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Ubiquitous global positioning is not feasible by GNSS alone, as it lacks accurate position fixes in dense urban centres and indoors. Hybrid positioning methods have been developed to aid GNSS in those environments. Fingerprinting localization in wireless local area networks (WLANs) is a promising aiding system because of its availability, accuracy, and error mechanisms opposed to that of GNSS. This article presents a low-cost approach to ubiquitous, seamless positioning based on a particle filter integrating GNSS pseudoranges and WLAN received signal strength indicators (RSSIs). To achieve accurate location estimates indoors/outdoors and in the transition zones, appropriate likelihood functions are essential as they determine the influence of each sensor information on the position estimate. We model the spatial RSSI distributions with Gaussian processes and use these models to predict RSSIs at the particle’s positions to obtain point estimates of the RSSI likelihood function. The particle filter’s performance is assessed with real data of two test trajectories in an environment challenging for GNSS and WLAN fingerprinting localization. Outcomes of an extended Kalman filter using pseudoranges and a WLAN position as observation is included as benchmark. The proposed algorithm achieves accurate and robust seamless localization with a median accuracy of five meters.

The global navigation satellite system (GNSS) is present in almost all domains of modern life and it provides the base for many applications and services ranging from transportation and logistics, via surveying and mapping, to an uncountable number of leisure activities. With the development of the Internet of Things, the amount of location-aware services and the demanded accuracy will increase further. In densely constructed urban areas and indoors, GNSS has deficits. Shadowing and multipath phenomenon, which are often the largest error sources in these situations [

A common strategy to achieve robust ubiquitous positioning is to support GNSS with additional sensor information. Different technologies are available and many of them have been used in combination with GNSS. Positioning systems based upon wireless local area networks (WLAN) are emerging from the large amount of options [

The approaches to using WLANs for localization are diverse. In this work, we resort to WLAN location fingerprinting for the reasons set forth as follows. WLAN location fingerprinting is based on the recognition of prerecorded signal strength (RSSI) readings. These RSSIs are ideally unique at different locations. This ideal is usually not achieved. Nonetheless, a heterogeneous signal strength distribution, achieved by diverse signal attenuations, facilitates the recognition of signal strength patterns. That applies in environments with many obstacles and thereby improves the localization accuracy. Hence, this method works best indoors and in urban areas. In contrast, GNSS is based upon the signal propagation delays between the satellites and the receiver, so called pseudoranges. Exact GNSS positioning demands the line-of-sight between receiver and satellites. Open outdoor environments meet this condition best; harsh GNSS environments are dense urban centres and indoors. The operation principles of both localization technologies differ completely. They are well suited to complement each other, thus motivating the integration of pseudoranges and received signal strengths.

Several authors studied hybrid positioning systems based on GNSS and WLAN. The approaches differ in the level of integration and in the kind of information used from each of the systems. In a survey of these approaches, we found four categories in which the fusion of information of GNSS and WLAN can be grouped [

The authors of [

We consider the fusion of pseudoranges directly with RSSIs more promising, because of their contrary error mechanisms. In [

This study extends the previous works and provides a solution that deals with the discrete fingerprints. We present a particle filter that integrates pseudoranges and RSSIs based on their likelihood functions, where a particle approximation of the signal strength likelihood function is obtained from a Gaussian process regression model. This method provides an automatic, well balanced weighting of the two sensor information sources and achieves accurate, robust, and smooth seamless positioning. We compare the algorithm with an extended Kalman filter that feeds WLAN position estimates as observation into a regular GPS extended Kalman filter.

To perform seamless location estimation in this study, we consider the problem of fusing WLAN RSSI with GNSS pseudoranges on a continuous state space. Fingerprinting techniques are based on spatial samples to construct the required radio map. Interpolating RSSI provides two principle advantages. First, it reduces the labor intensive construction of radio maps, because less fingerprints are needed to obtain a fingerprint database that is equally exact compared to without interpolation. Second and more importantly here, it provides the continuous model for the fingerprint database, facilitating the fusion of RSSI and pseudoranges.

This section explains interpolation of RSSI radio maps through Gaussian process regression.

Gaussian processes are stochastic processes, basically a generalization of multivariate Gaussian distributions to infinite dimension. Every point of the infinite input domain has a Gaussian random variable associated. The defining property is that any finite collection of those random variables has a joint multivariate Gaussian distribution. Gaussian processes are completely characterized by a mean function

Consider a nonlinear function

Gaussian process modelling can be seen from a Bayesian point of view. The basic characteristics of the latent function is described by a Gaussian process a priori distribution and the function that we want to infer is modelled by a Gaussian process a posteriori distribution. To model the latent function appropriately, the mean and covariance function of the prior distribution have to be chosen and their parameters, so called hyperparameters, need to be found. (The hyperparameters can be learned from the training data, which is described in Section

The observed RSSIs are spatially correlated; neighbouring RSSIs are usually more strongly correlated than RSSIs that are distant. This relationship between the RSSIs is modelled by a covariance function. Covariance functions are specified by kernels. For two different input positions in space,

The Gaussian process that describes a finite collection of observed, noisy RSSI samples is a multivariate Gaussian distribution

The described relationship between already observed RSSIs extends as well to not yet seen RSSIs, that is, to values we wish to predict. We denote those RSSIs with

By conditioning the joint Gaussian distribution (

The term

A final point we need to mention is how to obtain the hyperparameter of the mean and covariance function. The likelihood function of Gaussian process regression,

For notational convenience, we collect the hyperparameters in a vector

Assuming a normally distributed noise process and prior distribution, an analytic expression for the marginal likelihood can be derived [

The optimal hyperparameters are found by computing the partial derivatives of this function with respect to the hyperparameters and then applying a gradient search algorithm to find them.

The localization problem can be optimally described by the sequential Bayesian filter, a recursive framework that also enables fusing the sensory data. It propagates the location estimate over time based on the previous estimate of the mobile terminal’s position and arriving observations.

It consists of two steps that are recursively executed. The process update predicts the current location based on the previous one and a model of the mobile terminal’s motion. The process update is expressed by the Chapman-Kolmogorov equation [

One of the most versatile approximations to the recursive Bayesian estimation problem is particle filters. Particle filters rely on sampling from functions to approximate them. The versatility stems from their ability to approximate arbitrary functions. A detailed description of the generalized particle filter can be found in [

Complex integrals, as the ones that describe the sequential Bayesian estimator, can be approximated numerically if we can sample the involved functions. If the samples cover the function’s domain well, sums replace complex integrals while the simplified operation on the samples provides a sufficiently accurate approximation. We denote the samples by

Nevertheless, it is often not possible to sample a function, as it is unknown or too complex. This issue is circumvented by sampling a similar function,

In the context of recursive state estimation,

The described procedure constitutes the problem of particle degeneration; that is, after each of the iterations, only a few particles gain weights while, for the majority of particles, the weight is reduced, until just one particle concentrates almost the complete weight and the weight of the remaining particles is negligible.

The choice of the importance density may slow down this effect, but usually an additional resampling (with replacement) step is introduced to overcome it. During the resampling step, particles are multiplied according to their weights, so that particles that possess large weights are selected several times and particles with very small weights are selected once or possibly vanish.

As the resampling introduces further problems (principally reduces the diversity, because many particles are repeated), we resample when the degeneracy of the algorithm becomes severe. This can be assessed by the effective sample size

In this work, we choose the importance density to be the state transition density

This section starts with an explanation of the used models in Section

The state space for the self-localization problem is defined in a local level coordinate frame, where a position in space is denoted by

To model the motion of the mobile terminal, we have chosen a random walk velocity process as in [^{−1}, ^{−1} and ^{−1}, and ^{−1}.

This model results in a linear process model:

The noise covariance matrix is simply

This process model is rather unspecific and therefore very general. Matrix

A pseudorange describes the distance from the satellite to the receiver. This consists of the geometric distance, the difference between the satellite clocks and the receiver clock, and an ionospheric and tropospheric correction term. Most of these terms can be corrected using information transmitted by the satellites. However, errors occurring in the user segment remain. This is the receiver clock offset,

The error term

Notice that the receiver clock offset is not part of the state vector and it is not estimated by the particle filter. As in [

A likelihood function for the RSSI observations,

These RSSI estimates are obtained through Gaussian process regression; recall Section

Finally, to compute the likelihood that

Compared with the pseudorange likelihood function, the predicted RSSI and variance are independent of time, because they are inferred from the (static) radio map. The same test position yields the same prediction. In contrast, the standard deviation in the pseudorange likelihood function is independent of the location of the mobile platform; it is only determined by the signal reception conditions. The choice of the RSSI variance arises from measurement setup. For many access points, only a single packet was captured; hence, a reasonable deviation measure could not be estimated. An alternative would be to exclude the observations from these access points and then use only the sample deviation measure from the remaining RSSI.

This section combines the ideas previously described; it details the fusion of GPS pseudoranges and WLAN RSSI within the particle filter. Briefly, the key probability density functions of the sequential Bayesian estimator are approximated with particles and their weights and then plugged into the particle filter of Section

The probability density function that models the motion is already stated in (

When the filter is initialized, the prior density is usually not known. A common choice for

The measurement update is formally defined by (

A particle approximation of the pseudorange likelihood is simply obtained by computing the likelihood for each particle:

We proceed similarly for the RSSI likelihood function and compute the likelihood for each particle. This involves predicting a RSSI and variance value at each position of a particle; the RSSI likelihood function for the test positions

Pseudoranges and RSSIs are clearly independent of each other, thus fusing RSSIs and pseudoranges equals multiplying their likelihood functions. An approximation of the posterior density is given by

Likelihood functions provide information on the parameters only up to a multiplicative constant. To yield a valid probability density, the updated weights have to be normalized so that they sum up to unity.

In situations when no observation from one of the sensors was obtained, the likelihood function cannot be computed and is therefore ignored. If no measurement at all is available, the algorithm proceeds directly to the process update.

The influence of the measurements, either a pseudorange or a RSSI average, on the particles is controlled by these likelihood functions. On the one hand, the variances affect the particles weights. In the case of pseudoranges, it increases if the GPS observations are believed to be inexact or noisy. The variance of the RSSI likelihood function increases if the mobile terminal is in an area with few fingerprints, because, in these areas, information about RSSI is little. Large variances lead to small weights and vice versa. On the other hand, the position of a particle also affects its weight, because a particle far from the location indicated by an observation causes a large difference in the exponential of the functions, which decreases the weight. Due to these mechanisms, the proposed particle filter balances automatically between the two positioning systems.

The final position estimate results from the minimization of the mean squared error,

We compute also the standard deviation of the particles as quality measure of the point estimate:

To put the results of the proposed particle filter into context, we present them along with results obtained from an extended Kalman filter. This filter is based upon the process and measurement update stated in (

We present first the process and measurement models and then the update and the correction step of the extended Kalman filter.

The motion of the mobile terminal is described by the linear model (

Combining the state transition and the noise coupling matrices of the motion and the receiver clock model

Measurements to the extended Kalman filter are the pseudoranges and, if available, a position from WLAN. Thus, the measurement vector is

In the case that a position estimate from WLAN is available, the measurement matrix becomes simply

For completeness, we denote the general measurement model including all observed pseudoranges and a position from WLAN based system:

In the time update step of the extended Kalman filter, the mean,

The extended Kalman filter approximates (

To analyze the performance of the particle filter, we conducted experiments for two trajectories. We begin this section with a description of these experiments and continue with some notes concerning the implementation of the particle filter. The outcomes of these experiments are reported subsequently in Sections

The data used to evaluate our algorithm is from a test bed at the Universidad Autónoma de Querétaro. The test bed constitutes two relatively small buildings (about 8 × 40 meters) with roofed passageways through which the buildings are entered. These two buildings and a larger four-storey building in the south west surround a larger open space. In addition to the roofed passageways, several trees block the view to the sky. Figure

Test bed and trajectories. Circles indicate starting point of the trajectories. (Notice, the trajectory actually followed the existing paths, which are illustrated by densely dotted orange lines. The markers of the trajectories are the positions at which the WLAN data was recorded; they are obtained from the measurements overlaid on the test bed map. The mismatch between the trajectories and the background image is due to errors of the overlay procedure, errors of the experimenter marking the measurement positions on the map, and issues when dealing with geographic data, such as projections and coordinate transformations.)

This localization scenario presents a harsh environment for GNSS, as scattering, blockage and multipath propagation are very likely. The two buildings used in the indoor sections of the experiments are relatively lightweight. They are made of brick walls and the sectioning indoors is principally done by soft-partitions. As the climate favours open doors and windows, these buildings attenuate signals rather little; thus, the indoor environment is challenging for WLAN fingerprinting as well.

We recorded the RSSIs with a laptop with a consumer-grade wireless network interface card. To create the radio maps, RSSIs and MAC addresses need to be captured at certain, known locations. Therefore we modified JMapViewer, a map application providing access to OpenStreetMap data. By a click on the map, at the location that corresponds to that of the experimenter, the position is obtained and the WLAN data capturing process is initialized: RSSIs from all available access points and the corresponding MAC addresses are captured. A second click on the user interface, after three to five seconds, issues a command to compute the arithmetic mean and the variance of the RSSIs from each access point. The capturing process finishes by storing the WLAN data and the corresponding position (obtained by from the first click on the map) in a database.

This software and procedure were also used to record the WLAN data for the test trajectories. This resulted in a stop-and-go motion, which may not be the most common motion of a pedestrian, but this facilitates recording a ground truth. Again, the WLAN data at each position of a trajectory was recorded for a few seconds. The ground truth of both paths is depicted in Figure

The data sets of the trajectories also contain GPS raw data, from which pseudoranges, satellite positions, and pseudorange correction terms were obtained. This data was recorded continuously in time. The used receiver is an u-blox LEA-6T-0 GPS receiver ([

Time synchronization is achieved by associating a Julian date time-stamp directly after parsing the WLAN and GPS data, respectively. After adding the time-stamps, the data was postprocessed and subsequently stored in the databases. Time synchronization is at least accurate up to half a second, enough to estimate the location of a (walking) pedestrian every second.

During data recording, the experimenter held the laptop in front of his chest, the GPS antenna was mounted on the experimenters head, whereas the WLAN antenna was connected directly to the laptop. The experimenter’s body probably influenced the WLAN RSSIs and his head movements may have affected the GNSS data reception. Between the radio map survey phase and localization phase, there are more than 18 months. A degradation of the radio map is likely, nonetheless not severe, because the university’s official WLAN infrastructure is relatively stable.

The radio map (see Supplementary Material in [

Before the observation data is processed, it is synchronized with help of the assigned time-stamps.

The reception of all necessary GPS data, especially ephemerides, takes a few seconds. For that reason and the knowledge that a WLAN based location estimate is likely inexact in that area, we skip the first 35 seconds of Trajectory-2 and start the estimation with GPS observations available.

To initialize the filter we distributed the particles uniformly over the test bed and set the velocity to zero. The initial position estimate is close to the centroid of the initial particle distribution and thus relatively close to the centre of the test bed.

We repeat the estimation of a trajectory 50 times with random initialization of the particles. The results, that is RMSE, standard deviation, and the data to create the figures, are averages over these 50 repetitions.

The particle filter operates with 1000 particles. This assures a certain reliability of the filter outcomes.

Figure

Position estimates of the particle filter in GPS + WLAN, GPS-only, and WLAN-only configuration and of the extended Kalman filter and the ground truth of Trajectory-1.

The availability of sensory data confirms the described behaviour. Information about the availability can be deduced from Figure

Error of the particle filter in GPS + WLAN, GPS-only, and WLAN-only configuration and of the extended Kalman filter.

Taking into consideration that WLAN data was available all the time and GPS-only towards the end, the accuracy of the hybrid solution can be explained in more detail: up to minute 24.5, the estimates are governed by the RSSI observations. Therefore, the errors are small where fingerprints can be distinguished well, indoors and most of the time along the passageways. (The reader is referred to [

The error of the extended Kalman filter is initially equal to that of the GPS-only configuration. It takes about three minutes until a WLAN position estimate is considered by the extended Kalman filter. In that moment, the error decreases to the magnitude of the error of the particle filter. While the particle filter solution mainly ignores the GPS information, the extended Kalman filter occasionally weights the GPS data and deviates from the quite accurate WLAN-only solution. A better performance can be seen at the end of the path, when GPS data quality increases due to better visibility of the satellites. The GPS measurements get more weight while the WLAN data is weighted less. During the last minute, the extended Kalman filter outperforms the particle filter.

The precision of the algorithm can be assessed from Figure

Empirical error distribution function of the particle filter in GPS + WLAN, GPS-only, and WLAN-only configuration and of the extended Kalman filter for Trajectory-1.

The extended Kalman filter solution yielded an accuracy of 10 m at 50% and 20 m at 90% probability. That is about twice as low compared with the accuracy of the particle filter. The maximum error of the extended Kalman filter solution is about 30 m, whereas the maximum error of the particle filter is 15 m.

Table

Average RMS error and standard deviation of the particle filter in GPS + WLAN, GPS-only, and WLAN-only configuration and of the extended Kalman filter for Trajectory-1.

PF, GPS + WLAN | PF, GPS-only | PF, WLAN-only | EKF, GPS + WLAN | |
---|---|---|---|---|

RMSE (m) | 6.21 | 37.33 | 7.80 | 12.97 |

Avg. SD (m) | 5.81 | 48.27 | 6.02 | 2.35 |

The error distribution function and the standard deviation of the particle cloud show that the hybrid solution is not only more accurate but also more precise; its empirical error distribution function presents the lightest tails. The GPS + WLAN configuration also yielded the smallest standard deviation.

The overall performance of the filter for Trajectory-2 is depicted in Figure

Particle filter, extended Kalman filter estimates, and ground truth of Trajectory-2. Results of the particle filter are shown for the three configurations GPS + WLAN, GPS-only, and WLAN-only.

The extended Kalman filter shows a similar positioning performance. It estimates well the entering of the right building. On the semiopen passageway of the left building and around the small lawn area, the accuracy decreases as well; nevertheless, position estimates of the extended Kalman filter appear smoother than those of the particle filter. The accuracy of the extended Kalman filter estimates increase again towards the end of the path on the open space.

To reason about the causes of the described performances, we refer to Figure

Error of the particle filter in GPS + WLAN, GPS-only, and WLAN-only configuration and of the extended Kalman filter for Trajectory-2.

The low accuracy of the particle filter’s GPS + WLAN solutions about 24-25 min is because of the poor quality of WLAN and GPS observations. During that time interval, the WLAN observations are very inexact for which reason they are basically unregarded, and therefore the accuracy of the hybrid solution equals that of the GPS-only solution. Between minutes 34 and 35, the poor accuracy of the hybrid solution is caused by an inappropriate weighting of the observations. The filter is too confident about the GPS observations or estimates the quality of the WLAN observations as too poor, respectively. The same aspect is visible at the beginning around 23 min and also about 27.5 min. In general, however, the accuracy of the hybrid solution, again, leans towards the more accurate sensor information; it never presents the largest errors among the three configurations. Figure

The accuracy of the extended Kalman filter is also most of the time about 5 m and shows only a few peaks that are larger than 10 m; see, for example, minutes 24, 28, and 34. It is worth noting that in some occasions the extended Kalman filter presents the lowest errors; refer to minutes 25, 35, 37, and 38. In general, Figure

We examine again the cumulative distribution function of the error, as shown in Figure

Empirical error distribution function of the particle filter in GPS + WLAN, GPS-only, and WLAN-only configuration and of the extended Kalman filter for Trajectory-2.

The median accuracy of the extended Kalman filter is 5.5 m, only one meter larger than that of the particle filter hybrid solution. The error at 90% probability is, as for the particle filter in GPS + WLAN configuration, 10 m. The maximum error of the extended Kalman filter is about 18 m, that is almost 10 m less than the maximum error of the hybrid solution. However, the largest error of the particle filter stems clearly from the initial estimate, before the first observations were obtained; the maximum error of the extended Kalman filter occurred about 34 min.

Table

Average RMS error and standard deviation of the particle filter in GPS + WLAN, GPS-only, and WLAN-only configuration and of the extended Kalman filter for Trajectory-2.

PF, GPS + WLAN | PF, GPS-only | PF, WLAN-only | EKF, GPS + WLAN | |
---|---|---|---|---|

RMSE (m) | 6.68 | 7.88 | 13.36 | 6.49 |

Avg. SD (m) | 2.70 | 2.99 | 4.81 | 1.04 |

The stated error figures are specific for that system and scenario and shall be put into context. If the measurements of GPS and WLAN are severely degraded, the particle filter can only yield poor estimates. An idea about the quality of the measurements can be gained from Figure

Position estimates of the GPS-only solution, the GPS receiver, and the least squares solution. The black (GPS rcv.) and the teal trajectory (PF, GPS-only) were obtained from the same experimental run. The grey trajectory (GPS rcv.) was recorded during a different experiment along the same path, though, without the stops.

Figure

The commercial GPS receiver estimates (black path) the trajectory well at the beginning, until the path enters the right building. The opposite holds for the GPS-only solution of the particle filter; its estimates are pulled towards the open space. The indoor part is not recognized by the GPS receiver, whereas the outcomes of the GPS stand-alone solution are good in the indoor section. On the roofed passageway of the left building, only the GPS receiver provides more or less adequate estimates; the estimates appear of higher accuracy than that of the GPS-only solution. Later, on the passageway of the right building, the GPS receiver’s accuracy decreases again; its estimates cross the right building until they come back on track which in the receiver is on the open area. The GPS-only solution shows better results on the passageway of the right building, but on the open space the GPS receiver appears to be more accurate again.

The least squares solution illustrates the quality of the GPS measurements and the alternative trajectory of the GPS receiver shows the harshness of the environment. The estimates of the least squares solution are similar compared to that of the GPS-only solution, but much more noisy due to the missing motion model. Nonetheless, position fixes during the indoor part are surprisingly good. The alternative GPS trajectory is worse than the black trajectory, especially on the semiopen passageway of the right building and after surrounding the small lawn area; no position fixes could be estimated during the last minutes of the trajectory.

A comparison of the accuracy of the trajectory of the GPS receiver and the hybrid particle filter is shown in Figure

Magnitude error of hybrid GPS + WLAN solution and of GPS receiver.

For most of the time of the trajectory, 6 to 7 GPS observations are available, a fair amount, given the scenario. Only in a few epochs, the number of satellites decreases to four and only one time it is below four. That means, that during time intervals of poor GPS performance, the number of observations was fair enough to get a good position fix, but that the quality of the observations was not sufficient for accurate position estimates.

The integration of WLAN data improves the localization accuracy. The GPS receiver’s RMSE for that trajectory is 9.79 m, about three meters larger than the RMSE of the particle filter and of the extended Kalman filter.

The performance of GNSS degrades in areas with obstructed satellite-to-receiver link, because, for example, scattering and multipath effects delay the signal and increase the propagation time. However, the same obstructions attenuate WLAN signals so that the spatial RSSI distribution is rather heterogeneous. This facilitates distinguishing nearby RSSIs and improves the resolution and the accuracy of a WLAN fingerprint localization system. The opposite effect occurs in open areas, where GNSS’s position fixes are usually accurate, but position estimates relying on WLAN RSSI often show large errors. These large errors are caused by very similar RSSI patterns at distant locations.

As expected, the particle filter hybrid solution attains the highest accuracy and precision compared with the stand-alone solutions. The smaller error of the two stand-alone configurations presents an upper bound for the error of the hybrid solution.

In comparison with the extended Kalman filter, the proposed algorithms outperformed the extended Kalman filter in the indoor-like scenario. For Trajectory-2, the performance of the particle filter and the extended Kalman filter are comparable, the particle filter performed in average slightly worse than the extended Kalman filter. The extended Kalman filter estimates are more precise than the estimates of the particle filter. This is because of the little amounts of noise that are introduced in the process model of the particle filter to mitigate sample impoverishment (caused by resampling). However, the extended Kalman filter’s performance is considerably poorer (large position jumps) than that of the particle filter when only WLAN data was available. The integration of WLAN data works better in the particle filter. From our point of view the disadvantage that the extended Kalman filter presents in scenarios without or with few GPS data does not outweigh the small advantage shown in the scenario where GPS and WLAN data were basically available all the time.

Sections of low accuracy of the hybrid solution are due to the loss of one of the systems or due to very poor quality of one of the observations in combination with sharp direction turns and/or changes of the sky view. As for most of the time one of the systems operates reasonably well, extreme deviations from ground truth, as it is common for fusion on a position level and can be seen for the extended Kalman filter for Trajectory-1, can be avoided, because the continuous adaption of the weights results in smooth location estimates, also during indoor/outdoor transitions.

The chosen motion model is very general and versatile and served well in our experiments. However, an adequate model must be chosen according to the final application.

One drawback of our method is the computational complexity of the RSSI interpolation. Predicting RSSIs requires the inversion of the covariance matrix, which has a dimension equal to the number of used particles. One way to reduce the computational costs is to reduce the number of particles. To compensate the loss of accuracy due to reduction of particles, a better importance density is advisable. For some scenarios, an extended Kalman filter solution can achieve similar or better performance at lower computational complexity. Our methodology used a maximum likelihood estimator to estimate a position from WLAN RSSI; this is based as well on the Gaussian process regression. Replacing the used WLAN position estimation with a simpler algorithm (e.g.,

The ubiquity of the proposed method depends heavily on the dissemination of WLAN fingerprinting location systems, more precisely on the coverage with radio maps, and that they are accessible and compatible. For further thoughts on that we refer to [

One objective of this study was the exploitation of the contrary information provided by pseudoranges on the one hand and RSSI on the other hand. We consider the automatic weighting of the different sensor information as functioning, but it is also apparent that it is improvable. Some relatively simple and straight forward ideas and changes in the presented system are likely to improve the localization accuracy.

The simplest change is the use of a multiconstellation, multifrequency receiver. This improves the coverage because the use of those receivers increases the number of receivable signals, and it improves the localization performance because a second frequency enables a more accurate correction of GNSS errors. Exploiting the carrier phase information would significantly decrease GNSS positioning error; nevertheless, such receivers are just starting to penetrate the market. Additional improvement is expected from multipath mitigation methods in the receiver, for example, at the correlator stage, if these are not yet implemented in the used receiver. Multipath mitigation based on the RSSI data is also worth investigating.

On the WLAN side, the most crucial issue is the choice of the variance in the RSSI likelihood function. It appears advisable to consider time-dependent variance estimates that express the uncertainty of the WLAN observations and not of the predictions of the Gaussian process model. Combining the currently used RSSI variance, containing spatial information, and a RSSI variance estimated from the observed samples, containing temporal information, improves very likely the weighting between the two information sources. Approaches to reducing the computational costs of the interpolation of WLAN RSSI are another open point.

Dependent on the use case, one could create fingerprints only on the paths. This indirectly includes information of the environment and improves the localization performance by removing potentially ambiguous fingerprints. This idea also translates to the interpolation with Gaussian processes, because the variance in areas without fingerprints (training data) will be higher.

This study presents a new algorithm combining GPS pseudoranges and WLAN RSSIs. The proposed algorithm achieves accurate and robust seamless localization as it exploits the complementary information contained in the sensory data. We developed a likelihood function that overcomes the drawback of the spatially discrete fingerprints by interpolating RSSIs through Gaussian process regression. The integration of the RSSI likelihood function and the pseudorange likelihood function into the particle filter yields a fine grained, automatic weighting of GPS and WLAN observations, which improves the accuracy and precision when compared with the stand-alone solutions using only GPS or WLAN data. This gain in accuracy and precision comes from an increase in computational complexity. The extended Kalman filter used as benchmark, that integrates a WLAN position estimate with GPS pseudoranges, achieved in one scenario similar positioning performance compared to the proposed particle filter. However, without enough GPS data, the extended Kalman filter accuracy degrades much, which is why we consider the particle filter worth its complexity.

In realistic indoor/outdoor experiments, in an environment harsh for GNSS

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research was partially supported by the Consejo Nacional de Ciencia y Tecnología and the División de Investigación y Posgrado de la Facultad de Ingeniería de la Universidad Autónoma de Querétaro. The authors thank Karla Alejandra Rojas Camargo for the assistance in programming the data logger and data acquisition. Philipp Richter would also like to thank Eduardo Castaño-Tostado for his comments that improved this work.