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.

Robotic guides take visitors on a tour of a facility. Such robots must always know the position of the visitor for decision-making. Current tracking algorithms largely assume that the person will be nearly always visible. In the robotic guide application, a person’s visibility could be often lost for prolonged periods, especially when the robot is circumventing a corner or making a sharp turn. In such cases, a person cannot quickly come behind the limited field of view rear camera. We propose a new algorithm that can track people for prolonged times under such conditions. The algorithm is benefitted from an application-level heuristic that the person will be nearly always following the robot, which can be used to guess the motion. The proposed work uses a Particle Filter with a ‘follow-the-robot’ motion model for tracking. The tracking is performed in 3D using a monocular camera. Unlike approaches in the literature, the proposed work observes from a moving base that is especially challenging since a rotation of the robot can cause a large sudden change in the position of the human in the image plane that the approaches in the literature would filter out. Tracking in 3D can resolve such errors. The proposed approach is tested for three different indoor scenarios. The results showcase that the approach is significantly better than the baselines including tracking in the image and projecting in 3D, tracking using a randomized (non-social) motion model, tracking using a Kalman Filter and using LSTM for trajectory prediction.

Assimilation of continuously streamed monitored data is an essential component of a digital twin; the assimilated data are used to ensure the digital twin represents the monitored system as accurately as possible. One way this is achieved is by calibration of simulation models, whether data-derived or physics-based, or a combination of both. Traditional manual calibration is not possible in this context; hence, new methods are required for continuous calibration. In this paper, a particle filter methodology for continuous calibration of the physics-based model element of a digital twin is presented and applied to an example of an underground farm. The methodology is applied to a synthetic problem with known calibration parameter values prior to being used in conjunction with monitored data. The proposed methodology is compared against static and sequential Bayesian calibration approaches and compares favourably in terms of determination of the distribution of parameter values and analysis run times, both essential requirements. The methodology is shown to be potentially useful as a means to ensure continuing model fidelity.

This paper proposes a map-based localization system for autonomous vehicle self-localization in urban environments, which is composed of a pose graph mapping method and 3D curvature feature points – Monte Carlo Localization algorithm (3DCF-MCL). The advantage of 3DCF-MCL is that it combines the high accuracy of the 3D feature points registration and the robustness of particle filter. Experimental results show that 3DCF-MCL can provide an accurate localization for autonomous vehicles with the 3D point cloud map that generated by our mapping method. Compared with other map-based localization algorithms, it demonstrates that 3DCF-MCL outperforms them.

In various scenarios, the motion of a tracked object, for example, a pointing apparatus, pedestrian, animal, vehicle, and others, is driven by achieving a premeditated goal such as reaching a destination. This is albeit the various possible trajectories to this endpoint. This paper presents a generic Bayesian framework that utilizes stochastic models that can capture the influence of intent (viz., destination) on the object behavior. It leads to simple algorithms to infer, as early as possible, the intended endpoint from noisy sensory observations, with relatively low computational and training data requirements. This framework is introduced in the context of the novel predictive touch technology for intelligent user interfaces and touchless interactions. It can determine, early in the interaction task or pointing gesture, the interface item the user intends to select on the display (e.g., touchscreen) and accordingly simplify as well as expedite the selection task. This is shown to significantly improve the usability of displays in vehicles, especially under the influence of perturbations due to road and driving conditions, and enable intuitive contact-free interactions. Data collected in instrumented vehicles are shown to demonstrate the effectiveness of the proposed intent prediction approach.

A new method of forecasting mortality is introduced. The method is based on the continuous-time dynamics of the Lexis diagram, which given weak assumptions implies that the death count data are Poisson distributed. The underlying mortality rates are modelled with a hidden Markov model (HMM) which enables a fully likelihood-based inference. Likelihood inference is done by particle filter methods, which avoids approximating assumptions and also suggests natural model validation measures. The proposed model class contains as special cases many previous models with the important difference that the HMM methods make it possible to estimate the model efficiently. Another difference is that the population and latent variable variability can be explicitly modelled and estimated. Numerical examples show that the model performs well and that inefficient estimation methods can severely affect forecasts.

An improved FastSLAM based on the robust square-root cubature Kalman filter (RSRCKF) with partial genetic resampling is proposed in this paper. In the proposed method, RSRCKF is used to design the proposal distribution of FastSLAM and to estimate environment landmarks. The proposed method does not require a priori knowledge of the noise statistics. In addition, to increase diversity, it uses the genetic operators-based strategy to further improve the particle diversity. In fact, a partial genetic resampling operation is carried out to maintain the diversity of particles. The proposed method is compared with other methods via simulation and experimental data. It can be seen from the results that the proposed method provides significantly more accurate and robust estimation results compared with other methods even with fewer particles and unknown a priori. In addition, the consistency of the proposed method is better than that of other methods.

In the process of composing a double-differenced positioning model, it is difficult to separate different frequency signals between code division multiple access (CDMA) systems, the single-difference ambiguity of the pivot satellite and phase differential inter-system biases (PDISBs). Hence it is difficult to calibrate in advance the bias between systems in order to build an inter-system model which only needs one pivot satellite. Based on analysis of the stability of PDISB parameters for non-overlapping frequency CDMA systems, this study adopts a particle filter to estimate the fractional part of the PDISBs (F-PDISBs) between the systems and proposes a particle filter-based inter-system positioning model. Results show that the F-PDISBs and code DISBs for the baselines with the same receiver types and some with different receiver types are rather stable over time and for these baselines it is feasible to use a particle filter to estimate the F-PDISB parameters in the initial stage. Having attained the F-PDISBs, the inter-system model can be constructed to improve positioning accuracy in complex operational environments.

A prevalent problem in general state-space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous analysis of such approximations of smoothed distributions provided by the two-filter algorithms. We extend the results available for the approximation of smoothing distributions to these two-filter approaches which combine a forward filter approximating the filtering distributions with a backward information filter approximating a quantity proportional to the posterior distribution of the state, given future observations.

We consider the numerical approximation of the filtering problem in high dimensions, that is, when the hidden state lies in ℝd with large d. For low-dimensional problems, one of the most popular numerical procedures for consistent inference is the class of approximations termed particle filters or sequential Monte Carlo methods. However, in high dimensions, standard particle filters (e.g. the bootstrap particle filter) can have a cost that is exponential in d for the algorithm to be stable in an appropriate sense. We develop a new particle filter, called the space‒time particle filter, for a specific family of state-space models in discrete time. This new class of particle filters provides consistent Monte Carlo estimates for any fixed d, as do standard particle filters. Moreover, when there is a spatial mixing element in the dimension of the state vector, the space‒time particle filter will scale much better with d than the standard filter for a class of filtering problems. We illustrate this analytically for a model of a simple independent and identically distributed structure and a model of an L-Markovian structure (L≥ 1, L independent of d) in the d-dimensional space direction, when we show that the algorithm exhibits certain stability properties as d increases at a cost 𝒪(nNd2), where n is the time parameter and N is the number of Monte Carlo samples, which are fixed and independent of d. Our theoretical results are also supported by numerical simulations on practical models of complex structures. The results suggest that it is indeed possible to tackle some high-dimensional filtering problems using the space‒time particle filter that standard particle filters cannot handle.

We consider the time behaviour associated to the sequential Monte Carlo estimate of the backward interpretation of Feynman-Kac formulae. This is particularly of interest in the context of performing smoothing for hidden Markov models. We prove a central limit theorem under weaker assumptions than adopted in the literature. We then show that the associated asymptotic variance expression for additive functionals grows at most linearly in time under hypotheses that are weaker than those currently existing in the literature. The assumptions are verified for some hidden Markov models.

In this paper, we propose a tracking algorithm to detect power lines from millimeter-wave radar video. We propose a general framework of cascaded particle filters which can naturally capture the temporal correlation of the power line objects, and the power-line-specific feature is embedded into the conditional likelihood measurement process of the particle filter. Because of the fusion of multiple information sources, power line detection is more effective than the previous approach. Both the accuracy and the recall of power line detection are improved from around 68% to over 92%.

Nonlinear filter problems arise in many applications such as communications and signal processing. Commonly used numerical simulation methods include Kalman filter method, particle filter method, etc. In this paper a novel numerical algorithm is constructed based on samples of the current state obtained by solving the state equation implicitly. Numerical experiments demonstrate that our algorithm is more accurate than the Kalman filter and more stable than the particle filter.

The algorithm flow of an inertial-based Pedestrian Navigation System (PNS) can be divided into a trajectory-generation stage and trajectory-calibration stage. The Zero-velocity UPdaTe (ZUPT)-aided Extended Kalman Filter (EKF) algorithm is commonly used to resolve the trajectory of a walking person, but it still suffers from long-term drift. Many methods have been developed to suppress these drifts and thus to calibrate the trajectory generated by the previous stage. However, these methods have certain requirements, such as explicit map information or frequent location revisits, which are hard to satisfy in such situations as Search and Rescue (SAR) operations. A new approach is proposed in this paper that requires no explicit presupposition. This approach is based on a particle filter framework, with the weight of particles being adaptively adjusted according to the a priori knowledge of building structures and human behaviours. The distribution of particle weights is designed with awareness of the regular structures of buildings. The time-varying parameter of the distribution is acquired from a Hidden Markov Model (HMM) based on the foregoing odometry, which has a close relation with human behaviour. HMM is trained offline based on samples acquired in advance. Many real-world experiments under various scenarios were performed, and the results indicate good accuracy and robustness of the proposed approach.

In global localization under the framework of a particle filter, the acquiring of effective observations of the whole particle system will be greatly effected by the uncertainty of a prior-map, such as unspecific structures and noises. In this study, taking the uncertainty of the prior-map into account, a localizability-based action selection mechanism for mobile robots is proposed to accelerate the convergence of global localization. Localizability is defined to evaluate the observations according to the prior-map (probabilistic grid map) and observation (laser range-finder) models based on the Cramér-Rao Bound. The evaluation considers the uncertainty of the prior-map and does not need to extract any specific observation features. Essentially, localizability is the determinant of the inverse covariance matrix for localization. Specifically, at the beginning of every filtering step, the action, which makes the whole particle system to achieve the maximum localizability distinctness, is selected as the actual action. Then there will be the increased opportunities for accelerating the convergence of the particles, especially in the face of the prior-map with uncertainty. Additionally, the computational complexity of the proposed algorithm does not increase significantly, as the localizability is pre-cached off-line. In simulations, the proposed active algorithm is compared with the passive algorithm (i.e. global localization with the random robot actions) in environments with different degrees of uncertainty. In experiments, the effectiveness of the localizability is verified and then the comparative experiments are conducted based on an intelligent wheelchair platform in a real environment. Finally, the experimental results are compared and analyzed among the existing active algorithms. The results demonstrate that the proposed algorithm could accelerate the convergence of global localization and enhance the robustness against the system ambiguities, thereby reducing the failure probability of the convergence.

U.S. production has shifted from goods-producing to service-producing industries. We assess whether this shift contributed to the decline in U.S. output volatility over the period 1949–2005 and provide an estimate of its relative importance. Growth rates of GDP by industry are analyzed in a seemingly unrelated multivariate autoregression framework with time-varying innovation covariance matrices. These changing unobserved covariance matrices are modeled as a Wishart autoregressive process of order one, which results in a nonlinear state-space system. The particle filter is used to obtain estimates of the innovation covariance matrix at each point in time. Several counterfactual experiments make it possible to apportion the decline in output volatility between the shift in the sectoral composition and changes in innovations. Our main finding is that the shift into the service sector can explain about 30% of the decline in GDP's volatility, despite the fact that some sectors became even more volatile. This result is robust across a wide variety of alternative specifications.

Particle filter algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. For a given set of observations, the behaviour of particle filters, as the number of particles tends to infinity, is asymptotically Gaussian, and the asymptotic variance in the central limit theorem depends on the set of observations. In this paper we establish, under general assumptions on the hidden Markov model, the tightness of the sequence of asymptotic variances when considered as functions of the random observations as the number of observations tends to infinity. We discuss our assumptions on examples and provide numerical simulations.