{matrix} f (y_{k}^{β} | β_{k}) = φ (y_{k}^{β}; β_{k}, Σ_{k}^{β}), \end{matrix}

(9)

where

Σ_{k}^{β} \in R^{L \times L}

is the covariance matrix corresponding to the noise vector

n_{k}^{β}

Therefore, the whole measurements model, $f (y_{k}^{s} | x_{k})$ , for ranging areas is given by (6) and (9).

3.2.3. Fingerprinting Likelihood

The measurements model in fingerprinting areas is characterized by the likelihood $f (y_{k}^{f} | x_{k})$ .

During the offline phase, for the mth fingerprint, $f_{m}$ , we receive a set of $S_{m}^{(l)}$ RSS measurements, $y_{m}^{(l)}$ , from each one of the visible anchors. We assume that the random variable associated with such a set of measurements follows a Gaussian distribution with mean its sample mean, ${\bar{y}}_{m}^{(l)}$ , and standard deviation $σ_{m}^{(l)} / \sqrt{S_{m}^{(l)}}$ , where $σ_{m}^{(l)}$ is the sample standard deviation. During the online phase, given a set of received RSS measurements— $y_{k}^{f} \in R^{L_{k}}$ —the likelihood function of the fingerprint $f_{m}$ is given by

\begin{matrix} f (y_{k}^{f} | f_{m}) = \prod_{l = 1}^{L_{k}} φ (y_{k}^{(l)}; {\bar{y}}_{m}^{(l)}, \frac{σ_{m}^{(l)}}{\sqrt{S_{m}^{(l)}}}), \end{matrix}

(10)

where

y_{k}^{(l)}

is an RSS measurement received from the lth anchor in

t_{k}

By considering a Gaussian kernel to represent the region of the map corresponding to each fingerprint [26, 28], we can approximate the measurements model by a mixture of the individual likelihood at every point of the set ${f_{m}}_{m = 1}^{M}$ as

\begin{matrix} f (y_{k}^{f} | p_{k}) \approx \sum_{m = 1}^{M} f (y_{k}^{f} | f_{m}) φ (p_{k}; f_{m}, h^{2} I_{2}) \approx \sum_{m = 1}^{M} ω_{k}^{(m)} φ (p_{k}; f_{m}, h^{2} I_{2}), \end{matrix}

(11)

where

f_{m} \in R^{2}

includes the coordinates of the mth fingerprint and

h \in R

is a positive number called bandwidth [26, 35, 57]. (A practical choice for the bandwidth can be obtained as one-half the resolution of the involved data, in this case, the change in coordinates between two adjacent fingerprints [35].)

Figure 4 represents the performance of the likelihood function defined in (11). Figure 4(a) depicts the position of the fingerprints stored in the offline phase (in grey) as well as the position of the target during the online phase (in red). Figure 4(b) shows the likelihood values obtained in the area by means of (11) after receiving one RSS measurement in the online phase. Figure 4(c) shows the likelihood values in the fixed axis (indicated in Figure 4(b)) obtained by means of (11) for different numbers of RSS measurements received during the online phase. From Figure 4 we can conclude that the greater the number of measurements the more likely the position of the closest fingerprint to the actual position. Moreover, the use of a kernel mixture provides a continuous function that facilitates the information fusion under the Bayesian framework.

Figure 4

The defined likelihood for fingerprinting areas provides a continuous function that facilitates the information fusion under the Bayesian framework.

The previous likelihood can be augmented to incorporate the information conveyed by the fingerprints with respect to the path-loss exponents. In such a case, the fingerprint vector $f_{m} \in R^{2 + L}$ includes its positional coordinates as well as the path-loss exponents with respect to each anchor used for ranging localization. The path-loss exponent stored for the lth anchor and the mth fingerprint is obtained as [34, 35]

\begin{matrix} {\hat{β}}_{m}^{(l)} = \frac{α - {\bar{y}}_{m}^{(l)}}{10 \log_{10} ‖p^{(l)} - p^{(m)}‖}, \end{matrix}

(12)

where

{\bar{y}}_{m}^{(l)}

is the sample mean of the set of measurements received in the offline phase from the l-anchor at the mth fingerprint and

p^{(l)}

and

p^{(m)}

are the coordinates corresponding to such anchor and fingerprint, respectively.

Therefore, the measurements model, $f (y_{k}^{f} | x_{k})$ , for fingerprinting areas is given by

\begin{matrix} f (y_{k}^{f} | p_{k}, β_{k}) \approx \sum_{m = 1}^{M} ω_{k}^{(m)} φ ([p_{k}, β_{m}]; f_{m}, H), \end{matrix}

(13)

where

f_{m} \in R^{2}

includes the coordinates and the path-loss exponents for the mth fingerprint and

H \in R^{(2 + L) \times (2 + L)}

is a diagonal bandwidth matrix with positive diagonal elements

{h_{i}^{2}}_{i = 1, \dots, 2 + L}

[26, 35, 57].

4. Efficient Algorithms

The graphical model depicted in Figure 2 allows for optimal localization by means of the well-known Bayesian filtering process [45, 46]. In the following, we propose an efficient implementation for real-time localization systems in light devices.

4.1. Real-Time Filtering for Localization

Bayesian filtering acquires different expressions depending on the specific distributions of the dynamic model and the likelihood. The complexity constraints imposed by a real-time localization system and the tractability benefits of Gaussian family favor the selection of the latter for all the involved distributions [46]. Moreover, the lack of linearity in the models defined in Section 3 enforces the use of a suboptimal solution to the filtering problem. The most common is to linearize such models by Taylor series expansion (i.e., to use extended Kalman-like filters) [58]. In this paper, we select the unscented transformation since it better captures the higher order moments caused by the nonlinear transformation and avoids the computation of Jacobian and Hessian matrices [59, 60]. The complexity of both extended and unscented transformations is on the order of the cube of the dimension of the state, which cannot compromise their real-time operation [61]. Other approaches, such as particle filters or Gaussian mixture filters, are discarded since they suffer from the curse of dimensionality induced by the dimension of the state vector [61, 62]. (The number of filtered path-loss exponents, and consequently the dimension of the state, grows with the number of anchors used for ranging.)

Algorithm 1 shows the pseudocode of the unscented-based implementation for the proposed unified localization framework. (In Algorithm 1, $f (x_{1} | x_{0}) = f (x_{1})$ .)

Algorithm 1: Real-time filtering for unified localization.

(1) Initialization:

(2) Set π equal to the prior distribution of $x_{1}$ .

$μ_{π} ⟵ E \{x_{1}\}$

$Σ_{π} ⟵ E \{x_{1} x_{1}^{T}\} - μ_{π} μ_{π}^{T}$

(3) $π \leftarrow φ (x_{1}; μ_{π}, Σ_{π})$

(4) RecursiveBayesian inference:

(5) for $k = 1,2, \dots$ do

(6) (i) Prediction:

π⟵ ut_predict $(f (x_{k} | x_{k - 1}), π)$

(7) if $μ_{π} \in$ “Fingerprinting area” then

(8) (ii) Fingerprinting update:

π⟵ fp_update $(f (y_{k}^{f} | x_{k}), π)$

(9) else

(10) (iii) Path-loss estimation:

$\{β_{π}\}$ ⟵ pl_estimate $(y_{k}^{s}, {\{p^{(l)}\}}_{l = 1}^{L})$

(11) (iv) Ranging update:

π⟵ ut_update $(f (y_{k}^{s} | x_{k}), π)$

(12) end if

(13) return $E {x_{k} | y_{1 : k}} \leftarrow E {π} = μ_{π}$

(14) end for

In Algorithm 1, we utilize conventional predict (ut_predict()) and update functions (ut_update()) based on the unscented transformation [60, 63]. In the fingerprinting case, we update with a Gaussian mixture and approximate the posterior mixture density to a single Gaussian. This process is condensed within the functionfp_update() that we described in the next section. In the ranging case, we dynamically estimate the path-loss exponents previously to the update. This process is addressed in the functionpl_estimate() for which different alternatives can be adopted [34, 51–56].

4.2. Fingerprinting Update

As we stated in previous section, the real-time constraints favor the selection of the Gaussian family in the filtering process. However, we defined a Gaussian mixture for the likelihood in fingerprinting areas (see Section 3.2). The update step in Bayesian filtering consists of the product of the prediction and the likelihood (and a subsequent normalization), which leads to an exponential increase of the number of involved densities when using a likelihood mixture [45, 46]. In Algorithm 2 we address this issue by approximating the posterior mixture density to a single Gaussian density. This approximation is based on collapsing the M-component mixture arising after the update into one Gaussian with the same mean and covariance as the mixture.

Algorithm 2: Function to update state from fingerprints.

(1) function fp_update $({ω^{(m)}, P, f_{m}, H}_{m = 1}^{M}, μ, Σ)$

(2) Fingerprinting update:

(3) for $m = 1,2, \dots, M$ do

$S_{π}^{(m)} ⟵ P Σ P^{T} + H$

$K_{π}^{(m)} ⟵ Σ P^{T} {(S_{π}^{(m)})}^{- 1}$

$Σ_{π}^{(m)} ⟵ (I - K_{π}^{(m)} P) Σ$

$μ_{π}^{(m)} ⟵ μ + K_{π}^{(m)} (f_{m} - P μ)$

$ω_{π}^{(m)} ⟵ ω^{(m)} φ (f_{m}; P μ, S_{π}^{(m)})$

(4) end for

(5) Normalization:

${\{ω_{π}^{(m)}\}}_{m = 1}^{M} ⟵ \frac{{\{ω_{π}^{(m)}\}}_{m = 1}^{M}}{\sum_{m = 1}^{M} ω_{π}^{(m)}}$

(6) Gaussian approximation:

$μ_{π} ⟵ \sum_{m = 1}^{M} ω_{π}^{(m)} μ_{π}^{(m)}$

$Σ_{π} ⟵ \sum_{m = 1}^{M} ω_{π}^{(m)} (Σ_{π}^{(m)} + (μ_{π}^{(m)} - μ_{π}) {(μ_{π}^{(m)} - μ_{π})}^{T})$

(7) return $μ \leftarrow μ_{π}; Σ \leftarrow Σ_{π}$

(8) end function

Algorithm 2 shows the pseudocode of thefp_update() function, which takes as inputs the parameters that characterize the prediction, $φ (x_{k}; μ, Σ)$ , and the likelihood, $\sum_{m = 1}^{M} ω^{(m)} φ (P x_{k}; f_{m}, H)$ , where P is a matrix projecting the components of $x_{k}$ into the components stored in the fingerprints (position and path-loss exponents).

5. Results and Discussion

The goal of this section is to quantify the performance of the localization framework described in Section 3. The system is evaluated in the experimental case study of a human walking with a Smartphone that collects RSS measurements from the network. In the following, we describe the set-up for the experiments and present the performance results.

5.1. Experimental Set-Up

We selected WiFi as the underlying technology to provide indoor localization. WiFi technology is more accessible and less expensive than other alternative technologies such as RFID or UWB and has a longer range and larger bandwidth than ZigBee or Bluetooth. Moreover, from signals transmitted in the WiFi network, we can easily extract the RSS metric, while time- or angle-related measurements imply additional complexities and costs [35]. The anchors were Cisco Aironet 1600 Series Access Points (802.11a/g/n). The mobile target was a human with Smartphone LG Nexus 4 (802.11b/g/n) that covered the path shown in Figure 5(b). The total length of the path was approximately $120$ meters, implying a total time of $2$ minutes.

Figure 5

The proposed unified framework provides accurate localization via fingerprinting for critical areas and ready-to-use localization via ranging for noncritical spaces.

For fingerprinting localization, the database was created by storing at least $10$ RSS values from all the detectable access points (up to $25$ ) in the fingerprints marked in Figure 5(a). In the online phase, we employed $48$ RSS values per point.

For ranging localization, we employed $16$ RSS measurements per point from the $4$ access points plotted in Figure 5(a). All the RSS measurements were considerably affected by NLOS and multipath propagation conditions.

To obtain the localization results we utilized dynamic and measurements models described in Section 3. We also added zero-mean Gaussian priors for velocity and acceleration. For the dynamic model, we selected a diagonal noise covariance matrix, $Σ_{k}^{d}$ , with main diagonal values roughly $50$ % of the maximum [35, 45]. For the measurements model, we utilized fixed distribution parameters learned from previous works [34, 35].

5.2. Experimental Results

Figure 5(b) and Table 1 show the localization results in the mentioned path. For each implemented technique we provide the quartiles of the error in position estimates as well as the root mean square error (RMSE). We call (i)

kNN: the position estimates in the fingerprinting area with a conventional implementation based on k-Nearest Neighbor classification [15],

(ii)

ML: the position estimates in the ranging area with a conventional implementation based on maximum likelihood by using (6) [64],

(iii)

kNN + ML: the position estimates in the complete scenario with the conventional implementation based on k-Nearest Neighbor classification for fingerprinting and maximum likelihood for ranging [15, 64],

(iv)

FL: the position estimates in the fingerprinting area with the proposed algorithm,

(v)

RL: the position estimates in the ranging area with the proposed algorithm (as stated above, in order to dynamically estimate the path-loss exponents, we implemented the technique proposed in [34] based on maximizing the compatibility of the distances among anchors and target from a set of received RSS values and a set of constraints. However, other alternatives could have been implemented [52–56]),

(vi)

FL + RL: the position estimates in the complete scenario with the proposed unifying fingerprinting/ranging algorithm.

Table 1

Position estimation error quartiles and RMSE obtained with conventional and proposed algorithms.

		Quartiles	RMSE
Conventional	kNN	0.00 m-0.00 m-0.00 m	0.61 m
	ML	3.05 m-3.87 m-5.39 m	5.11 m
	kNN + ML	0.00 m-0.38 m-3.12 m	3.17 m

Proposed	FL	0.05 m-0.06 m-0.15 m	0.57 m
	RL	2.17 m-3.66 m-5.05 m	3.83 m
	FL + RL	0.06 m-0.39 m-2.91 m	2.39 m

From Figure 5(b) and Table 1 we can point out that (1) the proposed framework facilitates the shift from accurate fingerprinting to coarse ranging; (2) fingerprinting outperforms ranging in harsh environments while requiring greater calibration effort; and (3) the proposed approach improves the RMSE in ranging and fingerprinting and unified localization approximately $6.6$ %, $25.0$ %, and $24.7$ % with respect to conventional techniques, respectively. It is worth to mention that the quartiles for kNN are all equal to $0.00$ meters since we have selected online positions that matched those stored in the database.

6. Conclusions

This paper has presented a principled framework and efficient algorithms for unified fingerprinting and ranging localization based on Bayesian filtering. We have defined realistic continuous likelihood functions that adapt to the changing propagation conditions of the wireless channel. We have implemented the proposed framework with efficient algorithms via unscented transform and Gaussian mixture collapse. Under severe NLOS and multipath conditions, the presented techniques have obtained an error in position estimation of $2.39$ meters along a $120$ -meter-long path covering fingerprinting-only and ranging-only areas, remarkably outperforming conventional implementations.

Footnotes

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

This work has been supported by the project Sociedades Humano-Agente en Entornos Cloud Computing (Soha+C) under Grant SA213U13. The project was cofinaced with Junta de Castilla y León funds.

References

Wang

Zhou

Zhao

A survey from the perspective of evolutionary process in the internet of things

International Journal of Distributed Sensor Networks 2015 2015 9

462752

10.1155/2015/462752

Fortino

Guerrieri

Russo

Savaglio

Middlewares for smart objects and smart environments: overview and comparison

Internet of Things Based on Smart Objects 2014

Cham, Switzerland

Springer International

1 27

10.1007/978-3-319-00491-4_1

Perera

Zaslavsky

Christen

Georgakopoulos

Context aware computing for the internet of things: a survey

IEEE Communications Surveys & Tutorials 2014 16 1 414 454

10.1109/surv.2013.042313.00197

2-s2.0-84894668409

Celdran

A. H.

Clemente

F. J. G.

Perez

M. G.

Perez

G. M.

SeCoMan: a semantic-aware policy framework for developing privacy-preserving and context-aware smart applications

IEEE Systems Journal 2014

10.1109/JSYST.2013.2297707

Alonso

R. S.

Tapia

D. I.

Bajo

García

Ó.

De Paz

J. F.

Corchado

J. M.

Implementing a hardware-embedded reactive agents platform based on a service-oriented architecture over heterogeneous wireless sensor networks

Ad Hoc Networks 2013 11 1 151 166

10.1016/j.adhoc.2012.04.013

2-s2.0-84870056241

Corchado

J. M.

Bajo

Abraham

GerAmi: improving healthcare delivery in geriatric residences

IEEE Intelligent Systems 2008 23 2 19 25

10.1109/mis.2008.27

2-s2.0-41549138882

Fraile

J. A.

de Paz

Bajo

de Paz

J. F.

Pérez-Lancho

Context-aware multiagent system: planning home care tasks

Knowledge and Information Systems 2014 40 1 171 203

10.1007/s10115-013-0635-9

2-s2.0-84902205955

Van den Berg

Schumann

Kraft

Hoffmann

Telemedicine and telecare for older patients—a systematic review

Maturitas 2012 73 2 94 114

10.1016/j.maturitas.2012.06.010

2-s2.0-84873958765

Fischer

Gellersen

Location and navigation support for emergency responders: a survey

IEEE Pervasive Computing 2010 9 1 38 47

10.1109/mprv.2009.91

2-s2.0-75449102971

10.

K. F.

Smart home technology for telemedicine and emergency management

Journal of Ambient Intelligence and Humanized Computing 2013 4 5 535 546

10.1007/s12652-012-0129-8

2-s2.0-84884578415

11.

Parmar

S. N.

Designing and implementing navigation and positioning system for location based emergency services

Technology Systems and Management 2011 145 chapter 35

Berlin, Germany

Springer

248 253 Communications in Computer and Information Science

10.1007/978-3-642-20209-4_35

12.

Zhu

Mukhopadhyay

S. K.

Kurata

A review of RFID technology and its managerial applications in different industries

Journal of Engineering and Technology Management 2012 29 1 152 167

10.1016/j.jengtecman.2011.09.011

2-s2.0-82955235534

13.

Thiesse

Fleisch

On the value of location information to lot scheduling in complex manufacturing processes

International Journal of Production Economics 2008 112 2 532 547

10.1016/j.ijpe.2007.05.006

2-s2.0-39649103408

14.

Huchard

Paquier

Loeillet

Marangozov

Nicolai

J.-M.

Indoor deployment of a wireless sensor network for inventory and localization of mobile assets

Proceedings of the IEEE International Conference on RFID-Technologies and Applications (RFID-TA '12)

November 2012

Nice, France

369 372

10.1109/rfid-ta.2012.6404548

2-s2.0-84873144964

15.

Liu

Darabi

Banerjee

Liu

Survey of wireless indoor positioning techniques and systems

IEEE Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews 2007 37 6 1067 1080

10.1109/tsmcc.2007.905750

2-s2.0-36248934122

16.

Gustafsson

Gunnarsson

Mobile positioning using wireless networks: possibilities and fundamental limitations based on available wireless network measurements

IEEE Signal Processing Magazine 2005 22 4 41 53

10.1109/msp.2005.1458284

2-s2.0-22544466135

17.

Shen

Win

M. Z.

Fundamental limits of wideband localization—part I: a general framework

IEEE Transactions on Information Theory 2010 56 10 4956 4980

10.1109/tit.2010.2060110

2-s2.0-77956060110

18.

Prieto

Bahillo

Mazuelas

Fernandez

Lorenzo

R. M.

Abril

E. J.

Self-calibration of TOA/distance relationship for wireless localization in harsh environments

Proceedings of the IEEE International Conference on Communications (ICC '12)

June 2012

Ottawa, Canada

IEEE

571 575

10.1109/icc.2012.6364287

2-s2.0-84871971671

19.

Shen

Mazuelas

Win

M. Z.

Network navigation: theory and interpretation

IEEE Journal on Selected Areas in Communications 2012 30 9 1823 1834

10.1109/jsac.2012.121028

2-s2.0-84866908737

20.

Win

M. Z.

Conti

Mazuelas

Shen

Gifford

W. M.

Dardari

Chiani

Network localization and navigation via cooperation

IEEE Communications Magazine 2011 49 5 56 62

10.1109/MCOM.2011.5762798

2-s2.0-79955836255

21.

De Paz

J. F.

Tapia

D. I.

Alonso

R. S.

Pinzón

C. I.

Bajo

Corchado

J. M.

Mitigation of the ground reflection effect in real-time locating systems based on wireless sensor networks by using artificial neural networks

Knowledge and Information Systems 2013 34 1 193 217

10.1007/s10115-012-0479-8

2-s2.0-84872353357

22.

Küpper

Location-Based Services: Fundamentals and Operation 2005

Chichester, UK

John Wiley & Sons

23.

Prieto

Mazuelas

Bahillo

Fernandez

Lorenzo

R. M.

Abril

E. J.

Accurate and robust localization in harsh environments based on V2I communication

Vehicular Technologie—Deployment and Applications 2013 chapter 7

Rijeka, Croatia

InTech

10.5772/55263

24.

Mazuelas

Lorenzo

R. M.

Bahillo

Fernandez

Prieto

Abril

E. J.

Topology assessment provided by weighted barycentric parameters in harsh environment wireless location systems

IEEE Transactions on Signal Processing 2010 58 7 3842 3857

10.1109/tsp.2010.2047394

2-s2.0-77953805195

25.

Villarrubia

Bajo

De Paz

J. F.

Corchado

J. M.

Monitoring and detection platform to prevent anomalous situations in home care

Sensors 2014 14 6 9900 9921

10.3390/s140609900

2-s2.0-84901999793

26.

Kushki

Plataniotis

K. N.

Venetsanopoulos

A. N.

Intelligent dynamic radio tracking in indoor wireless local area networks

IEEE Transactions on Mobile Computing 2010 9 3 405 419

10.1109/TMC.2009.141

2-s2.0-75449103579

27.

Prieto

De Paz

J. F.

Villarrubia

Bajo

Corchado

J. M.

Unified fingerprinting/ranging localization for e-healthcare systems

Ambient Intelligence—Software and Applications, 6th International Symposium on Ambient Intelligence (ISAmI 2015) 2015 376

Cham

Springer

223 231 Advances in Intelligent Systems and Computing

10.1007/978-3-319-19695-4_23

28.

Honkavirta

Perälä

Ali-Löytty

Piché

A comparative survey of WLAN location fingerprinting methods

Proceedings of the 6th Workshop on Positioning, Navigation and Communication (WPNC '09)

March 2009

Hannover, Germany

IEEE

243 251

10.1109/wpnc.2009.4907834

2-s2.0-70349156292

29.

Chen

Mobile positioning in mixed LOS/NLOS conditions using modified EKF banks and data fusion method

IEICE Transactions on Communications 2009 92 4 1318 1325

10.1587/transcom.e92.b.1318

2-s2.0-70350247466

30.

Kobayashi

Suda

Analysis of wireless geolocation in a non-line-of-sight environment

IEEE Transactions on Wireless Communications 2006 5 2 672 681

10.1109/TWC.2006.1603982

2-s2.0-33645013395

31.

Falsi

Dardari

Mucchi

Win

M. Z.

Time of arrival estimation for UWB localizers in realistic environments

EURASIP Journal on Applied Signal Processing 2006 2006

032082

10.1155/asp/2006/32082

2-s2.0-33746875997

32.

Patwari

Hero

A. O.

III Perkins

Correal

N. S.

O'Dea

R. J.

Relative location estimation in wireless sensor networks

IEEE Transactions on Signal Processing 2003 51 8 2137 2148

10.1109/TSP.2003.814469

2-s2.0-0042665374

33.

Weiss

A. J.

On the accuracy of a cellular location system based on RSS measurements

IEEE Transactions on Vehicular Technology 2003 52 6 1508 1518

10.1109/tvt.2003.819613

2-s2.0-0344875689

34.

Mazuelas

Bahillo

Lorenzo

R. M.

Fernandez

Lago

F. A.

Garcia

Blas

Abril

E. J.

Robust indoor positioning provided by real-time rssi values in unmodified WLAN networks

IEEE Journal on Selected Topics in Signal Processing 2009 3 5 821 831

10.1109/jstsp.2009.2029191

2-s2.0-77952491808

35.

Prieto

Mazuelas

Bahillo

Fernández

Lorenzo

R. M.

Abril

E. J.

Adaptive data fusion for wireless localization in harsh environments

IEEE Transactions on Signal Processing 2012 60 4 1585 1596

10.1109/tsp.2012.2183126

2-s2.0-84858310875

36.

Kabir

M. H.

Kohno

A hybrid TOA-fingerprinting based localization of mobile nodes using UWB signaling for non line-of-sight conditions

Sensors 2012 12 8 11187 11204

10.3390/s120811187

2-s2.0-84865352791

37.

Zhang

Liu

Wang

An indoor hybrid localization approach based on signal propagation model and fingerprinting

International Journal of Smart Home 2013 7 6 157 170

10.14257/ijsh.2013.7.6.15

2-s2.0-84891770940

38.

Bybordi

Reggiani

Hybrid fingerprinting-EKF based tracking schemes for indoor passive localization

International Journal of Distributed Sensor Networks 2014 2014 11

351523

10.1155/2014/351523

2-s2.0-84919723209

39.

Bitew

M. A.

Hsiao

R.-S.

Lin

H.-P.

Lin

D.-B.

Hybrid indoor human localization system for addressing the issue of RSS variation in fingerprinting

International Journal of Distributed Sensor Networks 2015 2015 9

831423

10.1155/2015/831423

40.

Bajo

De Paz

J. F.

Villarrubia

Corchado

J. M.

Self-organizing architecture for information fusion in distributed sensor networks

International Journal of Distributed Sensor Networks 2015 2015 13

231073

10.1155/2015/231073

41.

Zato

Villarrubia

Sánchez

Barri

Rubión

Fernández

Rebate

Cabo

J. A.

Álamos

Sanz

Seco

Bajo

Corchado

J. M.

PANGEA—platform for automatic construction of organizations of intelligent agents

Distributed Computing and Artificial Intelligence 2012 151

Berlin, Germany

Springer

229 239 Advances in Intelligent and Soft Computing

10.1007/978-3-642-28765-7_27

42.

Bajo

Borrajo

M. L.

De Paz

J. F.

Corchado

J. M.

Pellicer

M. A.

A multi-agent system for web-based risk management in small and medium business

Expert Systems with Applications 2012 39 8 6921 6931

10.1016/j.eswa.2012.01.001

2-s2.0-84857641476

43.

Fisher

R. A.

On the mathematical foundations of theoretical statistics

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 1922 222 309 368

10.1098/rsta.1922.0009

44.

Kay

S. M.

Fundamentals of Statistical Signal Processing—Estimation Theory 1993

Upper Saddle River, NJ, USA

Prentice Hall

45.

Bar-Shalom

X. R.

Kirubarajan

Estimation with Applications to Tracking and Navigation: Theory Algorithms and Software 2001

New York, NY, USA

John Wiley & Sons

46.

Ristic

Arulampalam

Gordon

Beyond the Kalman Filter: Particle Filters for Tracking Applications 2004

Boston, Mass, USA

Artech House

47.

Prieto

Mazuelas

Bahillo

Fernandez

Lorenzo

R. M.

Abril

E. J.

Pedestrian navigation in harsh environments using wireless and inertial measurements

Proceedings of the 10th Workshop on Positioning, Navigation and Communication (WPNC '13)

March 2013

Dresden, Germany

10.1109/wpnc.2013.6533280

2-s2.0-84881126952

48.

Hashemi

The Indoor radio propagation channel

Proceedings of the IEEE 1993 81 7 943 968

10.1109/5.231342

2-s2.0-0027627694

49.

Tejedor

Bahillo

Mazuelas

Lorenzo

R. M.

Fernández

Abril

E. J.

Characterization and mitigation of range estimation errors for an RTT-based IEEE 802.11 indoor location system

Progress in Electromagnetics Research B 2009 15 217 244

2-s2.0-69949095803

50.

Prieto

Alonso

A. A.

de la Rosa

Carrera

Adaptive framework for uncertainty analysis in electromagnetic field measurements

Radiation Protection Dosimetry 2015 164 3 422 434

10.1093/rpd/ncu260

51.

Rodas

Escudero

C. J.

Dynamic path-loss estimation using a particle filter

International Journal of Computer Science Issues 2010 7 3 1 5

52.

Zeytinci

M. B.

Sari

Harmanci

F. K.

Anarim

Akar

Location estimation using RSS measurements with unknown path loss exponents

Eurasip Journal on Wireless Communications and Networking 2013 2013 1, article 178

10.1186/1687-1499-2013-178

2-s2.0-84894135430

53.

Shirahama

Ohtsuki

RSS-based localization in environments with different path loss exponent for each link

Proceedings of the IEEE 67th Vehicular Technology Conference (VTC '08)

May 2008

Singapore

1509 1513

10.1109/vetecs.2008.353

2-s2.0-47749129288

54.

Mao

Anderson

B. D. O.

Fidan

Path loss exponent estimation for wireless sensor network localization

Computer Networks 2007 51 10 2467 2483

10.1016/j.comnet.2006.11.007

ZBL1120.68020

2-s2.0-34247602476

55.

Alam

Balaie

A. T.

Dempster

A. G.

Dynamic path loss exponent and distance estimation in a vehicular network using doppler effect and received signal strength

Proceedings of the 72nd IEEE Vehicular Technology Conference Fall (VTC '10)

September 2010

Ottawa, Canada

IEEE

1 5

10.1109/VETECF.2010.5594457

56.

Zhang

Foh

C. H.

Seet

B.-C.

Fong

A. C. M.

RSS ranging based Wi-Fi localization for unknown path loss exponent

Proceedings of the Global Telecommunications Conference (GLOBECOM '11)

December 2011

Houston, Tex, USA

IEEE

1 5

10.1109/glocom.2011.6134334

2-s2.0-84863149336

57.

Scott

D. W.

Multivariate Density Estimation 1992

New York, NY, USA

John Wiley & Sons

58.

Sorenson

H. W.

Kalman Filtering: Theory and Application 1985

Piscataway, NJ, USA

IEEE

MR847460

59.

Julier

Uhlmann

Durrant-Whyte

H. F.

A new method for the nonlinear transformation of means and covariances in filters and estimators

IEEE Transactions on Automatic Control 2000 45 3 477 482

10.1109/9.847726

ZBL0973.93053

2-s2.0-0033723743

60.

Julier

S. J.

Uhlmann

J. K.

Unscented filtering and nonlinear estimation

Proceedings of the IEEE 2004 92 3 401 422

10.1109/jproc.2003.823141

2-s2.0-21244437999

61.

Daum

Nonlinear filters: beyond the kalman filter

IEEE Aerospace and Electronic Systems Magazine 2005 20 8 57 69

10.1109/maes.2005.1499276

2-s2.0-23844456306

62.

Mazuelas

Shen

Win

M. Z.

Belief condensation filtering

IEEE Transactions on Signal Processing 2013 61 18 4403 4415

10.1109/tsp.2013.2261991

63.

Julier

S. J.

Uhlmann

J. K.

Corrections to ‘unscented filtering and nonlinear estimation’

Proceedings of the IEEE 2004 92 12 1958

10.1109/jproc.2004.837637

2-s2.0-21244451078

64.

Caffery

J. J.

Jr.

A new approach to the geometry of TOA location

Proceedings of the 52nd IEEE Vehicular Technology Conference

September 2000

Boston, Mass, USA

IEEE

1943 1949

2-s2.0-0034497763