Tag Archives: Recursive Bayesian Estimation

Improving sensory information, diagnosis and fault tolerance by using multiple sensors and sensor fusion, with a good related work section (2.3) on fault tolerance on data fusion

Kaci Bader, Benjamin Lussier, Walter Schön, A fault tolerant architecture for data fusion: A real application of Kalman filters for mobile robot localization, Robotics and Autonomous Systems, Volume 88, February 2017, Pages 11-23, ISSN 0921-8890, DOI: 10.1016/j.robot.2016.11.015.

Multisensor perception has an important role in robotics and autonomous systems, providing inputs for critical functions including obstacle detection and localization. It is starting to appear in critical applications such as drones and ADASs (Advanced Driver Assistance Systems). However, this kind of complex system is difficult to validate comprehensively. In this paper we look at multisensor perception systems in relation to an alternative dependability method, namely fault tolerance. We propose an approach for tolerating faults in multisensor data fusion that is based on the more traditional method of duplication–comparison, and that offers detection and recovery services. We detail an example implementation using Kalman filter data fusion for mobile robot localization. We demonstrate its effectiveness in this case study using real data and fault injection.

Using the Bingham distribution of probability, which is defined on a d-dimensional sphere to be antipodally symmetric, to address the problem of angle periodicity in [0,2pi] when estimating orientation in a recursive filter

Gilitschenski, I.; Kurz, G.; Julier, S.J.; Hanebeck, U.D., Unscented Orientation Estimation Based on the Bingham Distribution, in Automatic Control, IEEE Transactions on , vol.61, no.1, pp.172-177, Jan. 2016, DOI: 10.1109/TAC.2015.2423831.

In this work, we develop a recursive filter to estimate orientation in 3D, represented by quaternions, using directional distributions. Many closed-form orientation estimation algorithms are based on traditional nonlinear filtering techniques, such as the extended Kalman filter (EKF) or the unscented Kalman filter (UKF). These approaches assume the uncertainties in the system state and measurements to be Gaussian-distributed. However, Gaussians cannot account for the periodic nature of the manifold of orientations and thus small angular errors have to be assumed and ad hoc fixes must be used. In this work, we develop computationally efficient recursive estimators that use the Bingham distribution. This distribution is defined on the hypersphere and is inherently more suitable for periodic problems. As a result, these algorithms are able to consistently estimate orientation even in the presence of large angular errors. Furthermore, handling of nontrivial system functions is performed using an entirely deterministic method which avoids any random sampling. A scheme reminiscent of the UKF is proposed for the nonlinear manifold of orientations. It is the first deterministic sampling scheme that truly reflects the nonlinear manifold of orientations.

Comparison of EKF and UKF for robot localization and a method of selection of a subset of the available sonar sensors

Luigi D’Alfonso, Walter Lucia, Pietro Muraca, Paolo Pugliese, Mobile robot localization via EKF and UKF: A comparison based on real data, Robotics and Autonomous Systems, Volume 74, Part A, December 2015, Pages 122-127, ISSN 0921-8890, DOI: 10.1016/j.robot.2015.07.007.

In this work we compare the performance of two well known filters for nonlinear models, the Extended Kalman Filter and the Unscented Kalman Filter, in estimating the position and orientation of a mobile robot. The two filters fuse the measurements taken by ultrasonic sensors located onboard the robot. The experimental results on real data show a substantial equivalence of the two filters, although in principle the approximating properties of the UKF are much better. A switching sensors activation policy is also devised, which allows to obtain an accurate estimate of the robot state using only a fraction of the available sensors, with a relevant saving of battery power.

One of the first thorough studies of Monte Carlo Localization with line-segment maps

Biswajit Sarkar, Surojit Saha, Prabir K. Pal, A novel method for computation of importance weights in Monte Carlo localization on line segment-based maps, Robotics and Autonomous Systems, Volume 74, Part A, December 2015, Pages 51-65, ISSN 0921-8890, DOI: 10.1016/j.robot.2015.07.001.

Monte Carlo localization is a powerful and popular approach in mobile robot localization. Line segment-based maps provide a compact and scalable representation of indoor environments for mobile robot navigation. But Monte Carlo localization has seldom been studied in the context of line segment-based maps. A key step of the approach–and one that can endow it with or rob it of the attributes of accuracy, robustness and efficiency–is the computation of the so called importance weight associated with each particle. In this paper, we propose a new method for the computation of importance weights on maps represented with line segments, and extensively study its performance in pose tracking. We also compare our method with three other methods reported in the literature and present the results and insights thus gathered. The comparative study, conducted using both simulated and real data, on maps built from real data available in the public domain clearly establish that the proposed method is more accurate, robust and efficient than the other methods.

A clarification and systematization of UKF

Menegaz, H.M.T.; Ishihara, J.Y.; Borges, G.A.; Vargas, A.N., A Systematization of the Unscented Kalman Filter Theory, in Automatic Control, IEEE Transactions on , vol.60, no.10, pp.2583-2598, Oct. 2015 DOI: 10.1109/TAC.2015.2404511.

In this paper, we propose a systematization of the (discrete-time) Unscented Kalman Filter (UKF) theory. We gather all available UKF variants in the literature, present corrections to theoretical inconsistencies, and provide a tool for the construction of new UKF’s in a consistent way. This systematization is done, mainly, by revisiting the concepts of Sigma-Representation, Unscented Transformation (UT), Scaled Unscented Transformation (SUT), UKF, and Square-Root Unscented Kalman Filter (SRUKF). Inconsistencies are related to 1) matching the order of the transformed covariance and cross-covariance matrices of both the UT and the SUT; 2) multiple UKF definitions; 3) issue with some reduced sets of sigma points described in the literature; 4) the conservativeness of the SUT; 5) the scaling effect of the SUT on both its transformed covariance and cross-covariance matrices; and 6) possibly ill-conditioned results in SRUKF’s. With the proposed systematization, the symmetric sets of sigma points in the literature are formally justified, and we are able to provide new consistent variations for UKF’s, such as the Scaled SRUKF’s and the UKF’s composed by the minimum number of sigma points. Furthermore, our proposed SRUKF has improved computational properties when compared to state-of-the-art methods.

Modelling ECGs with sums of gaussians and estimating them through switching Kalman Filters and the likelihood of each mode

Oster, J.; Behar, J.; Sayadi, O.; Nemati, S.; Johnson, A.E.W.; Clifford, G.D., Semisupervised ECG Ventricular Beat Classification With Novelty Detection Based on Switching Kalman Filters, in Biomedical Engineering, IEEE Transactions on , vol.62, no.9, pp.2125-2134, Sept. 2015, DOI: 10.1109/TBME.2015.2402236.

Automatic processing and accurate diagnosis of pathological electrocardiogram (ECG) signals remains a challenge. As long-term ECG recordings continue to increase in prevalence, driven partly by the ease of remote monitoring technology usage, the need to automate ECG analysis continues to grow. In previous studies, a model-based ECG filtering approach to ECG data from healthy subjects has been applied to facilitate accurate online filtering and analysis of physiological signals. We propose an extension of this approach, which models not only normal and ventricular heartbeats, but also morphologies not previously encountered. A switching Kalman filter approach is introduced to enable the automatic selection of the most likely mode (beat type), while simultaneously filtering the signal using appropriate prior knowledge. Novelty detection is also made possible by incorporating a third mode for the detection of unknown (not previously observed) morphologies, and denoted as X-factor. This new approach is compared to state-of-the-art techniques for the ventricular heartbeat classification in the MIT-BIH arrhythmia and Incart databases. F1 scores of 98.3% and 99.5% were found on each database, respectively, which are superior to other published algorithms’ results reported on the same databases. Only 3% of all the beats were discarded as X-factor, and the majority of these beats contained high levels of noise. The proposed technique demonstrates accurate beat classification in the presence of previously unseen (and unlearned) morphologies and noise, and provides an automated method for morphological analysis of arbitrary (unknown) ECG leads.

A novel non-linear bayesian filter for continuous time estimation with a nice comparison to discrete-time filters

Atiyeh Ghoreyshi and Terence D. Sanger, A Nonlinear Stochastic Filter for Continuous-Time State Estimation, IEEE Transactions on Automatic Control, vol. 60, no. 8, DOI: 10.1109/TAC.2015.2409910.

Nonlinear filters produce a nonparametric estimate of the probability density of state at each point in time. Currently known nonlinear filters include Particle Filters and the Kushner equation (and its un-normalized version: the Zakai equation). However, these filters have limited measurement models: Particle Filters require measurement at discrete times, and the Kushner and Zakai equations only apply when the measurement can be represented as a function of the state. We present a new nonlinear filter for continuous-time measurements with a much more general stochastic measurement model. It integrates to Bayes’ rule over short time intervals and provides Bayes-optimal estimates from quantized, intermittent, or ambiguous sensor measurements. The filter has a close link to Information Theory, and we show that the rate of change of entropy of the density estimate is equal to the mutual information between the measurement and the state and thus the maximum achievable. This is a fundamentally new class of filter that is widely applicable to nonlinear estimation for continuous-time control.

Substituting the update step of a bayesian filter by a maximum likelihood optimisation in order to use non-linear observation models in a (linear-transition) Kalman framework

Damián Marelli, Minyue Fu, and Brett Ninness, Asymptotic Optimality of the Maximum-Likelihood Kalman Filter for Bayesian Tracking With Multiple Nonlinear Sensors, IEEE Transactions on signal processing, vol. 63, no. 17, DOI: 10.1109/TSP.2015.2440220.

Bayesian tracking is a general technique for state estimation of nonlinear dynamic systems, but it suffers from the drawback of computational complexity. This paper is concerned with a class of Wiener systems with multiple nonlinear sensors. Such a system consists of a linear dynamic system followed by a set of static nonlinear measurements. We study a maximum-likelihood Kalman filtering (MLKF) technique which involves maximum-like-lihood estimation of the nonlinear measurements followed by classical Kalman filtering. This technique permits a distributed implementation of the Bayesian tracker and guarantees the boundedness of the estimation error. The focus of this paper is to study the extent to which the MLKF technique approximates the theoretically optimal Bayesian tracker. We provide conditions to guarantee that this approximation becomes asymptotically exact as the number of sensors becomes large. Two case studies are analyzed in detail.

A brief general explanation of Rao-Blacwellization and a new way of applying it to reduce the variance of a point estimation in a sequential bayesian setting

Petetin, Y.; Desbouvries, F., Bayesian Conditional Monte Carlo Algorithms for Nonlinear Time-Series State Estimation, Signal Processing, IEEE Transactions on , vol.63, no.14, pp.3586,3598, DOI: 10.1109/TSP.2015.2423251.

Bayesian filtering aims at estimating sequentially a hidden process from an observed one. In particular, sequential Monte Carlo (SMC) techniques propagate in time weighted trajectories which represent the posterior probability density function (pdf) of the hidden process given the available observations. On the other hand, conditional Monte Carlo (CMC) is a variance reduction technique which replaces the estimator of a moment of interest by its conditional expectation given another variable. In this paper, we show that up to some adaptations, one can make use of the time recursive nature of SMC algorithms in order to propose natural temporal CMC estimators of some point estimates of the hidden process, which outperform the associated crude Monte Carlo (MC) estimator whatever the number of samples. We next show that our Bayesian CMC estimators can be computed exactly, or approximated efficiently, in some hidden Markov chain (HMC) models; in some jump Markov state-space systems (JMSS); as well as in multitarget filtering. Finally our algorithms are validated via simulations.

Accelerating the updating stage of a PF through selection of a few representative particles and interpolation of their weights to the rest, with interesting methods for selection and interpolation and a nice related work of efficiency-improved PFs

Shabat, G.; Shmueli, Y.; Bermanis, A.; Averbuch, A., Accelerating Particle Filter Using Randomized Multiscale and Fast Multipole Type Methods, Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.37, no.7, pp.1396,1407, July 1 2015, DOI: 10.1109/TPAMI.2015.2392754.

Particle filter is a powerful tool for state tracking using non-linear observations. We present a multiscale based method that accelerates the tracking computation by particle filters. Unlike the conventional way, which calculates weights over all particles in each cycle of the algorithm, we sample a small subset from the source particles using matrix decomposition methods. Then, we apply a function extension algorithm that uses a particle subset to recover the density function for all the rest of the particles not included in the chosen subset. The computational effort is substantial especially when multiple objects are tracked concurrently. The proposed algorithm significantly reduces the computational load. By using the Fast Gaussian Transform, the complexity of the particle selection step is reduced to a linear time in n and k , where n is the number of particles and k is the number of particles in the selected subset. We demonstrate our method on both simulated and on real data such as object tracking in video sequences.