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?????????, ?????????, ????????? et al. · Scholarworks@UNIST (Ulsan National Institute of Science and Technology) · 2015

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Derivation of recursive Bayesian estimation.

Beren Millidge (11524078), Mufeng Tang (12266723), Mahyar Osanlouy (12292551) et al. · Figshare · 2024

<div><p>One of the key problems the brain faces is inferring the state of the world from a sequence of dynamically changing stimuli, and it is not yet clear how the sensory system achieves this task. A well-established computational framework for describing perceptual processes in the brain is provided by the theory of predictive coding. Although the original proposals of predictive coding have discussed temporal prediction, later work developing this theory mostly focused on static stimuli, and key questions on neural implementation and computational properties of temporal predictive coding networks remain open. Here, we address these questions and present a formulation of the temporal predictive coding model that can be naturally implemented in recurrent networks, in which activity dynamics rely only on local inputs to the neurons, and learning only utilises local Hebbian plasticity. Additionally, we show that temporal predictive coding networks can approximate the performance of the Kalman filter in predicting behaviour of linear systems, and behave as a variant of a Kalman filter which does not track its own subjective posterior variance. Importantly, temporal predictive coding networks can achieve similar accuracy as the Kalman filter without performing complex mathematical operations, but just employing simple computations that can be implemented by biological networks. Moreover, when trained with natural dynamic inputs, we found that temporal predictive coding can produce Gabor-like, motion-sensitive receptive fields resembling those observed in real neurons in visual areas. In addition, we demonstrate how the model can be effectively generalized to nonlinear systems. Overall, models presented in this paper show how biologically plausible circuits can predict future stimuli and may guide research on understanding specific neural circuits in brain areas involved in temporal prediction.</p></div>

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Batch and Recursive Bayesian Estimation

Simo Särkkä, Lennart Svensson · Cambridge University Press eBooks · 2023

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Recursive Bayesian estimation: bearings-only applications

Rickard Karlsson, Fredrik Gustafsson · IEE Proceedings - Radar Sonar and Navigation · 2005

Recursive Bayesian estimation methods are applied to several angle-only applications. Air-to-air passive ranging, in addition to an air-to-sea application with terrain induced constraints, is discussed. The incorporation of terrain information improves estimation performance. The bearings-only problem is also discussed using experimental data from a torpedo, i.e. sea-to-sea with a passive sonar sensor. The Bayesian estimation problem is solved using the particle filter and the marginalised particle filter. For comparison, a filter bank method using range parameterised extended Kalman filters is used.

Cited by 91

Recursive bayesian estimation using gaussian sums

H.W. Sorenson, D. Alspach · Automatica · 1971

Cited by 945

Approximate Bayesian Recursive Estimation: On Approximation Errors

M. (Miroslav) Kárný, K. (Kamil) Dedecius · ASEP · 2012

Adaptive systems rely on recursive estimation of a firmly bounded complex- ity. As a rule, they have to use an approximation of the posterior proba- bility density function (pdf), which comprises unreduced information about the estimated parameter. In recursive setting, the latest approximate pdf is updated using the learnt system model and the newest data and then ap- proximated. The fact that approximation errors may accumulate over time course is mostly neglected in the estimator design and, at most, checked ex post. The paper inspects this problem.

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Recursive Bayesian Estimation Applied to Autonomous Vehicles

Annie M. Westerlund, Helena Jakobsson Larsson · Chalmers Publication Library (Chalmers University of Technology) · 2015

This thesis presents an implementation of a sequential extended Kalman filter applied to position, velocity and\nattitude estimation of autonomous vehicles. The filter is self-tuning by the introduction of a particle swarm\notimization which tunes the process noise covariance. The sensor fusion is adaptive through the means of\ncorrector signals. It accepts correctors in position, velocity and attitude, in all possible combinations. The\nalgorithm also includes an extended Kalman filter for quaternion update in order to make the estimations\nmore robust when implementing sensor fusion \nexibility. The filter architecture developed in this thesis is\ncalled the adaptive self-tuning extended Kalman filter, or the ASTEK filter. The algorithm was first tested in\nMATLAB/Simulink and then implemented and finalized in C++ in order to facilitate real-time performance.\nFrom testings on a truck, the RMS error for estimating position using a GPS corrector lies in the interval\n[10􀀀4; 0:002] m, for velocity in [10􀀀4; 0:02] m/s, and for the estimated attitude in [10􀀀3; 0:21] degrees, depending\non the road and driving mode. When using a 2D map corrector, that is correcting for x, y, and yaw, the RMS\nestimations of roll and pitch are higher and lying in the interval [1.1, 3.1]. However, it is kept stable as a result\nfrom the quaternion EKF, whereas the z-direction diverges as expected. The results show that the algorithm is\nable to produce estimations of high accuracy and that the corrector signals may vary dynamically. Moreover,\nthe results show how different roads and driving modes in\nuence the estimation and error evolution.

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Bayesian recursive estimation on the rotation group

Sofia Suvorova, Howard Caygill, Bill Moran · 2013

Tracking of the orientation of a rigid body based on directional measurements is a key issue in many applications. Configurations in this sense are precisely representable as elements of the rotation group SO(3), and the issue devolves to one of tracking on this group, for which and algorithm is described here. Its novelty derives from the use of maximum entropy distributions on these groups as models for the priors, and from the approximation algorithms that permit numerical implementation of such a model. These solutions can be written in a recursive form. While the general ideas apply in all dimensions, the focus of this paper is on the important 3-dimensional case. It is impossible to compute the exact solution; instead, obtained here is a highly effective approximation. It is shown that, in contrast with other approaches, the algorithm described here produces outputs which are both very accurate and statistically meaningful.

Cited by 7

Recursive Bayesian Methods For Sequential Parameter-State Estimation

Yinan Huang · eCommons (Cornell University) · 2010

A central theme in applied and computational statistics is the accurate and efficient methods of inference. The Bayesian paradigm performs inference based on the posterior distribution of unknown quantities. Throughout decades, there has been an enormous literature on computational Bayesian methods. Practical implementations, while succussful to different degrees, usually impose certain restrictions on the specific model structure. As more applications rely on complex model dynamics, more challenges remain to tackle the curse of high dimensionality and the analytical intractability of many non-Gaussian distributions. This thesis builds on existing research in the field of sequential Bayesian estimation for a general class of state-space models. We establish recursive Bayesian simulation algorithms to estimate parameters and states for a variety of diffusion and jump stochastic models. Our main work and contribution are two-fold. First, we build a particle filter framework for Levy-type state-space models. Particle filters are efficient numerical simulation techniques ideally suitable for highly nonlinear models, with a significant computational advantage over the standard Markov Chain Monte Carlo. Our particle filters can effectively estimate parameters and state variables for non-Gaussian dynamics. We perform empirical testing on financial time series, and find that certain Levy-type small jump processes can be a substitute of the usual Brownian motion-based random walk models. In addition, we propose a general Variational Bayes Particle Filter framework. It is applicable to a wider class of models with a large number of dimensions. Secondly, we build a Variational Bayes estimator for Hidden Markov Models with observational jumps. This is a typical setup for numerous biostatistical data analysis, where huge amounts of streaming data need to be sequentially filtered for potential evidence of the existence of quantitative traits or genetic features. Our algorithm works to identify and classify different responses. The hidden Markov estimator is robust and highly adaptable. In addition, this thesis also includes a self-contained chapter on the technique of Markovian projection. It reduces a complicated multi-dimensional dynamics to a one-dimensional simple Markovian process with identical marginal distributions, therefore keeping certain path-independent expectation values invariant. The projection has certain implications in the pricing of European-style options in financial mathematics. We provide a theorem generalizing existing results to the general Levy jump models, and discuss calibration issues.

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Recursive bayesian state estimation from doppler-shift measurements

Branko Ristić, Alfonso Farina · Figshare · 2011

The problem is recursive Bayesian estimation of position and velocity of a moving object using asynchronous measurements of Doppler-shift frequencies at several separate locations. By adopting a stochastic dynamic target motion model and assuming that the frequency of the emitting tone is known, the paper develops the theoretical Carmer-Rao lower bound for the estimation error as a good indicator of target state observability. Furthermore, a particle filter for the recursive target state estimation is developed and its error performance compared to the theoretical CRLB. Initialisation of the particle filter using Doppler-shift measurement presents itself as a serious challenge.

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Mobile Robotic Radiation Surveying Using Recursive Bayesian Estimation

Robert Blake Anderson, Mitch Pryor, Sheldon Landsberger · 2019

Nuclear facilities require wide-area surveys and remote response to the detection of abnormal radiation levels. These typically require a large number of measurement locations using fixed search patterns. Such approaches are time-consuming, require extended radiation exposure, and are difficult to routinely replicate by technicians. This paper presents an automated method of detecting and locating single or multiple small gamma-ray sources in an unstructured environment, requiring significantly fewer measurements than traditional methods and without a need for post-processing. A mobile robot can collect higher-precision data than practically possible by a human and removes the technician from the radiation area. This is enabled by addressing complexities that previously made automation difficult including supervisory control, obstacle avoidance, sensor positioning over a large height range, recognizing environmental complexities (shielding, etc and modifying survey parameters based on aberrant readings. The developed solution uses a mobile platform with a height-adjustable (up to 2.44 meters) radiation detector. Recursive Bayesian Estimation (RBE) is used to update a probability distribution of the location and intensity of source(s) after each measurement. The likelihood function is determined using radiation transport and detector models. Isotopic identification via a gamma library search aids data analysis by distinguishing counts from different sources. Computation considerations are discussed including predicting and localizing multiple sources.

Cited by 10

Recursive Bayesian state estimation for passive sonar localization.

Colin W. Jemmott, R. Lee Culver · The Journal of the Acoustical Society of America · 2010

A model-based recursive Bayesian signal processing framework is shown to localize a moving source emitting a low-frequency tonal signal in a shallow water environment. Source motion maps spatial variation in transmission loss into amplitude modulation of the signal received on a passive horizontal array. Acoustic propagation modeling predicts this variability, which is used to estimate source range, depth, range rate, and acoustic level. Uncertainty in transmission loss resulting from uncertainty in environmental parameters is predicted using Monte Carlo modal propagation modeling. Monte Carlo marginalization over environmental uncertainty provides robustness against data-model mismatch. The maximum entropy method is used to construct a probability density function (pdf) of transmission loss at each range depth location based on the Monte Carlo results. The resulting pdfs belong to the exponential family and result in an implementable recursive Bayesian processor. The physics of acoustic modeling determine the form of the processor through the transmission loss pdfs and are an intimate part of the localization technique. This processor is distinct from Bayesian matched field processing in that it neither relies on a vertical array nor computes modal amplitudes from received data. Results using SWellEx-96 will be shown. [Work supported by ONR Undersea Signal Processing.]

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Recursive Bayesian estimation of effective defibrillation shock intensities

L.M. Rust, Jay B. Jordan · Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society · 1992

A recursive method for computing optimum Bayesian estimates of effective defibrillation doses is presented. The method produces the same results as previously reported Bayesian techniques with a significant savings in computational complexity. The value of shock intensity required to return the most information about the value of ED50 is provided sequentially at each iterative step. The results show that the up-down algorithm provides significantly more information than the step-up or step-down algorithms. ED50 estimates are refined optimally at each step providing an optimal variable length procedure.

Cited by 1

A new Bayesian recursive technique for parameter estimation

Yasir Kaheil, M. Kashif Gill, Mac McKee et al. · Water Resources Research · 2006

The performance of any model depends on how well its associated parameters are estimated. In the current application, a localized Bayesian recursive estimation (LOBARE) approach is devised for parameter estimation. The LOBARE methodology is an extension of the Bayesian recursive estimation (BARE) method. It is applied in this paper on two different types of models: an artificial intelligence (AI) model in the form of a support vector machine (SVM) application for forecasting soil moisture and a conceptual rainfall‐runoff (CRR) model represented by the Sacramento soil moisture accounting (SAC‐SMA) model. Support vector machines, based on statistical learning theory (SLT), represent the modeling task as a quadratic optimization problem and have already been used in various applications in hydrology. They require estimation of three parameters. SAC‐SMA is a very well known model that estimates runoff. It has a 13‐dimensional parameter space. In the LOBARE approach presented here, Bayesian inference is used in an iterative fashion to estimate the parameter space that will most likely enclose a best parameter set. This is done by narrowing the sampling space through updating the “parent” bounds based on their fitness. These bounds are actually the parameter sets that were selected by BARE runs on subspaces of the initial parameter space. The new approach results in faster convergence toward the optimal parameter set using minimum training/calibration data and fewer sets of parameter values. The efficacy of the localized methodology is also compared with the previously used BARE algorithm.

Cited by 12Open access

Computational Intelligence Sequential Monte Carlos for Recursive Bayesian Estimation

Ayub Hanif · UCL Discovery (University College London) · 2013

Recursive Bayesian estimation using sequential Monte Carlos methods is a powerful numerical technique to understand latent dynamics of non-linear non-Gaussian dynamical systems. Classical sequential Monte Carlos suffer from weight degeneracy which is where the number of distinct particles collapse. Traditionally this is addressed by resampling, which effectively replaces high weight particles with many particles with high inter-particle correlation. Frequent resampling, however, leads to a lack of diversity amongst the particle set in a problem known as sample impoverishment. Traditional sequential Monte Carlo methods attempt to resolve this correlated problem however introduce further data processing issues leading to minimal to comparable performance improvements over the sequential Monte Carlo particle filter. A new method, the adaptive path particle filter, is proposed for recursive Bayesian estimation of non-linear non-Gaussian dynamical systems. Our method addresses the weight degeneracy and sample impoverishment problem by embedding a computational intelligence step of adaptive path switching between generations based on maximal likelihood as a fitness function. Preliminary tests on a scalar estimation problem with non-linear non-Gaussian dynamics and a non-stationary observation model and the traditional univariate stochastic volatility problem are presented. Building on these preliminary results, we evaluate our adaptive path particle filter on the stochastic volatility estimation problem. We calibrate the Heston stochastic volatility model employing a Markov chain Monte Carlo on six securities. Finally, we investigate the efficacy of sequential Monte Carlos for recursive Bayesian estimation of astrophysical time series. We posit latent dynamics for both regularized and irregular astrophysical time series, calibrating fifty-five quasar time series using the CAR(1) model. We find the adaptive path particle filter to statistically significantly outperform the standard sequential importance resampling particle filter, the Markov chain Monte Carlo particle filter and, upon Heston model estimation, the particle learning algorithm particle filter. In addition, from our quasar MCMC calibration we find the characteristic timescale τ to be first-order stable in contradiction to the literature though indicative of a unified underlying structure. We offer detailed analysis throughout, and conclude with a discussion and suggestions for future work.

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Triangulation of Bayesian networks with recursive estimation of distribution algorithms

Txomin Romero, Pedro Larrañaga · International Journal of Approximate Reasoning · 2008

Cited by 30

Active Sound Source Localization by Pinnae with Recursive Bayesian Estimation

Wataru Odo, Daisuke Kimoto, Makoto Kumon et al. · Journal of Robotics and Mechatronics · 2017

[abstFig src='/00290001/05.jpg' width='300' text='Schematic of the proposed system for actively localizing the sound source' ] Animals use two ears to localize the source of a sound, and this paper considers a robot system that localizes a sound source by using two microphones with active external reflectors that mimic movable pinnae. The body of the robot and the environment both affect the propagation of sound waves, which complicates mapping the acoustic cues to the source. The mapping may be multimodal, and the observed acoustic cues may lead to the incorrect estimation of the locations. In order to achieve sound source localization with such multimodal likelihoods, this paper presents a method for determining a configuration of active pinnae, which uses prior knowledge to optimize their location and orientation, and thus attenuates the effects of pseudo-peaks in the observations. The observations are also adversely affected by noise in the sensor signals, and thus Bayesian inference approach to process them is further introduced. Results of experiments that validate the proposed method are also presented.

Cited by 5Open access

The Bayesian Approach to Recursive State Estimation: Implementation and Application.

Stuart Kramer · Defense Technical Information Center (DTIC) · 1985

In Bayesian estimation, the objective is to calculate the complete density function for an unknown quantity conditioned on noisy observations of that quantity. This work considers recursive estimation of a nonlinear discrete-time system state using successive observations. The formal recursion for the density function is easily written, but generally there is no closed form solution. The numerical solution proposed here is obtained by modifying the recursion and using a simple piece-wise constant approximation to the density functions. The critical part of the algorithm then becomes a discrete linear convolution that can be realized using FFT's. Keywords: error analysis; and parameter estimation.

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Recursive Bayesian Estimation of Bat Flapping Flight Using Kinematic Trees

Matt Bender, Hunter M. McClelland, Andrew J. Kurdila et al. · AIAA Modeling and Simulation Technologies Conference · 2016

Cited by 8

Recursive Bayesian Estimation of Respiratory Motion in Nuclear Medicine Imaging.

Abd Rahni, A. A. · Surrey Research Insight Open Access (The University of Surrey) · 2012

The most sensitive approach currently recognised for functional imaging of the human body is nuclear medicine. Although there has been significant technological improvement in system spatial resolution and sensitivity, scan times are still much longer than the period of the single breath-hold typically used in X-ray CT. The image acquisition process thus occurs over multiple respiratory cycles. Together with the improvement in image spatial resolution, these considerations make patient respiratory motion an increasingly significant issue to be addressed, especially regarding the potential issue of image blurring due to such motion. This thesis follows the approach of using an external source of information for estimating an inverse motion field to be used in compensating respiratory motion. The external source of information or surrogate is proposed to be a stereo camera capture of the anterior surface of the torso. Previous similar approaches to the problem can be categorised as regression whereby a deterministic map of internal motion from the external torso surface is found and then used in estimation. However, this thesis proposes recursive Bayesian estimation as an alternative method of inferring internal motion, given an observation of external surface motion of the torso. The advantage of recursive Bayesian estimation is mainly two-fold; firstly, uncertainties can be accounted for explicitly. This is desirable given the nature of respiratory motion. Secondly, recursive Bayesian estimation allows modelling estimation of respiratory motion in a manner that better approximates the physical system, whereby the observation of the external surface is the result of internal motion. In this aspect both models of the correspondence of the surface to internal motion and the temporal evolution of internal motion are used, in addition to modelling the uncertainties involved. The evaluation of recursive Bayesian estimation is based on two sources of 4D respiratory data, motion simulated by the XCAT phantom and 4D MRI. These sources of 4D data are chosen as they are dynamic volumetric representations of the respiratory motion. Using these sources of 4D data, there are three major contributions of the thesis. Firstly, a representation of internal and external motion of the torso is evaluated. The characteristics of the motion found are shown to be in agreement with previous studies. Secondly, a framework of training and testing both models of internal-external motion correspondence and temporal evolution of internal motion are then evaluated. Non-linear models were, on average, found to be more accurate given the evaluation used. Finally, a framework of respiratory motion estimation based on recursive Bayesian estimation which combines the former two contributions is evaluated. Based on the evaluation used, recursive Bayesian estimation was on average, found to be more accurate than deterministic mapping, even though the same types of non-linear models are used in both methods of motion estimation. Within the limits of the evaluation performed, this can be attributed to the two aforementioned advantages of recursive Bayesian. The recursive Bayesian estimation framework proposed is flexible and can be modified for the required estimation approach. The thesis is concluded with suggestions on its application in the clinical scenario and directions for future work.

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