# Hybrid RSS-RTT Localization Scheme for Indoor Wireless Networks

- A. Bahillo
^{1}Email author, - S. Mazuelas
^{1}, - R. M. Lorenzo
^{2}, - P. Fernández
^{2}, - J. Prieto
^{2}, - R. J. Durán
^{2}and - E. J. Abril
^{2}

**2010**:126082

https://doi.org/10.1155/2010/126082

© A. Bahillo et al 2010

**Received: **16 September 2009

**Accepted: **10 March 2010

**Published: **21 April 2010

## Abstract

Nowadays, a variety of information related to the distance between two wireless devices can be easily obtained. This paper presents a hybrid localization scheme that combines received signal strength (RSS) and round-trip time (RTT) information with the aim of improving the previous localization schemes. The hybrid localization scheme is based on an RSS ranging technique that uses RTT ranging estimates as constraints among other heuristic constraints. Once distances have been well estimated, the position of the mobile station (MS) to be located is estimated using a new robust least-squared multilateration (RLSM) technique that combines the RSS and RTT ranging estimates mitigating the negative effect of outliers. The hybrid localization scheme coupled with simulations and measurements demonstrates that it outperforms the conventional RSS-based and RTT-based localization schemes, without using either a tracking technique or a previous calibration stage of the environment.

## Keywords

## 1. Introduction

Intense research work is recently being carried out to design and build localization schemes that can operate in indoor environments and achieve a degree of accuracy, reliability, and cost comparable to the well-known Global Navigation Satellite Systems (GNSS). Accurate indoor localization is an important challenge for commercial, public safety, and military applications [1, 2]. In commercial applications for residential and nursing homes, there is an increasing need to track people with special needs, such as children and elderly people who are out of regular visual supervision, navigate the blind, and find specific items in warehouses. For public safety and military applications, indoor localization systems are needed to track inmates in prisons or navigate police officers, fire fighters, and soldiers to complete their missions inside buildings. Among the many technological possibilities that have been considered for indoor localization schemes such as infrared, ultrasonic, and artificial vision, radiofrequency-based schemes predominate today due to their availability, low cost, and coverage range.

The purpose of localization schemes is to find the unknown position of a mobile station (MS) given a set of measurements. The localization process consists of two main steps. Firstly, selected localization metrics between the MS and the reference points or anchors are performed. Secondly, these metrics are processed through a positioning algorithm to estimate the location coordinates of the MS. As the measurements of metrics become less reliable, the complexity of the positioning algorithm increases. The localization metrics may be classified into two broad categories: direction-based and range-based systems. Direction-based systems utilize antenna arrays and angle of arrival (AOA) estimation techniques to infer the MS position [3], while the received signal strength (RSS) and the time of arrival (TOA) of the received signals are the metrics used for range-based techniques [4–7]. The possibility of combining different localization metrics encourages to develop hybrid schemes that exploit the complementary behavior of metrics to improve the overall accuracy of the localization schemes. For instance, in [8] the Cramér-Rao Bound (CRB) on location estimation accuracy of two different hybrid schemes based on the combination of RSS and either TOA or TDOA (Time Difference Of Arrival) measurements is computed, concluding that, for short-range networks, the hybrid schemes offer improved accuracy with respect to conventional TOA and TDOA schemes. In [9] an algorithm of neural networks is implemented for the hybrid scheme that combines RSS and TOA measurements, enhancing the overall performance of the hybrid localization scheme. As range-based methods need measurements from more than two anchors for positioning in two dimensions, AOA measurements are incorporated to reduce the network overload. For instance, a hybrid algorithm is presented by incorporating AOA data in a time-based method, needing measurements from only two anchors for line-of-sight (LOS) [10] and non-LOS (NLOS) environments [11].

Time-based and direction-based measurements are highly correlated with the MS position [3, 12], but AOA and TOA localization metrics are not available to inexpensive and common wireless systems, due to the need for antenna arrays and time synchronization or complex timing requirements, respectively. On the contrary, the RSS indicator is widely available and provides a cost-effective means of position estimation, although in indoor environments the propagation phenomena cause the RSS localization metric to poorly correlate with distance [12]. The aim of this paper is to provide a new hybrid strength time-based method for indoor localization that takes advantage of easily available RSS measurements and does not need time synchronization thanks to RTT (Round-Trip Time) measurements. A previous essay [13] proposes a hybrid localization scheme that combines RSS and RTT measurements. However, it is implemented for open areas, taking RTT measured values from the cellular network and TOA measured values from GNSS. As indoor environments impose more technological challenges than open areas, in this paper, a new hybrid RSS-RTT localization scheme that operates in indoor environments and in common IEEE 802.11 wireless networks is proposed to overcome indoor impairments and improve the accuracy of the MS location estimation with respect to RTT-only and RSS-only schemes. In order to do that, the RSS and RTT measurements are carried out at the MS that is going to be located by using the printed circuit board (PCB) proposed in [14].

The paper is divided as follows: Section 2 provides an overview of the RTT-based and RSS-based ranging techniques. Section 3 describes the new hybrid RSS-RTT ranging technique, providing important simulation results. Section 4 describes a new multilateration technique that combines RSS and RTT range estimates to find the MS position. This section also includes simulation results and measurements inside a building. Finally, conclusions are summarized in Section 5.

## 2. Previous Work

Ranging techniques have significant effects on location accuracy and system complexity [12, 15]. This section outlines the previous work related to two ranging techniques whose performance was individually evaluated: RSS-based and RTT-based ranging methods.

### 2.1. RSS-Based Ranging

RSS ranging is based on the principle that says that the greater the distance between two wireless nodes is, the weaker their relative received signals are. However, the relationship between the RSS values and the distance depends on a large number of unpredictable factors. In fact, small changes in position or direction may result in dramatic differences in RSS values. The attenuation caused by the distance that separates two wireless nodes is known as path-loss, and it is modeled to be inversely proportional to the distance between the emitter and the receiver raised to a certain exponent. This exponent is known as path-loss exponent [16]. Other factors that affect RSS values are the multipath or fast fading factor and the shadowing or slow fading factor. These two factors can be modeled with Rayleigh or Rician and log-normal distributions [17, 18], respectively. However, the fast fading term can be eliminated by averaging the RSS values over a time interval [19].

where is the actual distance between the MS and the anchor , is the power measured at a reference distance and it depends on several factors: averaged fast and slow fading, antennas gains, and transmitted power. In practice, can be often known beforehand [21] and its value will be valid as long as the antenna gains and the transmitted power remain constant. The term is the path-loss exponent corresponding to the path connecting the MS to the anchor , while denotes a zero mean Gaussian random variable caused by slow fading. The conventional textbook explanation for the slow fading is the multiplicative model which assumes that there are several random multiplicative factors attenuating the received signal, and the logarithm of their product approaches the Gaussian distribution for a sufficiently large number of such factors [22]. The expression (1) has been widely used in the literature to describe RSS values as a function of the distance between two wireless nodes. Common examples of the use of this expression are the known propagation models of Okumura-Hata or Egli [16].

where is the estimated distance from the MS to the anchor , is the power measured at the reference distance of one meter, is the received power from the anchor averaged over the time interval , and is the path-loss exponent. The difference between the estimated and the actual distances is defined as the range estimate error, where the variance of this error is at least as high as the inverse of the Fisher information. For analytical details on computing the CRB and the Fisher information see [5]. The expression (2) is used to obtain range estimates from RSS values once the parameters and are known. As mentioned above, is easy to obtain from a few RSS measurements taken in a place of reference and it can be assumed to be constant, as long as the antenna gains and the transmitted power also remain constant. However, assuming as a constant would be a simplification of reality because propagation conditions between the MS and the anchor are unpredictable and could change abruptly in time. For this reason, the values of that characterize the propagation environment between the MS and each anchor have to be dynamically updated. In [5] the values of are updated at each time interval based on maximizing an objective function. This objective function quantifies the compatibility of all the range estimates between the MS and each anchor as follows:

However, in the general case, as all the range estimates are not precise, the circles do not intersect at a single point. It is clear that the further the equations of the expression (3) differ from zero the further the circles would cut at a single point. In this case, solving (3) requires significant complexity, and it is difficult to analyze. Therefore, instead of using the circles as the equations to determine , the radical axes of all pairs of circles can be used. The radical axis of two circles is the locus of points at which tangents drawn to both circles have the same length. Analytically, the radical axis can be easily obtained by subtracting the two circles equations involved. Thus, the complex problem of solving an over-determined system of quadratic equations is reduced to solve an over-determined system of linear equations defined by the radical axes.

The expression (5) is a nonlinear least squares problem that can be solved by using the Levenberg-Marquardt algorithm [23, 24], where a rough approximation of the path-loss exponents such as can be chosen as an initial guess. Indeed, the problem formulation is an iterative process that starts by choosing an initial guess for the path-loss exponents , and whose values will be modified iteratively with the aim of minimizing the expression (5). The process of updating the values finishes when the expression (5) is equal to zero or the maximum number of iterations has been reached. Once the path-loss exponents are accurately estimated, the range estimates are obtained by using the expression (2).

Therefore, accurate range estimates can be obtained only from RSS measurements by using the RSS-based ranging technique introduced in this section and explained in detail in [5].

### 2.2. RTT-Based Ranging

where is the estimated distance from the MS to the anchor and is the location estimator of the actual RTT between both wireless nodes. In [26], the Hölder mean with the shape parameter of the Weibull distribution as Hölder parameter was found to be one of the best location estimators of the actual RTT when the MS and the anchor remain in LOS. The parameters and are the intercept and slope of the linear regression model, respectively. These parameters are computed so that the estimated distance best fits the actual one. They do not depend on the environment where the wireless localization system is going to be deployed, but on the wireless nodes to be used, that is, the MS and the anchors. They are previously obtained in a LOS scenario, not necessarily in the same environment where the wireless localization system is going to be deployed.

where is the actual distance and is the error in LOS. This error is defined as the difference between the estimated and the actual distances when the MS and the anchor are in LOS. This error follows a zero mean Gaussian distribution and it is a product of electronic errors (electronic noise), since a PCB is used to quantify the RTT, and also of the RTT location estimator, since it is asymptotically Gaussian and a large amount of measurements have been carried out.

where is a random variable that represents the effect of the NLOS. The random variable depends on the environment where the MS is going to be located and it has been modeled with a wide range of statistical distributions, such as Gaussian, Exponential, and Gamma, [2, 27–30], or by means of distributions obtained from specific scattering models [31]. There are several techniques that deal with the NLOS effect. The easiest method is simply to place anchors at additional locations and select those from LOS. However, one objective of this paper is to deploy a wireless localization scheme in a common and unmodified wireless network. Therefore, complex techniques that minimize the contribution of NLOS paths [32] or techniques that focus on the identification of NLOS anchors and discard them for localization [33] have to be used. Nevertheless, their reliability remains questionable in an indoor environment with abundant scatters where almost all anchors will be in NLOS. Therefore, it is crucial to use techniques that manage to introduce, in the location process, the information that actually resides in the NLOS measurements. In a previous work [26], the effect of severe NLOS was corrected from the range estimates applying the prior NLOS measurement correction (PNMC) technique [34] with dynamic estimation of the NLOS parameters [35]. The PNMC technique estimates the ratio of NLOS present in a record of time-based measurements from each anchor and corrects those measurements in a previous stage to the location process. This processing relies on the dynamic statistical estimate of the NLOS measurements present in the record. For a detailed information on the PNMC technique see [34].

Therefore, accurate range estimates can be obtained by using the RTT-based ranging technique introduced in this section and explained in detail in [26, 35].

## 3. Hybrid RSS-RTT Ranging Technique

The more information you have when beginning your search, the easier it will be to locate your target. From this point of view, the RTT and RSS information gathered in the MS and related to the distance to anchors will be used together to improve the ranging accuracy. The way in which the hybrid RSS-RTT ranging technique works is as follows.

In [5] a feasible set of path-loss exponents was derived using four different constraints based on heuristic reasoning. Nevertheless, the advantage to be exploited in this paper is the fact that a simple device, such as the PCB proposed in [14], can gather both the RSS and RTT information from anchors and, consequently, RTT-based range estimates can also be used. Thus, a hybrid RSS-RTT ranging technique is proposed. It consists in imposing constraints to the RSS-based ranging technique from the RTT-based ranging estimates which correlate closely to the actual distance.

The constraint from the RTT-based ranging estimates is as follows:

where is a polyhedral set of constraints, and the expression (9) can be solved applying variants of the Levenberg-Marquardt algorithm [36]. In this paper, the centre of the polyhedron has been chosen as the initial guess for the path-loss exponents in the RSS-based range method introduced in the previous section.

### 3.1. Simulations

On one hand, according to the expression (1), for each actual position and time interval with , 100, RSS values from each anchor were modeled. In the latter expression, was set to −56.5 dBm, and was simulated as uniform random variables. In particular, , where are the 6 different path-loss exponents that characterize the propagation channel from the 6 anchors sorted according to their proximity to the MS. Finally, the standard deviation of the shadow fading was simulated as a uniform random value between 2.85 dBm and 3.45 dBm. On the other hand, according to the expression (8) for each actual position and time interval , 100 values from each anchor were modeled, where was simulated as a Gaussian random variable with zero mean and m, and was simulated as an Exponential random variable with the parameter uniformly distributed, . All of these simulation values were chosen as the most feasible ones based on the values obtained in previous trials with measurement equipments.

At each actual position the RSS and RTT values from the four most powerful anchors were used as inputs of the hybrid RSS-RTT ranging technique previously described. Although important information might be cut from the remaining anchors, there is one main motivation behind our taking only four anchors: the higher the number of anchors you take into account in the hybrid algorithm, the longer the time the algorithm needs to converge and find the optimal path-loss exponents. Therefore, there is a trade-off between information or accuracy in the path-loss exponent estimation and the time response.

Finally, it is worth mentioning that none of the ranging methods described in this paper need any calibration of the environment since they are dynamic methods that try to adapt themselves to the dynamic nature of radiofrequency signals in cluttered environments, such as the indoor one.

## 4. Hybrid RSS-RTT Multilateration Technique

After having estimated the distances between the MS and the anchors, the location of the MS can be found by multilateration, a common and well-known operation to find the MS location by using its range estimates to three or more anchors whose positions are previously known. Fortunately, additional capabilities can be included to multilateration methods to find the MS position more accurately. Since measurements outliers naturally occur in an indoor environment due to the complex propagation of the transmitted signal between the MS and the anchors, this section proposes a new multilateration technique based on a robust least-squared method with the aim of accurately finding the MS position from both the RTT and RSS-range estimates.

Solving problem (19) requires significant complexity and it is difficult to analyze. Therefore, instead of using the circles as the equations to determine the MS location, the radical axes of all the pairs of circles will be used [37]. The radical axis of two circles is the locus of points at which tangents drawn to both circles have the same length. It can be easily obtained by subtracting the two circles' equations involved. In this way, the complex problem of solving an over-determined system of quadratic equations is reduced to solve an over-determined system of linear equations.

where is an estimate of the actual MS position. Note that as depends on and, in general, does not match the actual distance, the solution of (23) has to be found in the least-squared sense. In this paper, this method is denoted as the least-squared multilateration method (LSM).

where denotes the median of the vector . This method will be denoted as the robust least-squared multilateration method (RLSM).

### 4.1. Simulations

In this subsection, the accuracy improvement of the hybrid localization scheme that mixes the RSS and RTT range estimates is compared to the methods that are only based on RSS or RTT range estimates by using the RLSM and LSM methods, respectively. In order to do that, the range estimates performed in the simulation scenario described in Section 3 were used. At each actual position, only the range estimates from the four most powerful anchors were used. Therefore, in order to estimate the MS position, the LSM method uses four range estimates, that is, four RSS-based or four RTT-based, while the RLSM method uses 8 range estimates, that is, four RSS-based and four RTT-based.

### 4.2. Experimental Setup

Obviously, the position accuracy could be improved using some tracking techniques, such as Kalman or particle filters, but the aim of this paper is to show the feasibility and reliability of the path-loss exponent estimates, range estimates, and MS position estimates without using any of those filtering techniques.

## 5. Conclusions

This paper proposes a complete hybrid localization scheme based on the RSS and RTT information, analyzing it and putting it into action in a cluttered indoor environment. A previous PCB has been taken as RSS and RTT measuring system, and an already deployed IEEE 802.11 wireless infrastructure has been used as indoor wireless technology. As a first step, a previous RSS-based ranging technique has been improved with the RTT-based range estimates as constraints, which correlate more closely with distance. In this way, the accuracy achieved by the RSS-only and RTT-only schemes has been improved. As a second step, the MS position has been estimated using a new multilateration technique that combines the previous RSS and RTT range estimates based on a robust least-squared method. The hybrid localization scheme coupled with simulations and measurements in a cluttered indoor environment demonstrates that it outperforms the conventional RSS-based and RTT-based indoor localization schemes without using either a tracking technique or a previous calibration stage of the environment.

Hybrid localization systems have experienced a flurry of research in recent years. However, there still remain multiple areas of open research that will help systems to meet the requirements of applications that have to operate in harsh propagation environments where GNSS typically fails, such as inside buildings. These are (i) Interference mitigation: To date, the majority of research effort ignores the effects of interference on time estimation accuracy, and few papers propose robust interference mitigation techniques. (ii) Inertial Measurements Units (IMU): the integration of RSS and RTT information with IMU information, such as the one reported by accelerometers, gyroscopes, and magnetometers, could provide location estimations more precise. (iii) Secure ranging: in certain scenarios, the localization process may be subject to hostile attacks. While some works have presented secure localization algorithms (see, e.g., [38, 39]), less attention has been paid to secure ranging.

## Declarations

### Acknowledgment

This research is partially supported by the general Board of Telecomunication of the council of public works from Castilla-León (Spain).

## Authors’ Affiliations

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