An Introduction to Twisted Particle Filters and Parameter Estimation in Non-linear State-space Models

Twisted particle filters are a class of sequential Monte Carlo methods recently introduced by Whiteley and Lee to improve the efficiency of marginal likelihood estimation in state-space models. The purpose of this article is to extend the twisted particle filtering methodology, establish accessible theoretical results which convey its rationale, and provide a demonstration of its practical performance within particle Markov chain Monte Carlo for estimating static model parameters. We derive twisted particle filters that incorporate systematic or multinomial resampling and information from historical particle states, and a transparent proof which identifies the optimal algorithm for marginal likelihood estimation. We demonstrate how to approximate the optimal algorithm for nonlinear state-space models with Gaussian noise and we apply such approximations to two examples: a range and bearing tracking problem and an indoor positioning problem with Bluetooth signal strength measurements. We demonstrate improvements over standard algorithms in terms of variance of marginal likelihood estimates and Markov chain autocorrelation for given CPU time, and improved tracking performance using estimated parameters.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Observability of Path Loss Parameters in WLAN-Based Simultaneous Localization and Mapping

Indoor positioning by means of received signal strengths has been gathering much interest since the massive presence of wireless local area networks (WLANs) in buildings. Theoretical approaches rely on the perfect knowledge of the APs' positions and propagation conditions; since this is unrealistic in real world, we estimate such knowledge as well as the building map from data by applying Simultaneous Localization and Mapping (SLAM). In this paper we address the joint estimation of the path loss parameters, namely the transmitted power and the path loss exponent, this latter being usually approximated in the literature by the free space value. We provide examples that show the relevance of estimating both parameters and analyze observability issues from the point of view of estimation theory. The integration of the parameter estimation in a WLAN based SLAM algorithm - WiSLAM - has been carried out and the results are discussed

Combining wireless and visual tracking for an indoor environment

There has been a lot of research done towards both camera and Wi-Fi tracking respectively, both these techniques have their benefits and drawbacks. By combining these technologies it is possible to eliminate their respective weaknesses, to increase the possibilities of the system as a whole. This is accomplished by fusing the sensor data from Wi-Fi and camera before inserting it in a particle filter. This will result in a more accurate and robust localization system

Multisensor Poisson Multi-Bernoulli Filter for Joint Target-Sensor State Tracking

In a typical multitarget tracking (MTT) scenario, the sensor state is either assumed known, or tracking is performed in the sensor's (relative) coordinate frame. This assumption does not hold when the sensor, e.g., an automotive radar, is mounted on a vehicle, and the target state should be represented in a global (absolute) coordinate frame. Then it is important to consider the uncertain location of the vehicle on which the sensor is mounted for MTT. In this paper, we present a multisensor low complexity Poisson multi-Bernoulli MTT filter, which jointly tracks the uncertain vehicle state and target states. Measurements collected by different sensors mounted on multiple vehicles with varying location uncertainty are incorporated sequentially based on the arrival of new sensor measurements. In doing so, targets observed from a sensor mounted on a well-localized vehicle reduce the state uncertainty of other poorly localized vehicles, provided that a common non-empty subset of targets is observed. A low complexity filter is obtained by approximations of the joint sensor-feature state density minimizing the Kullback-Leibler divergence (KLD). Results from synthetic as well as experimental measurement data, collected in a vehicle driving scenario, demonstrate the performance benefits of joint vehicle-target state tracking.Comment: 13 pages, 7 figure

Extracting More Data from LiDAR in Forested Areas by Analyzing Waveform Shape

Light Detection And Ranging (LiDAR) in forested areas is used for constructing Digital Terrain Models (DTMs), estimating biomass carbon and timber volume and estimating foliage distribution as an indicator of tree growth and health. All of these purposes are hindered by the inability to distinguish the source of returns as foliage, stems, understorey and the ground except by their relative positions. The ability to separate these returns would improve all analyses significantly. Furthermore, waveform metrics providing information on foliage density could improve forest health and growth estimates. In this study, the potential to use waveform LiDAR was investigated. Aerial waveform LiDAR data were acquired for a New Zealand radiata pine plantation forest, and Leaf Area Density (LAD) was measured in the field. Waveform peaks with a good signal-to-noise ratio were analyzed and each described with a Gaussian peak height, half-height width, and an exponential decay constant. All parameters varied substantially across all surface types, ruling out the potential to determine source characteristics for individual returns, particularly those with a lower signal-to-noise ratio. However, pulses on the ground on average had a greater intensity, decay constant and a narrower peak than returns from coniferous foliage. When spatially averaged, canopy foliage density (measured as LAD) varied significantly, and was found to be most highly correlated with the volume-average exponential decay rate. A simple model based on the Beer-Lambert law is proposed to explain this relationship, and proposes waveform decay rates as a new metric that is less affected by shadowing than intensity-based metrics. This correlation began to fail when peaks with poorer curve fits were included