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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Indoor location systems, especially those using wireless sensor networks, are used in many application areas. While the need for these systems is widely proven, there is a clear lack of accuracy. Many of the implemented applications have high errors in their location estimation because of the issues arising in the indoor environment. Two different approaches had been proposed using WLAN location systems: on the one hand, the so-called deductive methods take into account the physical properties of signal propagation. These systems require a propagation model, an environment map, and the position of the radio-stations. On the other hand, the so-called inductive methods require a previous training phase where the system learns the received signal strength (RSS) in each location. This phase can be very time consuming. This paper proposes a new stochastic approach which is based on a combination of deductive and inductive methods whereby wireless sensors could determine their positions using WLAN technology inside a floor of a building. Our goal is to reduce the training phase in an indoor environment, but, without an loss of precision. Finally, we compare the measurements taken using our proposed method in a real environment with the measurements taken by other developed systems. Comparisons between the proposed system and other hybrid methods are also provided.

Currently, sensor networks are the main part of many monitoring and control systems. Many of them tend to be wireless because it allows them to be spatially distributed. Wireless Sensor Networks (WSNs) [

Since the 1950s, location systems have been incorporated into our lives. In the 1980s the Global Position System (GPS) [

Previous technologies are not adequate for indoor environments. This is mainly due to the signal characteristics. Other wireless technologies, such as IEEE 802.11a/b/g [

A study about the oscillation of the received signal is shown in reference [

Temporal variations: when the receiver remains in a fixed position, the signal level measured varies as time goes by.

Small-Scale variations: the signal level changes when the device is moving over small distances (less than the wavelength). In IEEE 802.11 b/g technologies the wavelength is 12.5 cm.

Large-Scale variations: the signal level varies with the distance due to the attenuation that the radio frequency (RF) signal suffers with the distance.

Besides these typical variations of the RF signal together with the receiver mobility, we have also considered the temperature and humidity variations, the effect of opening and closing doors, the changes in the localization of the furniture, and the presence and movement of human beings, which are all characteristics of indoor environments. These variations have already been analyzed in [

All these systems can be used in different applications. Localization in sensor networks has attracted a large research effort in the last decade. Some WSNs location systems application areas are:

Emergencies: When we want to locate an individual in the case of an emergency (injury or criminal attacks) or in a life-threatening situation. Both can be located using the positioning capability of the mobile device.

Information: It can be used in public places such as swimming pools, museums, conferences, etc. in order to provide information service about this place to the user depending on his position.

Navigation: When the user needs to meet the situation of addresses, positions, directions in an indoor places such as big supermarkets, commercial centers, etc.

Discovery: When it is necessary to find or locate things or persons in indoor places. It is very useful to locate people with Alzheimer or to locate disabled people with very little motion.

Security: It can be used to avoid theft, to move unwanted items, etc. Wireless sensors would be in specific places, when the sensors transfer a position threshold they send an alarm.

Tracking: When it is required to track a device or person inside a building.

There are two main methods to estimate the position in indoor environments. On the one hand, there are the so-called deductive methods. These take into account the physical properties of signal propagation. They require a propagation model, topological information about the environment, and the exact position of the base stations. On the other hand, there are the so-called inductive methods. These require a previous training phase, where the system learns the signal strength in each location. The main shortcoming of this approach is that the training phase can be very expensive. The complex indoor environment makes the propagation model task very hard. It is difficult to improve deductive methods when there are many walls and obstacles because deductive methods work estimating the position mathematically with the real measures taken directly from environment in the training phase [

In this work we present a hybrid location system using a new stochastic approach which is based on a combination of deductive and inductive methods. This system has been developed for wireless sensor networks using the IEEE 802.11b/g standard in order to use a deployed wireless access network that is also used for internet access and data transfer. On the other hand, the aforementioned technology allows us to cover a hard indoor environment without many base stations. The goal of this work is to reduce the training phase without losing precision.

The remainder of this paper is organized as follows. Section 2 presents the best known related work on location methods in sensor networks. Our hybrid location system is described in Section 3. Section 4 shows the efficiency of our system. It shows real measurements and compares our proposal with other systems. A comparison between our proposal and other hybrid systems proposed in the literature is shown in Section 5. Section 6 concludes the paper and discloses our planned future work.

The main location systems in WSNs are based either on the GPS [

The well-known analytical techniques used in localization algorithms are the angle of arrival (AOA), the time of arrival (TOA) and the time difference of arrival (TDOA) [

As shown in reference [

In [

R. Schmidt proposed, in reference [

A paper where the authors explain another trilateration based location system is [

Reference [

The techniques based on RSS are easier to implement. This is due to the fact that standard wireless devices possess features for measuring this value. As indicated in [

Inductive methods use location techniques based on RSS profiles. This technique consists of building a map according to the signal strength behavior with respect to the coverage area. A sensor location can be estimated with the gathered information from several base stations. These access points or base stations work with the signal strength vector. The vector is obtained from the RSS model and probabilistic techniques or various methods based on neighbors. With this information the system can estimate the possible area where the sensor could be located.

This method uses two parameters: a) the likelihood that an object is in this area and b) the precision of the signal strength. This second parameter depends on, for example, the size and the type of the location area. With these types of systems, the final user does not require any additional hardware for the localization process. These algorithms give very low localization errors using the IEEE 802.11 technology [

There are statistical models based on the signal strength, where the distance between different sensors is obtained by the calculation of a Cramér-Rao bound (CRB) on the location estimation precision possible for a given set of measurements (see reference [

Reference [

Siddiqi

Another important inductive location system is LANDMARC (see reference [

There are other papers where the authors propose hybrid systems. In [

There are few works related with the hybrid location techniques in sensors networks. In reference [

In [

If we analyze the hybrid location systems in WLAN, regardless of whether they are sensor networks or any network, there are several proposed systems. In [

Finally, another hybrid location method is proposed in [

The Euclidean models are optimum when there are multiple access points. Although some works show that the statistical properties of the RSS signal is stationary under certain circumstances, the distribution of the RSS is not usually Gaussian, it is often left-skewed and the standard deviation varies according to the signal level. Signals from multiple APs are mostly independent and the interference from other APs using the same frequency does not have a significant impact on the RSS pattern. Consequently, the coverage areas can be grouped together as a group of clusters. More than one cluster may represent one location because of the multimodal distribution of the RSS. In such a case, using a simple Euclidean distance to determine the location may easily classify some patterns into a wrong location. Our proposal combines the advantages of the deductive and inductive methods in order to provide more accurate measurements in hard environments (few base stations and/or few trained points).

In this section we explain the mathematical assumptions used in our proposal. We analyse the inductive and deductive methods from a statistical point of view. In this way, we can describe our hybrid model.

The location estimation problem can be statistically stated as follows. For simplicity, the true distribution Pr(X = x) and Pr(X = x | Y = y) are denoted as Pr(x) and Pr(y). The model parameters are denoted by p( ).

Let ^{j}

The methodology used is based on the definition of a function Pr(

The denominator in

In

On the one hand, the _{i}_{i}_{i}

On the other hand, the

If we assume that each observation ^{j}^{j}^{j}^{j}^{j}_{0}^{j}^{j}_{0}^{j}_{0}

In this work, we assume that (^{j}^{j}^{j}^{j}_{w}^{j}_{w}^{j}_{w}^{j}_{0}_{0}^{2}) be the normal distribution with mean ^{2}.

In the inductive approach we assume that the signal distribution for each training sample location is known in advance. Taking a sample for all possible locations is not a realistic assumption. However, for a given location we can have several training samples near to our location. In the hybrid approach we are interested in combining the information of both previous approaches to improve the system. That is, we know the signal distribution for several training samples near our location and we know how the signal is attenuated from the location of these samples to our actual location. Without loss of generality, we can write:

We assume that Pr(_{i}

Now, we define the random variable (^{j}^{j}_{i}) in the same manner as (^{j}^{j}_{0}^{j}_{0}_{i}^{j}

_{i}^{j}_{i}^{j}_{wi}^{j}_{σ}_{i}^{j}

From _{i}^{j}

In the training phase, we have estimated p(_{i}^{j}_{i},B^{j}

This section shows the results obtained from a real environment to test our proposal. First, we will test the errors based on the number of samples and based on the number of base stations. Then, we compare it with other commercial and implemented location systems.

To assess our proposal, we have deployed the approach in an indoor wireless environment. This place is located on the first floor of the “A building” in the “Campus Gandia” of the Polytechnic University of Valencia. The distribution of this floor is shown in

Our proposal takes into account k nearest neighbour samples from a position using Euclidian distance (see

This happens because the method obtains relative distances from the samples to the sensor and when the method begins to use measures that are not close to the sensor the error increases. Obviously, the smaller the area is, where the sensor can be found, the lower the error in its location will be. More samples will give higher relative distances and therefore the error of location will be greater.

Our first conclusion, based on the previous graph, is that given a fixed number of samples, there will be a value of number of samples where the location error will be the optimal. Then, if the number of samples used to train the system is greater, the estimated position will be more accurate because there will be closer samples.

In order to test the influence of the number of APs in our proposal, we measured the error of the approach adding access point one by one in each location (in the same place of the 56 samples previously taken). In

Bearing in mind this tendency, we have estimated which function follows the error when the number of APs of the indoor environment varies.

It should be noted, that when there are more than five APs the improvement appreciation in terms localization error is minimal when a new AP is added to the indoor environment.

In order to compare our proposal with others, we have evaluated five wireless sensor location systems:

Inductive 1. This is an inductive location system which has enough a number of samples for an adequate training.

Inductive 2. It is also an inductive location system, but in this case, the number of samples is very low.

Deductive. This system uses the method based on the equation of spread that we have seen in subsection 4.3.

The Hybrid method. This is our proposed method.

Ekahau, which is the basis of many currently used location systems [

For the inductive methods we used a system described in our previous work [_{i}

In the test phase, all these systems were tested for 40 locations (all these locations were different that the training ones, they were randomly placed and they were not inside the training grid). For each location we gathered a mean of 15 RSS consecutive values. This let us take into account the signal variability in the measurements. Each one of the test samples has been applied to the different location methods. Then, we estimate the error measuring the Euclidean distance between the output of the method and the real location of the sample.

We note that the Inductive 2 method has a higher localization error than the others. This method had 56 training samples. They were few compared with the Inductive 1 method (312 samples). This difference gives considerably more accuracy in the Inductive 1 than the Inductive 2 method.

With regards to the deductive model, we note that it did not give good results because the floor where the measurements were taken had many walls, so there was very little accuracy when we estimated their loss.

The hybrid model proposed in this paper has a stable and optimal graph compared to the rest of systems (with few training measures low errors were obtained). As noted in

Finally, the Ekahau system together with the Inductive 2 system are the methods with the worst results.

In ^{▲}”means statistical confidence of 99%. “^{Δ}” means statistical confidence of 90%.

This section compares our proposal with the hybrid methods found in the literature. In

The next analyzed feature is the number of stages to ascertain the final position. In this case, our system has two stages. The best solution is one stage because of simplicity. As we can see in

In this paper two different approaches had been discussed. The so-called deductive methods, which require a model of propagation, a topological information of the environment, and the exact position of the radio stations, and the so-called inductive methods, which require a previous training phase where the system learns the signal strength in each location. The main shortcoming of this approach is that in some scenarios, the training phase cannot be done or could be very expensive. On the other hand, the Euclidean models are optimum when there are multiple access points and few walls.

In this work we present a hybrid location system using a new stochastic approach which is based on a combination of deductive and inductive methods. This system has been developed for wireless sensor networks using IEEE 802.11b/g standard in order to use a deployed wireless access network that is also used for internet access and data transfer.

We have tested the errors based on the number of samples and based on the number of base stations. We have estimated an experimental equation based on the graph trends of the errors of the measures obtained. We have compared our proposal with several methods in order to check our approach.

Our system uses a small set of training samples (inductive information). Given the actual signal strength, we use the closest training samples as a starting point. Then, the deductive propagation model is used to obtain the shift from the training samples. A stochastic approach is used whereby the optimal location can be estimated as the point that maximizes the product of probabilities from each of the closest training samples

Our proposal combines the advantages of the deductive and inductive methods in order to provide accurate measurements in hard environments (few base stations and/or few trained points). The goal of this work has been to reduce the training phase without losing precision. Now, we are trying to find the proposed model by adding other methods in order to obtain more accurate results.

The proposed method is useful in cases where a good training phase is not practical (very few samples can be taken in advance), and the precise location of some access points is not known. These environments could be military, such as troop deployments inside buildings or discovery squads for hard environments, environments where the radio coverage is not known in advance (unknown deployments), or even environments where there the APs can be on or off at any time (dynamic environments). We are currently working on enhancing the precision of the proposed model. In future work we will evaluate the performance our proposal in hard environments.

Proposed algorithm.

Test bench place used in the experiments.

Average location estimation error as a function of the number of samples.

Average location estimation error as a function of the number of APs.

Comparative of average location error.

Variables.

found location | ^{j} |
location of base-station | |

current observation | _{0} |
reference distance for signal strength measured | |

number of base station | _{0}^{j} |
mean signal strength measured to _{0} | |

^{j} |
signal strength from base-station |
^{j} |
Euclidian distance between ^{j} |

set of training data | attenuation variation index | ||

number of training samples | _{w}^{j} |
attenuation caused by the obstacles from base-station | |

_{i} |
training sample _{i}_{i}_{i} |
number of wall crossed | |

_{i} |
location of training sample |
_{0} |
wall average attenuation |

_{i} |
observation of training sample |
_{σ} |
zero-mean normal distributed random variable with standard deviation σ. |

_{i}^{j} |
signal strength of training sample |
_{i}^{j} |
distance from _{i}^{j} |

^{j} |
base-station ^{j}^{j}_{0}^{j} |
_{wi}^{j} |
wall attenuation obtained from _{i}^{j} |

Average errors and standard deviation to the surveyed approaches.

1.23^{▲} |
3.02^{▲} |
2.75^{▲} |
1.80 | 2.04^{Δ} | |

0.62 | 2.12 | 1.73 | 0.74 | 1.61 |

Hybrid location systems comparison.