Non-Gaussian BLE-Based Indoor Localization Via Gaussian Sum Filtering Coupled with Wasserstein Distance

The time-series state and parameter estimations of indoor localization continue to be a topic of growing importance. To deal with the nonlinear and positive skewed non-Gaussian dynamic of indoor CSS–TOF (Chirp-Spread-Spectrum Time-of-Flight) ranging measurements and position estimations, Monte Carlo Bayesian smoothers are promising as involving the past, present, and future observations. However, the main problems are how to derive trackable smoothing recursions and to avoid the degeneracy of particle-based smoothed distributions. To incorporate the backward smoothing density propagation with the forward probability recursion efficiently, we propose a lightweight Marginalized Particle Smoother (MPS) for nonlinear and non-Gaussian errors mitigation. The performance of the position prediction, filtering, and smoothing are investigated in real-world experiments carried out with vehicle on-board sensors. Results demonstrate the proposed smoother enables a great tool by reducing temporal and spatial errors of mobile trajectories, with the cost of a few sequence delay and a small number of particles. Therefore, MPS outperforms the filtering and smoothing methods under weak assumptions, low computation, and memory requirements. In the view that the sampled trajectories stay numerically stable, the MPS form is validated to be applicable for time-series position tracking.

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Treatment of non-Gaussian tails of multiple Coulomb scattering in track fitting with a Gaussian-sum filter

Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment ◽

10.1016/j.nima.2005.11.134 ◽

2006 ◽

Vol 559 (1) ◽

pp. 158-161 ◽

Cited By ~ 1

Author(s):

A. Strandlie ◽

J. Wroldsen

Keyword(s):

Coulomb Scattering ◽

Gaussian Sum ◽

Multiple Coulomb Scattering ◽

Non Gaussian

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Convolution PHD Filtering for Nonlinear Non-Gaussian Models

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.213.344 ◽

2011 ◽

Vol 213 ◽

pp. 344-348

Author(s):

Jian Jun Yin ◽

Jian Qiu Zhang

Keyword(s):

Parallel Implementation ◽

Gaussian Mixture ◽

Probability Hypothesis Density ◽

Gaussian Sum ◽

Multi Target Tracking ◽

Lower Complexity ◽

Observation Noise ◽

Non Gaussian ◽

Convolution Filters ◽

Cphd Filter

A novel probability hypothesis density (PHD) filter, called the Gaussian mixture convolution PHD (GMCPHD) filter was proposed. The PHD within the filter is approximated by a Gaussian sum, as in the Gaussian mixture PHD (GMPHD) filter, but the model may be non-Gaussian and nonlinear. This is implemented by a bank of convolution filters with Gaussian approximations to the predicted and posterior densities. The analysis results show the lower complexity, more amenable for parallel implementation of the GMCPHD filter than the convolution PHD (CPHD) filter and the ability to deal with complex observation model, small observation noise and non-Gaussian noise of the proposed filter over the existing Gaussian mixture particle PHD (GMPPHD) filter. The multi-target tracking simulation results verify the effectiveness of the proposed method.

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Carrier Phase-based RAIM Algorithm Using a Gaussian Sum Filter

Journal of Navigation ◽

10.1017/s0373463310000330 ◽

2010 ◽

Vol 64 (1) ◽

pp. 75-90 ◽

Cited By ~ 5

Author(s):

Ho Yun ◽

Youngsun Yun ◽

Changdon Kee

Keyword(s):

Gaussian Distribution ◽

Carrier Phase ◽

Phase Error ◽

Critical Role ◽

Gaussian Mixture ◽

Error Distribution ◽

Integrity Monitoring ◽

Gaussian Sum ◽

Carrier Phase Error ◽

Non Gaussian

Carrier phase measurements are used to provide high-accuracy estimates of position. For safety-of-life navigation applications such as precision approach and landing, integrity plays a critical role. Carrier phase-based Receiver Autonomous Integrity Monitoring (CRAIM) has been investigated for many years (Pervan et al, 1998; Feng et al, 2007). Assuming that the carrier phase error has a Gaussian distribution, conventional CRAIM algorithms were directly derived from the Pseudorange-based RAIM (PRAIM). However, the actual carrier phase error does not exactly follow the Gaussian distribution, hence the performance of the conventional CRAIM algorithm is not optimal.To approach this problem, this paper proposes a new CRAIM algorithm that uses Gaussian sum filters. A Gaussian sum filter can deal with any non-Gaussian error distribution and accurately present the posterior distributions of states. In this paper, a new method of making a Gaussian mixture model, which follows the true error distribution, is introduced. Additionally an integrity monitoring algorithm, using a Gaussian sum filter, is described in detail. The simulation results show that the proposed algorithm can have about 18% smaller Minimum Detectable Bias (MDB) and generates about 20% lower protection levels than those of the conventional CRAIM algorithm. In other words, by considering a non-Gaussian carrier phase error distribution, the new algorithm can improve the accuracy and the availability.

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