Particle Filter Implementation Research Articles

A Weight-Based Cutoff Resampling Method for Accelerated Particle Filtering

The particle filter is known to be a powerful tool for the estimation of moving targets guided by nonlinear dynamics and sensors. The filter, however, is known to suffer from degeneracy — a feature of one particle gathering all the weight, thus causing the filter to completely diverge. Degeneracy problems become more evident when the sensors are accurate and/or the target maneuvers greatly. The resampling step in the particle filter is critical because it avoids degeneracy of particles by eliminating the wasteful use of particles that do not contribute to the posterior probability density function. The conventional resampling methods, despite being unbiased in approximating the posterior density, involve exhaustive and sequential communication within the particles and thus are computationally expensive. Hence conventional resampling is a major bottleneck for fast implementation of particle filters for real-time tracking. In this paper, we propose a new approach of filtering that requires resampling of only a minimum number of the most important particles that contribute to the posterior density. Minimizing the resampling operation to over a few important particles substantially accelerates the filtering process. We show the merits of the proposed method via simulations using a nonlinear example.

On off-line and on-line Bayesian filtering for uncertainty quantification of structural deterioration

Abstract Data-informed predictive maintenance planning largely relies on stochastic deterioration models. Monitoring information can be utilized to update sequentially the knowledge on model parameters. In this context, on-line (recursive) Bayesian filtering algorithms typically fail to properly quantify the full posterior uncertainty of time-invariant model parameters. Off-line (batch) algorithms are—in principle—better suited for the uncertainty quantification task, yet they are computationally prohibitive in sequential settings. In this work, we adapt and investigate selected Bayesian filters for parameter estimation: an on-line particle filter, an on-line iterated batch importance sampling filter, which performs Markov Chain Monte Carlo (MCMC) move steps, and an off-line MCMC-based sequential Monte Carlo filter. A Gaussian mixture model approximates the posterior distribution within the resampling process in all three filters. Two numerical examples provide the basis for a comparative assessment. The first example considers a low-dimensional, nonlinear, non-Gaussian probabilistic fatigue crack growth model that is updated with sequential monitoring measurements. The second high-dimensional, linear, Gaussian example employs a random field to model corrosion deterioration across a beam, which is updated with sequential sensor measurements. The numerical investigations provide insights into the performance of off-line and on-line filters in terms of the accuracy of posterior estimates and the computational cost, when applied to problems of different nature, increasing dimensionality and varying sensor information amount. Importantly, they show that a tailored implementation of the on-line particle filter proves competitive with the computationally demanding MCMC-based filters. Suggestions on the choice of the appropriate method in function of problem characteristics are provided.

Local-To-Global Hypotheses for Robust Robot Localization.

Many robust state-of-the-art localization methods rely on pose-space sample sets that are evaluated against individual sensor measurements. While these methods can work effectively, they often provide limited mechanisms to control the amount of hypotheses based on their similarity. Furthermore, they do not explicitly use associations to create or remove these hypotheses. We propose a global localization strategy that allows a mobile robot to localize using explicit symbolic associations with annotated geometric features. The feature measurements are first combined locally to form a consistent local feature map that is accurate in the vicinity of the robot. Based on this local map, an association tree is maintained that pairs local map features with global map features. The leaves of the tree represent distinct hypotheses on the data associations that allow for globally unmapped features appearing in the local map. We propose a registration step to check if an association hypothesis is supported. Our implementation considers a robot equipped with a 2D LiDAR and we compare the proposed method to a particle filter. We show that maintaining a smaller set of data association hypotheses results in better performance and explainability of the robot’s assumptions, as well as allowing more control over hypothesis bookkeeping. We provide experimental evaluations with a physical robot in a real environment using an annotated geometric building model that contains only the static part of the indoor scene. The result shows that our method outperforms a particle filter implementation in most cases by using fewer hypotheses with more descriptive power.

InPhase: Phase-based Ranging and Localization

Ranging and subsequent localization have become more and more critical in today’s factories and logistics. Tracking goods precisely enables just-in-time manufacturing processes. We present the InPhase system for ranging and localization applications. It employs narrowband 2.4 GHz IEEE 802.15.4 radio transceivers to acquire the radio channel’s phase response. In comparison, most other systems employ time-of-flight schemes with Ultra Wideband transceivers. Our software can be used with existing wireless sensor network hardware, providing ranging and localization for existing devices at no extra cost. The introduced Complex-valued Distance Estimation algorithm evaluates the phase response to compute the distance between two radio devices. We achieve high ranging accuracy and precision with a mean absolute error of 0.149 m and a standard deviation of 0.104 m. We show that our algorithm is resilient against noise and burst errors from the phase-data acquisition. Further, we present a localization algorithm based on a particle filter implementation. It achieves a mean absolute error of 0.95 m in a realistic 3D live tracking scenario.

Rao-Blackwellized Particle Filter with Neural Network using Low-Cost Range Sensor in Indoor Environment

Implementation of Rao-Blackwellized Particle Fil-ter (RBPF) in grid-based simultaneous localization and mapping (SLAM) algorithm with range sensors is commonly developed by using sensor with dense measurements such as laser rangefinder. In this paper, a more cost convenient solution was explored where implementation of array of infrared sensors equipped on a mobile robot platform was used. The observation from array of infrared sensors are noisy and sparse. This adds more uncertainty in the implementation of SLAM algorithm. To compensate for the high uncertainties from robot’s observations, neural network was integrated with the grid-based SLAM algorithm. The result shows that the grid-based SLAM algorithm with neural network has better accuracy compared to the grid-based SLAM algorithm without neural network for the aforementioned mobile robot implementation. The algorithm improves the map accuracy by 21% and reduce robot’s state estimate error significantly. The better performance is due to the improvement in accuracy of grid cells’ occupancy value. This affects the importance weight computation in RBPF algorithm hence resulting a better map accuracy and robots state estimate. This finding shows that a promising grid-based SLAM algorithm can be obtained by using merely array of infrared sensors as robot’s observation.

Comparison of 3D scan matching techniques for autonomous robot navigation in urban and agricultural environments

Global navigation satellite system (GNSS) is the standard solution for solving the localization problem in outdoor environments, but its signal might be lost when driving in dense urban areas or in the presence of heavy vegetation or overhanging canopies. Hence, there is a need for alternative or complementary localization methods for autonomous driving. In recent years, exteroceptive sensors have gained much attention due to significant improvements in accuracy and cost-effectiveness, especially for 3D range sensors. By registering two successive 3D scans, known as scan matching, it is possible to estimate the pose of a vehicle. This work aims to provide in-depth analysis and comparison of the state-of-the-art 3D scan matching approaches as a solution to the localization problem of autonomous vehicles. Eight techniques (deterministic and probabilistic) are investigated: iterative closest point (with three different embodiments), normal distribution transform, coherent point drift, Gaussian mixture model, support vector-parametrized Gaussian mixture and the particle filter implementation. They are demonstrated in long path trials in both urban and agricultural environments and compared in terms of accuracy and consistency. On the one hand, most of the techniques can be successfully used in urban scenarios with the probabilistic approaches that show the best accuracy. On the other hand, agricultural settings have proved to be more challenging with significant errors even in short distance trials due to the presence of featureless natural objects. The results and discussion of this work will provide a guide for selecting the most suitable method and will encourage building of improvements on the identified limitations.

FPGA Implementation of Particle Filters for Robotic Source Localization

Particle filtering is very reliable in modelling non-Gaussian and non-linear elements of physical systems, which makes it ideal for tracking and localization applications. However, a major drawback of particle filters is their computational complexity, which inhibits their use in real-time applications with conventional CPU or DSP based implementation schemes. The re-sampling step in the particle filters creates a computational bottleneck since it is inherently sequential and cannot be parallelized. This paper proposes a modification to the existing particle filter algorithm, which enables parallel re-sampling and reduces the effect of the re-sampling bottleneck. We then present a high-speed and dedicated hardware architecture incorporating pipe-lining and parallelization design strategies to supplement the modified algorithm and lower the execution time considerably. From an application standpoint, we propose a novel source localization model to estimate the position of a source in a noisy environment using the particle filter algorithm implemented on hardware. The design has been prototyped using Artix-7 field-programmable gate array (FPGA), and resource utilization for the proposed system is presented. Further, we show the execution time and estimation accuracy of the high-speed architecture and observe a significant reduction in computational time. Our implementation of particle filters on FPGA is scalable and modular, with a low execution time of about 5.62 μs for processing 1024 particles (compared to 64 ms on Intel Core i7-7700 CPU with eight cores clocking at 3.60 GHz) and can be deployed for real-time applications.

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

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.

Multiple-Hypothesis Vision-Based Landing Autonomy

This paper presents a novel state estimation system for unmanned aerial vehicle landing. A novel vision algorithm that detects a portion of the marker is developed, and this algorithm extends the detectable range of the vision system for any known marker. A vision-aided navigation algorithm is derived within extended Kalman particle filter and Rao–Blackwellized particle filter frameworks in addition to a standard extended Kalman filter framework. These multihypothesis approaches not only deal well with a highly nonlinear and non-Gaussian distribution of the measurement errors of vision but also result in numerically stable filters. The computational costs are reduced compared to a naive implementation of particle filter, and these algorithms run in real time. This system is validated through numerical simulation, image-in-the-loop simulation, and flight tests.

Likelihood Induced by Moment Functions using Particle Filter: A Comparison of Particle GMM and Standard MCMC Methods

Particle filtering is a useful statistical tool which can be used to make inference on the latent variables and the structural parameters of state space models by employing it inside MCMC algorithms (Flury and Shephard, 2011). It only relies on two assumptions (Gordon et al, 1993): a: The ability to simulate from the dynamic of the model; b: The predictive measurement density can be computed. In practice the second assumption may not be obvious and implementations of particle filter can become difficult to conduct. Gallant, Giacomini and Ragusa (2016) have recently developed a particle filter which does not rely on the structural form of the measurement equation. This method uses a set of moment conditions to induce the likelihood function of a structural model under a GMM criteria. The semiparametric structure allows to use particle filtering where the standard techniques are not applicable or difficult to implement. On the other hand, the GMM representation is less efficient than the standard technique and in some cases it can affect the proper functioning of particle lter and in turn deliver poor estimates. The contribution of this paper is to provide a comparison between the standard techniques, as Kalman filter and standard bootstrap particle filter, and the method proposed by Gallant et al (2016) in order to measure the performance of particle filter with GMM representation.

Integrating Moving Platforms in a SLAM Agorithm for Pedestrian Navigation.

In 3D pedestrian indoor navigation applications, position estimation based on inertial measurement units (IMUss) fails when moving platforms (MPs), such as escalators and elevators, are not properly implemented. In this work, we integrate the MPs in an upper 3D-simultaneous localization and mapping (SLAM) algorithm which is cascaded to the pedestrian dead-reckoning (PDR) technique. The step and heading measurements resulting from the PDR are fed to the SLAM that additionally estimates a map of the environment during the walk in order to reduce the remaining drift. For integrating MPs, we present a new proposal function for the particle filter implementation of the SLAM to account for the presence of MPs. In addition, a new weighting function for features such as escalators and elevators is developed and the features are learned and stored in the learned map. With this, locations of MPs are favored when revisiting the MPs again. The results show that the mean height error is about 0.1 m and the mean position error is less than 1 m for walks with long distances along the floors, even when using multiple floor level changes with different numbers of floors in a multistory environment. For walks with short walking distances and many floor level changes, the mean height error can be higher (about 0.5 m). The final floor number is in all cases except one correctly estimated.

A random finite set approach for dynamic occupancy grid maps with real-time application

Grid mapping is a well-established approach for environment perception in robotic and automotive applications. Early work suggests estimating the occupancy state of each grid cell in a robot’s environment using a Bayesian filter to recursively combine new measurements with the current posterior state estimate of each grid cell. This filter is often referred to as binary Bayes filter. A basic assumption of classical occupancy grid maps is a stationary environment. Recent publications describe bottom-up approaches using particles to represent the dynamic state of a grid cell and outline prediction-update recursions in a heuristic manner. This paper defines the state of multiple grid cells as a random finite set, which allows to model the environment as a stochastic, dynamic system with multiple obstacles, observed by a stochastic measurement system. It motivates an original filter called the probability hypothesis density / multi-instance Bernoulli (PHD/MIB) filter in a top-down manner. The paper presents a real-time application serving as a fusion layer for laser and radar sensor data and describes in detail a highly efficient parallel particle filter implementation. A quantitative evaluation shows that parameters of the stochastic process model affect the filter results as theoretically expected and that appropriate process and observation models provide consistent state estimation results.

APPLICATION OF MODIFIED UNSCENTED KALMAN FILTER AND UNSCENTED PARTICLE FILTER TO SOLVING TRACKING PROBLEMS

The paper describes two modified implementations of unscented Kalman filter (UKF) and unscented particle filter (UPF) to solve nonlinear filtering problem for discrete-time dynamic space model (DSSM). DSSM is supposed to be nonlinear with additive Gaussian noise. The considered algorithm modifications are based on combination of UD-factorization of covariance matrices with sequential Kalman filter. The solution of tracking problem is illustrated for two cases. In the first case the problem of estimate of movable target coordinates from observed noised bearing is considered (a problem of passive location). In the second case the problem of an active location is described when noisy values of a distance to the accompanied object besides a bearing are available to the observer. Moreover, in the second case the motion model is extended by means of introducing a new parameter (a maneuver) such as an angle of velocity direction. To examine robustness of the considered algorithms in active target tracking problem (the second case) an arbitrary maneuver that differs from the initially given one in the motion model is considered as an observation.

Prognosis and Remaining Useful Life Estimation of Lithium-Ion Battery with Optimal Multi-Level Particle Filter and Genetic Algorithm

Prognosis and remaining useful life (RUL) estimation of components and systems (C&S) are vital for intelligent asset-integrity management. The implementation of the traditional multi-level particle filter (TRMPF) has improved prognosis when compared with the one-step traditional particle filter that depended on the first-order state equation. However, despite this improvement, the need to enhance the accuracy of fault prognosis, diagnosis and detection cannot be overemphasized. To this end, an optimal multi-level particle filter (OPMPF) algorithm that combines genetic algorithm (GA) optimization and multi-level particle filter (MPF) techniques is used to predict the RUL of the C&S in order to enhance the accuracy of the estimation at different forms of deterioration in operation. A 9-fold cross-validation ensemble MPF that utilized lithium-ion (Li+) batteries’ charge capacity decay to test the developed OPMPF algorithm showed an improvement of over 200% in the estimated RUL when compared with the TRMPF estimation.

Error Modelling for Multi-Sensor Measurements in Infrastructure-Free Indoor Navigation.

The long-term objective of our research is to develop a method for infrastructure-free simultaneous localization and mapping (SLAM) and context recognition for tactical situational awareness. Localization will be realized by propagating motion measurements obtained using a monocular camera, a foot-mounted Inertial Measurement Unit (IMU), sonar, and a barometer. Due to the size and weight requirements set by tactical applications, Micro-Electro-Mechanical (MEMS) sensors will be used. However, MEMS sensors suffer from biases and drift errors that may substantially decrease the position accuracy. Therefore, sophisticated error modelling and implementation of integration algorithms are key for providing a viable result. Algorithms used for multi-sensor fusion have traditionally been different versions of Kalman filters. However, Kalman filters are based on the assumptions that the state propagation and measurement models are linear with additive Gaussian noise. Neither of the assumptions is correct for tactical applications, especially for dismounted soldiers, or rescue personnel. Therefore, error modelling and implementation of advanced fusion algorithms are essential for providing a viable result. Our approach is to use particle filtering (PF), which is a sophisticated option for integrating measurements emerging from pedestrian motion having non-Gaussian error characteristics. This paper discusses the statistical modelling of the measurement errors from inertial sensors and vision based heading and translation measurements to include the correct error probability density functions (pdf) in the particle filter implementation. Then, model fitting is used to verify the pdfs of the measurement errors. Based on the deduced error models of the measurements, particle filtering method is developed to fuse all this information, where the weights of each particle are computed based on the specific models derived. The performance of the developed method is tested via two experiments, one at a university’s premises and another in realistic tactical conditions. The results show significant improvement on the horizontal localization when the measurement errors are carefully modelled and their inclusion into the particle filtering implementation correctly realized.

RFS‐based extended target multipath tracking algorithm

The issue of extended target multipath tracking has been studied. Based on the geometry model on the sea surface, a novel extended target multipath tracking algorithm is proposed under the random finite sets (RFS) framework. In the algorithm, extended target probability hypothesis density (ET-PHD) filter is used as a pre-processor, and multipath Bernoulli filter (MPBF) is used as main processor. The outputs of the ET-PHD filter are treated as pseudo-measurements and fed into the MPBF. At last, probability of existence and target state are estimated from the outputs of MPBF. In contrast with the existing extended target filter and multipath filter, the proposed algorithm does not attempt to get the rigorous solution and avoids the high computational complexity. In order to get the solution of the algorithm, its particle filter implementation has been proposed. Results of simulation show that the proposed algorithm estimates target state accurately. Comparing with extended target Bernoulli filter, the proposed algorithm has good tracking performance at the presence of multipath effect.

An Unscented Kalman-Particle Hybrid Filter for Space Object Tracking

Optimal and consistent estimation of the state of space objects is pivotal to surveillance and tracking applications. However, probabilistic estimation of space objects is made difficult by the non-Gaussianity and nonlinearity associated with orbital mechanics. In this paper, we present an unscented Kalman-particle hybrid filtering framework for recursive Bayesian estimation of space objects. The hybrid filtering scheme is designed to provide accurate and consistent estimates when measurements are sparse without incurring a large computational cost. It employs an unscented Kalman filter (UKF) for estimation when measurements are available. When the target is outside the field of view (FOV) of the sensor, it updates the state probability density function (PDF) via a sequential Monte Carlo method. The hybrid filter addresses the problem of particle depletion through a suitably designed filter transition scheme. To assess the performance of the hybrid filtering approach, we consider two test cases of space objects that are assumed to undergo full three dimensional orbital motion under the effects of J 2 and atmospheric drag perturbations. It is demonstrated that the hybrid filters can furnish fast, accurate and consistent estimates outperforming standard UKF and particle filter (PF) implementations.

Parallel implementation of color-based particle filter for object tracking in embedded systems

Recently, embedded systems have become popular because of the rising demand for portable, low-power devices. A common task for these devices is object tracking, which is an essential part of various applications. Until now, object tracking in video sequences remains a challenging problem because of the visual properties of objects and their surrounding environments. Among the common approaches, particle filter has been proven effective in dealing with difficulties in object tracking. In this research, we develop a particle filter based object tracking method using color distributions of video frames as features, and deploy it in an embedded system. Because particle filter is a high-complexity algorithm, we utilize computing power of embedded systems by implementing a parallel version of the algorithm. The experimental results show that parallelization can enhance the performance of particle filter when deployed in embedded systems.

A Multisensor Multi-Bernoulli Filter

In this paper we derive a multi-sensor multi-Bernoulli (MS-MeMBer) filter for multi-target tracking. Measurements from multiple sensors are employed by the proposed filter to update a set of tracks modeled as a multi-Bernoulli random finite set. An exact implementation of the MS-MeMBer update procedure is computationally intractable. We propose an efficient approximate implementation by using a greedy measurement partitioning mechanism. The proposed filter allows for Gaussian mixture or particle filter implementations. Numerical simulations conducted for both linear-Gaussian and non-linear models highlight the improved accuracy of the MS-MeMBer filter and its reduced computational load with respect to the multi-sensor cardinalized probability hypothesis density filter and the iterated-corrector cardinality-balanced multi-Bernoulli filter especially for low probabilities of detection.

MULTI-TARGET DETECTION FROM FULL-WAVEFORM AIRBORNE LASER SCANNER USING PHD FILTER

Abstract. We propose a new technique to detect multiple targets from full-waveform airborne laser scanner. We introduce probability hypothesis density (PHD) filter, a type of Bayesian filtering, by which we can estimate the number of targets and their positions simultaneously. PHD filter overcomes some limitations of conventional Gaussian decomposition method; PHD filter doesn’t require a priori knowledge on the number of targets, assumption of parametric form of the intensity distribution. In addition, it can take a similarity between successive irradiations into account by modelling relative positions of the same targets spatially. Firstly we explain PHD filter and particle filter implementation to it. Secondly we formulate the multi-target detection problem on PHD filter by modelling components and parameters within it. At last we conducted the experiment on real data of forest and vegetation, and confirmed its ability and accuracy.