Rao-Blackwellized Particle Filter Research Articles

An evidential approach to SLAM, path planning, and active exploration

Probability theory has become the standard framework in the field of mobile robotics because of the inherent uncertainty associated with sensing and acting. In this paper, we show that the theory of belief functions with its ability to distinguish between different types of uncertainty is able to provide significant advantages over probabilistic approaches in the context of robotics. We do so by presenting solutions to the essential problems of simultaneous localization and mapping (SLAM) and planning based on belief functions. For SLAM, we show how the joint belief function over the map and the robot's poses can be factored and efficiently approximated using a Rao-Blackwellized particle filter, resulting in a generalization of the popular probabilistic FastSLAM algorithm. Our SLAM algorithm produces occupancy grid maps where belief functions explicitly represent additional information about missing and conflicting measurements compared to probabilistic grid maps. The basis for this SLAM algorithm are forward and inverse sensor models, and we present general evidential models for range sensors like sonar and laser scanners. Using the generated evidential grid maps, we show how optimal decisions can be made for path planning and active exploration. To demonstrate the effectiveness of our evidential approach, we apply it to two real-world datasets where a mobile robot has to explore unknown environments and solve different planning problems. Finally, we provide a quantitative evaluation and show that the evidential approach outperforms a probabilistic one both in terms of map quality and navigation performance.

Model reduction and parameter estimation of non-linear dynamical biochemical reaction networks.

Parameter estimation for high dimension complex dynamic system is a hot topic. However, the current statistical model and inference approach is known as a large p small n problem. How to reduce the dimension of the dynamic model and improve the accuracy of estimation is more important. To address this question, the authors take some known parameters and structure of system as priori knowledge and incorporate it into dynamic model. At the same time, they decompose the whole dynamic model into subset network modules, based on different modules, and then they apply different estimation approaches. This technique is called Rao-Blackwellised particle filters decomposition methods. To evaluate the performance of this method, the authors apply it to synthetic data generated from repressilator model and experimental data of the JAK-STAT pathway, but this method can be easily extended to large-scale cases.

A Semi-Markov Decision Model for Recognizing the Destination of a Maneuvering Agent in Real Time Strategy Games

Recognizing destinations of a maneuvering agent is important in real time strategy games. Because finding path in an uncertain environment is essentially a sequential decision problem, we can model the maneuvering process by the Markov decision process (MDP). However, the MDP does not define an action duration. In this paper, we propose a novel semi-Markov decision model (SMDM). In the SMDM, the destination is regarded as a hidden state, which affects selection of an action; the action is affiliated with a duration variable, which indicates whether the action is completed. We also exploit a Rao-Blackwellised particle filter (RBPF) for inference under the dynamic Bayesian network structure of the SMDM. In experiments, we simulate agents’ maneuvering in a combat field and employ agents’ traces to evaluate the performance of our method. The results show that the SMDM outperforms another extension of the MDP in terms of precision, recall, andF-measure. Destinations are recognized efficiently by our method no matter whether they are changed or not. Additionally, the RBPF infer destinations with smaller variance and less time than the SPF. The average failure rates of the RBPF are lower when the number of particles is not enough.

Bayesian Train Localization with Particle Filter, Loosely Coupled GNSS, IMU, and a Track Map

Train localization is safety-critical and therefore the approach requires a continuous availability and a track-selective accuracy. A probabilistic approach is followed up in order to cope with multiple sensors, measurement errors, imprecise information, and hidden variables as the topological position within the track network. The nonlinear estimation of the train localization posterior is addressed with a novel Rao-Blackwellized particle filter (RBPF) approach. There, embedded Kalman filters estimate certain linear state variables while the particle distribution can cope with the nonlinear cases of parallel tracks and switch scenarios. The train localization algorithm is further based on a track map and measurements from a Global Navigation Satellite System (GNSS) receiver and an inertial measurement unit (IMU). The GNSS integration is loosely coupled and the IMU integration is achieved without the common strapdown approach and suitable for low-cost IMUs. The implementation is evaluated with real measurements from a regional train at regular passenger service over 230 km of tracks with 107 split switches and parallel track scenarios of 58.5 km. The approach is analyzed with labeled data by means of ground truth of the traveled switch way. Track selectivity results reach 99.3% over parallel track scenarios and 97.2% of correctly resolved switch ways.

Smooth Variable Structure Filter VSLAM

Simultaneous localization and mapping (SLAM) is vital for autonomous robot navigation. The robot must build a map of its environment while tracking its own motion through that map. There are many ways to approach the problem, mostly based on the sequential probabilistic approach, based around extended Kalman filter (EKF) or the Rao-Blackwellized particle filter. In order to improve the SLAM solution and to overcome some of the EKF and PF limitations, especially when the process and observation models contain uncertain parameters, we propose to use a robust approach to solve the SLAM problem based on variable structure theory. The new alternative called Smooth Variable Structure Filter SVSF is a predictor corrector estimator based on sliding mode control and estimation concepts. It has been demonstrated that the (SVSF) is stable and very robust face modeling uncertainties and noises. Visual SVSF-SLAM is implemented, validated and compared with EKF-SLAM filter. The comparison confirms the efficient and the robustness of localization and mapping using SVSF-SLAM.

An Improved FastSLAM Algorithm Based on Revised Genetic Resampling and SR-UPF

FastSLAM is a popular framework which uses a Rao-Blackwellized particle filter to solve the simultaneous localization and mapping problem (SLAM). However, in this framework there are two important potential limitations, the particle depletion problem and the linear approximations of the nonlinear functions. To overcome these two drawbacks, this paper proposes a new FastSLAM algorithm based on revised genetic resampling and square root unscented particle filter (SR-UPF). Double roulette wheels as the selection operator, and fast Metropolis-Hastings (MH) as the mutation operator and traditional crossover are combined to form a new resampling method. Amending the particle degeneracy and keeping the particle diversity are both taken into considerations in this method. As SR-UPF propagates the sigma points through the true nonlinearity, it decreases the linearization errors. By directly transferring the square root of the state covariance matrix, SR-UPF has better numerical stability. Both simulation and experimental results demonstrate that the proposed algorithm can improve the diversity of particles, and perform well on estimation accuracy and consistency.

Sequential Bayesian Algorithms for Identification and Blind Equalization of Unit-Norm Channels

In many estimation problems of interest, the unknown parameters reside on spherical manifolds. As most common filtering algorithms assume that parameters have Gaussian prior distributions, their application to such problems leads to suboptimal performance. In this letter, we propose a model in which the unknown unit-norm parameter vectors have Fisher–Bingham (F-B) prior distributions. We show that if the observations relate to the parameters via Gaussian likelihoods, the F-B priors form a conjugate model that yields closed-form, recursive estimators that naturally take into account the restrictions on the unknowns. We apply this model to a communication setup with multiple gain-controlled FIR frequency-selective channels, deriving a novel maximum a posteriori (MAP) channel parameter estimator and a blind equalizer based on Rao–Blackwellized particle filters. As we verify via Monte Carlo numerical simulations, the F-B model leads to superior performance compared to previous algorithms that adopt mismatched Gaussian prior models.

A novel particle filter approach for indoor positioning by fusing WiFi and inertial sensors

WiFi fingerprinting is the method of recording WiFi signal strength from access points (AP) along with the positions at which they were recorded, and later matching those to new measurements for indoor positioning. Inertial positioning utilizes the accelerometer and gyroscopes for pedestrian positioning. However, both methods have their limitations, such as the WiFi fluctuations and the accumulative error of inertial sensors. Usually, the filtering method is used for integrating the two approaches to achieve better location accuracy. In the real environments, especially in the indoor field, the APs could be sparse and short range. To overcome the limitations, a novel particle filter approach based on Rao Blackwellized particle filter (RBPF) is presented in this paper. The indoor environment is divided into several local maps, which are assumed to be independent of each other. The local areas are estimated by the local particle filter, whereas the global areas are combined by the global particle filter. The algorithm has been investigated by real field trials using a WiFi tablet on hand with an inertial sensor on foot. It could be concluded that the proposed method reduces the complexity of the positioning algorithm obviously, as well as offers a significant improvement in position accuracy compared to other conventional algorithms, allowing indoor positioning error below 1.2m.

RB Particle Filter Time Synchronization Algorithm Based on the DPM Model.

Time synchronization is essential for node localization, target tracking, data fusion, and various other Wireless Sensor Network (WSN) applications. To improve the estimation accuracy of continuous clock offset and skew of mobile nodes in WSNs, we propose a novel time synchronization algorithm, the Rao-Blackwellised (RB) particle filter time synchronization algorithm based on the Dirichlet process mixture (DPM) model. In a state-space equation with a linear substructure, state variables are divided into linear and non-linear variables by the RB particle filter algorithm. These two variables can be estimated using Kalman filter and particle filter, respectively, which improves the computational efficiency more so than if only the particle filter was used. In addition, the DPM model is used to describe the distribution of non-deterministic delays and to automatically adjust the number of Gaussian mixture model components based on the observational data. This improves the estimation accuracy of clock offset and skew, which allows achieving the time synchronization. The time synchronization performance of this algorithm is also validated by computer simulations and experimental measurements. The results show that the proposed algorithm has a higher time synchronization precision than traditional time synchronization algorithms.

Gaussian Kernel Posterior Elimination for Fast Look-Ahead Rao-Blackwellised Particle Filtering for SLAM

In this paper, we explore a method for posterior elimination for fast computation of the look-ahead Rao-Blackwellised Particle Filtering (Fast la-RBPF) algorithm for the simultaneous localization and mapping (SLAM) problem in the probabilistic robotics framework. In the case when a lot of SLAM states need to be estimated, large posterior states associated with the correct state may be outnumbered by multiple non-zero smaller posteriors. We show that by masking the low posterior weight states with a Gaussian kernel prior to weight selection the accuracy of the la-RBPF SLAM algorithm can be improved. Simulation results reveal that integrated with the proposed method the fast la-RBPF SLAM performance is enhanced over both the existing RBPF SLAM and the unmodified la-RBPF SLAM algorithms.

Indoor Mobile Robot Localization and Mapping Based on Ambient Magnetic Fields and Aiding Radio Sources

In robotics, the problem of concurrently addressing the localization and mapping is well defined as simultaneous localization and mapping (SLAM) problem. Since the SLAM procedure is usually recursive, maintaining a certain error bound on the current position estimate is a critical issue. However, when the robot is kidnapped (i.e., the robot is moved by an intentional or unintentional user) or suffers from locomotion failure (due to large slip and falling), the robot will inevitably lose its current position. In this case, immediate recovery of the robot position is essential for seamless operation. In this paper, we present a method of solving both SLAM and relocation problems by employing ambient magnetic and radio measurements. The proposed SLAM is realized in the Rao-Blackwellized particle filter- and grid-based SLAM frameworks, where we exploit the local heading corrections from the magnetic measurements. For the relocation, we design the location signatures using the magnetic and radio measurements, and examine each of the Monte Carlo localization-based and multilayer perceptron-based relocation methods with real-world data. We implement the proposed SLAM and relocation algorithms in an embedded system and verify the feasibility of the proposed methods as an online robot navigation system.

Rao-Blackwellized Particle Smoothers for Conditionally Linear Gaussian Models

Sequential Monte Carlo (SMC) methods, such as the particle filter, are by now one of the standard computational techniques for addressing the filtering problem in general state-space models. However, many applications require post-processing of data offline. In such scenarios the smoothing problem--in which all the available data is used to compute state estimates--is of central interest. We consider the smoothing problem for a class of conditionally linear Gaussian models. We present a forward-backward-type Rao-Blackwellized particle smoother (RBPS) that is able to exploit the tractable substructure present in these models. Akin to the well known Rao-Blackwellized particle filter, the proposed RBPS marginalizes out a conditionally tractable subset of state variables, effectively making use of SMC only for the "intractable part" of the model. Compared to existing RBPS, two key features of the proposed method are: (i) it does not require structural approximations of the model, and (ii) the aforementioned marginalization is done both in the forward direction and in the backward direction.

A Particle-Filtering Approach for Real-Time Estimation of Thermal Conductivity and Temperature Tracking in Homogeneous Masses

Knowledge of the thermal conductivity is a key factor for several applications, which benefits from easy and cheap estimation procedures. We consider an existing experimental layout, and we propose a Rao-Blackwellized particle filter that jointly approximates the posterior distribution of the temperatures and analytically estimates the unknown thermal conductivity of a homogeneous mass. Its main advantage is the sequential estimation of the conductivity. In contrast, in other approaches, all of the temperatures need to be stored before processing the data. The results obtained with a polymethylmethacrylate specimen provide good estimates and demonstrate the real-time applicability of the approach.

Group-SMA Algorithm Based Joint Estimation of Train Parameter and State

The braking rate and train arresting operation is important in the train braking performance. It is difficult to obtain the states of the train on time because of the measurement noise and a long calculation time. A type of Group Stochastic M-algorithm (GSMA) based on Rao-Blackwellization Particle Filter (RBPF) algorithm and Stochastic M-algorithm (SMA) is proposed in this paper. Compared with RBPF, GSMA based estimation precisions for the train braking rate and the control accelerations were improved by 78% and 62%, respectively. The calculation time of the GSMA was decreased by 70% compared with SMA.

Multiple-model Rao-Blackwellized particle probability hypothesis density filter for multitarget tracking

Multitarget tracking (MTT) is a frequent topic in visual surveillance systems. Although the multiple-model probability hypothesis density (MM-PHD) filter plays an important role in the MTT, both computerized intractability and imprecise estimate are still inevitable. To solve the problems, a novel filter is presented in this paper. Different from the previous work, the Rao-Blackwellized particle filtering algorithm is incorporated with the MM-PHD filter to reduce computational load, where the sequence Monte Carlo method is adopted to estimate the nonlinear state of targets, and the linear state is predicted using the Kalman filter with the information embedded in the estimated nonlinear state. With respect to tracking precision, we find that the reweighting scheme can be realized for the numberestimate of both undetected targets and false alarms. The result is useful in balancing the required particle number in order to stabilize target estimates during the surveillance period. The illustrative simulation is finally provided to show the effectiveness of the proposed filter.

DV-SLAM (Dual-Sensor-Based Vector-Field SLAM) and Observability Analysis

In this paper, the observability of the conventional vector field simultaneous localization and mapping (SLAM) is examined by using the Fisher information matrix (FIM). If a mobile robot integrates sensor measurements while moving with a fixed heading, the measurements will be ambiguous because its measurement model is based on bilinear interpolation. To resolve the ambiguity, the authors proposed the novel dual-sensor-based vector-field SLAM (DV-SLAM), which is fully observable by using a mobile robot equipped with two sensors in a specific location to measure vector field signals. By examining its FIM, the condition is derived for the proposed DV-SLAM to be fully observable regardless of how the robot moves. The proposed DV-SLAM is implemented based on the Rao-Blackwellized particle filter with Earth's magnetic field sensors. Simulation and experimental results demonstrate that the proposed dual-sensor-based approach greatly improves the performance of the vector-field SLAM compared with the conventional approach.

Stereovision-Based Multiple Object Tracking in Traffic Scenarios Using Free-Form Obstacle Delimiters and Particle Filters

In this paper we present a stereovision-based approach for tracking multiple objects in crowded environments where, typically, the road lane markings are not visible and the surrounding infrastructure is not known. The proposed technique relies on measurement data provided by an intermediate occupancy grid derived from processing a stereovision-based elevation map and on free-form object delimiters extracted from this grid. Unlike other existing methods that track rigid objects using also rigid representations, we present a particle filter-based solution for tracking visual appearance-based free-form obstacle representations. At each step, the particle state is described by two components, i.e., the object's dynamic parameters and its estimated geometry. In order to solve the high-dimensionality state-space problem, a Rao-Blackwellized particle filter is used. By accurately modeling the object geometry using the polygonal lines instead of a 3-D box and, at the same time, separating the position and speed tracking from the geometry tracking at the estimator level, the proposed solution combines the efficiency of the rigid model with the benefits of a flexible object model.

2A2-M05 環境磁場を用いた移動ロボットの軌跡推定と環境地図構築

A SLAM (Simultaneous Localization and Mapping) problem is major in mobile robotics field about past two decades. In order to solve the problem, a camera and a LIDAR (Light Detection and Ranging) are generally used. In contrast, this paper proposes a new solution for the problem using a magnetic sensor. Our method is simple since an observation model in RBPF (Rao-Blackwellized Particle Filter)-SLAM is replaced by that of a magnetic sensor. However, magnetic sensor-based SLAM has a problem that is so narrow measurement range of the sensor. To deal with the problem, we use a heuristic method to determine surround magnetic field. We conducted experiments in actual outdoor environments including loops and verified its accuracy by using a LIDAR. Through the experiments, it was shwon that our method can close loops and build consistent maps; magnetic and geometric.

Recursive Maximum Likelihood Identification of Jump Markov Nonlinear Systems

We present an online method for joint state and parameter estimation in jump Markov non-linear systems (JMNLS). State inference is enabled via the use of particle filters which makes the method applicable to a wide range of non-linear models. To exploit the inherent structure of JMNLS, we design a Rao-Blackwellized particle filter (RBPF) where the discrete mode is marginalized out analytically. This results in an efficient implementation of the algorithm and reduces the estimation error variance. The proposed RBPF is then used to compute, recursively in time, smoothed estimates of complete data sufficient statistics. Together with the online expectation maximization algorithm, this enables recursive identification of unknown model parameters including the transition probability matrix. The method is also applicable to online identification of jump Markov linear systems(JMLS). The performance of the method is illustrated in simulations and on a localization problem in wireless networks using real data.

Bearings-only maneuvering target tracking based on truncated quadrature Kalman filtering

In this paper, a novel bearings-only maneuvering target tracking algorithm based on truncated quadrature Kalman filtering (TQKF) is proposed. In the proposed method, when the target maneuvers, in order to reduce the effect on performance duo to the increasing variance of the prior distribution, a modified prior distribution based on the current measurement is proposed. In the update step, the first two moments of the modified prior distribution is approximately estimated based on the least square estimation method and Gauss–Hermite quadrature rule, and the posterior distribution is jointly updated by using the prior distribution and the modified prior distribution. Moreover, in order to adaptively choose the estimated results obtained by the prior PDF and the truncated prior PDF, a fuzzy logic approach in which a Gaussian membership function is employed is proposed to determine the weight α. Finally, the experiment results show that the proposed algorithm results in more accurate tracking than the existing one, namely, the unscented Kalman filter (UKF), the quadrature Kalman filter (QKF), interact multiple model extended Kalman filter (IMMEKF) and multiple model Rao–Blackwellized particle filter (MMRBPF).