Fast Kernel Density Estimation Using Gaussian Filter Approximation

Bullmann, Markus; Fetzer, Toni; Ebner, Frank; Deinzer, Frank; Grzegorzek, Marcin

doi:10.23919/icif.2018.8455686

Cited by 10 publications

(12 citation statements)

References 17 publications

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“…This does not avoid that the calculated state is somewhere in between the local maxima if the approximated posterior is multimodal. Realistic scenarios are often represented by multimodal densities and therefore it is common that some particles are share the highest weight [31]. In such scenarios, a good way to receive the pedestrian's position is to recover the probability density function from the sample set itself, by using a non-parametric estimator.…”

Section: Particle Filteringmentioning

confidence: 99%

“…In such scenarios, a good way to receive the pedestrian's position is to recover the probability density function from the sample set itself, by using a non-parametric estimator. As shown in [31], this can be done in a computationally-efficiency manner using an approximation of a kernel density estimator (KDE). Despite reducing the overall variance, it can be observed that such a method does not significantly reduce the error in the general case.…”

Section: Particle Filteringmentioning

confidence: 99%

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Comparison of 2.4 GHz WiFi FTM- and RSSI-Based Indoor Positioning Methods in Realistic Scenarios

Bullmann

Fetzer

Ebner

et al. 2020

Sensors

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With the addition of the Fine Timing Measurement (FTM) protocol in IEEE 802.11-2016, a promising sensor for smartphone-based indoor positioning systems was introduced. FTM enables a Wi-Fi device to estimate the distance to a second device based on the propagation time of the signal. Recently, FTM has gotten more attention from the scientific community as more compatible devices become available. Due to the claimed robustness and accuracy, FTM is a promising addition to the often used Received Signal Strength Indication (RSSI). In this work, we evaluate FTM on the 2.4 GHz band with 20 MHz channel bandwidth in the context of realistic indoor positioning scenarios. For this purpose, we deploy a least-squares estimation method, a probabilistic positioning approach and a simplistic particle filter implementation. Each method is evaluated using FTM and RSSI separately to show the difference of the techniques. Our results show that, although FTM achieves smaller positioning errors compared to RSSI, its error behavior is similar to RSSI. Furthermore, we demonstrate that an empirically optimized correction value for FTM is required to account for the environment. This correction value can reduce the positioning error significantly.

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Section: Particle Filteringmentioning

confidence: 99%

Section: Particle Filteringmentioning

confidence: 99%

Comparison of 2.4 GHz WiFi FTM- and RSSI-Based Indoor Positioning Methods in Realistic Scenarios

Bullmann

Fetzer

Ebner

et al. 2020

Sensors

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“…However, in complex scenarios like a multimodal representation of the posterior, such methods fail to provide an accurate statement about the most probable state. Thus, in [5] we present a approximation scheme of kernel density estimates (KDE). Recovering the probability density function using an efficient KDE algorithm yields a promising approach to solve the state estimation problem in a more profound way.…”

Section: Related Workmentioning

confidence: 99%

“…Within this work we present a simple yet efficient method that enables a particle filter to fully recover from sample impoverishment. We also use an approach for finding an exact estimation of the pedestrian’s current position by using an approximation scheme of the kernel density estimation (KDE) [5].…”

Section: Introductionmentioning

confidence: 99%

“…To sum up, this work presents an updated version of the winning localization system of the smartphone-based competition at IPIN 2016 [4,7], including the improvements and newly developed methods that have been made since then [3,5,6,8]. This is the first time that all these previously acquired findings have been fully combined and applied simultaneously.…”

Section: Introductionmentioning

confidence: 99%

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Smartphone-Based Indoor Localization within a 13th Century Historic Building

Fetzer

Ebner

Bullmann

et al. 2018

Sensors

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Within this work we present an updated version of our indoor localization system for smartphones. The pedestrian’s position is given by means of recursive state estimation using a particle filter to incorporate different probabilistic sensor models. Our recently presented approximation scheme of the kernel density estimation allows to find an exact estimation of the current position, compared to classical methods like weighted-average. Absolute positioning information is given by a comparison between recent Wi-Fi measurements of nearby access points and signal strength predictions. Instead of using time-consuming approaches like classic fingerprinting or measuring the exact positions of access points, we use an optimization scheme based on a set of reference measurements to estimate a corresponding Wi-Fi model. This work provides three major contributions to the system. The most essential contribution is the novel state transition based on continuous walks along a navigation mesh, modeling only the building’s walkable areas. The localization system is further updated by incorporating a threshold-based activity recognition using barometer and accelerometer readings, allowing for continuous and smooth floor changes. Within the scope of this work, we tackle problems like multimodal densities and sample impoverishment (system gets stuck) by introducing different countermeasures. For the latter, a simplification of our previous solution is presented for the first time, which does not involve any major changes to the particle filter. The goal of this work is to propose a fast to deploy localization solution, that provides reasonable results in a high variety of situations. To stress our system, we have chosen a very challenging test scenario. All experiments were conducted within a 13th century historic building, formerly a convent and today a museum. The system is evaluated using 28 distinct measurement series on four different test walks, up to 310 m length and 10 min duration. It can be shown, that the here presented localization solution is able to provide a small positioning error, even under difficult conditions and faulty measurements. The introduced filtering methods allow for a real fail-safe system, while the optimization scheme enables an on-site setup-time of less then 120 min for the building’s 2500 m2 walkable area.

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