a particle filter based framework for real time state estimation of a non linear hyperbolic pde system describing transient flows in co2 pipelines in this work pressure temperature and mass flow observations are assimilated into a fluid flow model describing the dynamics of co2 flow in liquid or dense phase during normal pipeline operations the goal is to improve its state estimates using two sequential monte carlo smc methods namely the sequential importance resampling sir filter and the auxiliary sampling importance resampling filter asir after constructing a state space model of the nonisothermal single phase flow model the sir and asir filters are implemented the state variables are updated with simulated measurements the partial differential equations are semi discretized via a fourth order five point approximation and solved with the fourth order runge kutta method to obtain finite dimensional discrete time state space representations the system states are then combined into an augmented state vector the resulting nonlinear state space model is used for the design of the particle filter that provides real time estimations of the system states numerical experiments were carried out in order to 1 examine the impact of ensemble size on accuracy and computational cost 2 analyze the effects of different model and observation error covariance structures on the filters performance and 3 investigate the robustness of the filters by adding a student s t distributed noise to the model

sparse grid quadrature nonlinear filtering in this paper a novel nonlinear filter named sparse grid quadrature filter sgqf is proposed the filter utilizes weighted sparse grid quadrature points to approximate the multi dimensional integrals in the nonlinear bayesian estimation algorithm the locations and weights of the univariate quadrature points with a range of accuracy levels are determined by the moment matching method then the univariate quadrature point sets are extended to form a multi dimensional grid using the sparse grid theory compared with the conventional point based methods the estimation accuracy level of the sgqf can be flexibly controlled and the number of sparse grid quadrature points for the sgqf is a polynomial of the dimension of the system which alleviates the curse of dimensionality for high dimensional problems the unscented kalman filter ukf is proven to be a subset of the sgqf at the level 2 accuracy the performance of this filter is demonstrated by an orbit estimation problem the simulation results show that the sgqf achieves higher accuracy than the extended kalman filter ekf the ukf and the cubature kalman filter ckf in addition the sgqf is computationally much more efficient than the multi dimensional gauss hermite quadrature filter ghqf with the same performance

truncated unscented kalman filtering we devise a filtering algorithm to approximate the first two moments of the posterior probability density function pdf the novelties of the algorithm are in the update step if the likelihood has a bounded support we can use a modified prior distribution that meets bayes rule exactly applying a kalman filter kf to the modified prior distribution referred to as truncated kalman filter tkf can vastly improve the performance of the conventional kalman filter particularly when the measurements are informative relative to the prior the application of the tkf to practical problems in which the measurement noise pdf has unbounded support is achieved by imposing several approximating assumptions which are valid only when the measurements are informative this implies that we adaptively choose between an approximation to the kf or the tkf according to the information provided by the measurement the resulting algorithm based on the unscented transformation is referred to as truncated unscented kf

renyi divergence and kullback leibler divergence renyi divergence is related to renyi entropy much like kullback leibler divergence is related to shannon s entropy and comes up in many settings it was introduced by renyi as a measure of information that satisfies almost the same axioms as kullback leibler divergence and depends on a parameter that is called its order in particular the renyi divergence of order 1 equals the kullback leibler divergence we review and extend the most important properties of renyi divergence and kullback leibler divergence including convexity continuity limits of sigma algebras and the relation of the special order 0 to the gaussian dichotomy and contiguity we also show how to generalize the pythagorean inequality to orders different from 1 and we extend the known equivalence between channel capacity and minimax redundancy to continuous channel inputs for all orders and present several other minimax results

fluctuation theorems for quantum master equations a quantum fluctuation theorem for a driven quantum subsystem interacting with its environment is derived based solely on the assumption that its reduced density matrix obeys a closed evolution equation i e a quantum master equation qme quantum trajectories and their associated entropy heat and work appear naturally by transforming the qme to a time dependent liouville space basis that diagonalizes the instantaneous reduced density matrix of the subsystem a quantum integral fluctuation theorem a steady state fluctuation theorem and the jarzynski relation are derived in a similar way as for classical stochastic dynamics

a monte carlo approach to nonnormal and nonlinear state space modeling abstract a solution to multivariate state space modeling forecasting and smoothing is discussed we allow for the possibilities of nonnormal errors and nonlinear functionals in the state equation the observational equation or both an adaptive monte carlo integration technique known as the gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework the methodology is a general strategy for obtaining marginal posterior densities of coefficients in the model or of any of the unknown elements of the state space missing data problems including the k step ahead prediction problem also are easily incorporated into this framework we illustrate the broad applicability of our approach with two examples a problem involving nonnormal error distributions in a linear model setting and a one step ahead prediction problem in a situation where both the state and observational equations are nonlinear and involve unknown parameters

the second laws of quantum thermodynamics the second law of thermodynamics places constraints on state transformations it applies to systems composed of many particles however we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath is there a second law of thermodynamics in this regime here we find that for processes which are approximately cyclic the second law for microscopic systems takes on a different form compared to the macroscopic scale imposing not just one constraint on state transformations but an entire family of constraints we find a family of free energies which generalize the traditional one and show that they can never increase the ordinary second law relates to one of these with the remainder imposing additional constraints on thermodynamic transitions we find three regimes which determine which family of second laws govern state transitions depending on how cyclic the process is in one regime one can cause an apparent violation of the usual second law through a process of embezzling work from a large system which remains arbitrarily close to its original state these second laws are relevant for small systems and also apply to individual macroscopic systems interacting via long range interactions by making precise the definition of thermal operations the laws of thermodynamics are unified in this framework with the first law defining the class of operations the zeroth law emerging as an equivalence relation between thermal states and the remaining laws being monotonicity of our generalized free energies

filtering of stochastic nonlinear differential systems via a carleman approximation approach this paper deals with the state estimation problem for stochastic nonlinear differential systems driven by standard wiener processes and presents a filter that is a generalization of the classical extended kalman bucy filter ekbf while the ekbf is designed on the basis of a first order approximation of the system around the current estimate the proposed filter exploits a carleman like approximation of a chosen degree v ges 1 the approximation procedure applied to both the state and the measurement equations allows to define an approximate representation of the system by means of a bilinear system for which a filtering algorithm is available from the literature numerical simulations on an example show the improvement in terms of sample error covariance of the filter based on the first order second order and third order system approximations v 1 2 3

structure identification for gene regulatory networks via linearization and robust state estimation abstract inferring causal relationships among cellular components is one of the fundamental problems in understanding biological behaviours the well known extended kalman filter ekf has been proved to be a useful tool in simultaneously estimating both structure and actual gene expression levels of a gene regulatory network grn first order approximations however unavoidably result in modelling errors but the ekf based method does not take either unmodelled dynamics or parametric uncertainties into account which makes its estimation performances not very satisfactory to overcome these problems a sensitivity penalization based robust state estimator is adopted in this paper for revealing the structure of a grn based on the specific structure of the estimation problem it has been proved that under some weak conditions both the ekf based method and the method suggested in this paper provide a consistent estimate but the suggested method has a faster convergence speed compared with both the ekf and the unscented kalman filter ukf based methods simulation results and real data based estimations consistently show that both convergence speed and parametric estimation accuracy can be appreciably improved these lead to significant reductions in both false positive errors and false negative errors and may imply helpfulness of the suggested method in better understanding the structure and dynamics of actual grns

quantization based filtering method using first order approximation the quantization based filtering method see g pages and h pham bernoulli 11 2005 pp 893 932 g pages h pham and j printems optimal quantization methods and applications to numerical problems in finance in handbook of computational and numerical methods in finance s t rachev ed birkhauser boston 2004 pp 253 297 is a grid based approximation method to solve nonlinear filtering problems with discrete time observations it relies on off line preprocessing of some signal grids in order to construct fast recursive schemes for filter approximation we give here an improvement of this method by taking advantage of the stationary quantizer property the key ingredient is the use of vanishing correction terms to describe schemes based on piecewise linear approximations convergence results are given and numerical results are presented for the particular cases of linear gaussian model and stochastic volatility models

spectral bayesian estimation for general stochastic hybrid systems abstract general stochastic hybrid systems gshs have been formulated to represent various types of uncertainties in hybrid dynamical systems in this paper we propose computational techniques for bayesian estimation of gshs in particular the fokker planck equation that describes the evolution of uncertainty distributions along gshs is solved by spectral techniques where an arbitrary form of probability density of the hybrid state is represented by a mixture of fourier series the method is based on splitting the fokker planck equation represented by an integro partial differential equation into the partial differentiation part for continuous diffusion and the integral part for discrete transition and integrating the solution of each part the propagated density function is used with a likelihood function in the bayes formula to estimate the hybrid state for given sensor measurements the unique feature of the proposed technique is that the probability density describing complete stochastic properties of the hybrid state is constructed without relying on the common gaussian assumption in contrast to other methods that compute certain expected values such as mean or variance we apply the proposed method to the estimation of two examples the bouncing ball model and the dubins vehicle model we show that the proposed technique yields propagated densities consistent with monte carlo simulations more accurate estimates over the gaussian based approach and some computational benefits over a particle filter

particle filters for state estimation of jump markov linear systems jump markov linear systems jmls are linear systems whose parameters evolve with time according to a finite state markov chain in this paper our aim is to recursively compute optimal state estimates for this class of systems we present efficient simulation based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed lag smoothing problem our algorithms combine sequential importance sampling a selection scheme and markov chain monte carlo methods they use several variance reduction methods to make the most of the statistical structure of jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problems of on line deconvolution of impulsive processes and of tracking a maneuvering target are considered it is shown that our algorithms outperform the current methods

conditional posterior cramer rao lower bounds for nonlinear sequential bayesian estimation the posterior cramerrao lower bound pcrlb for sequential bayesian estimators which was derived by tichavsky in 1998 provides a performance bound for a general nonlinear filtering problem however it is an offline bound whose corresponding fisher information matrix fim is obtained by taking the expectation with respect to all the random variables namely the measurements and the system states as a result this unconditional pcrlb is not well suited for adaptive resource management for dynamic systems the new concept of conditional pcrlb is proposed and derived in this paper which is dependent on the actual observation data up to the current time and is implicitly dependent on the underlying system state therefore it is adaptive to the particular realization of the underlying system state and provides a more accurate and effective online indication of the estimation performance than the unconditional pcrlb both the exact conditional pcrlb and its recursive evaluation approach including an approximation are derived further a general sequential monte carlo solution is proposed to compute the conditional pcrlb recursively for nonlinear non gaussian sequential bayesian estimation problems the differences between this new bound and existing measurement dependent pcrlbs are investigated and discussed illustrative examples are also provided to show the performance of the proposed conditional pcrlb

fixed interval smoothing for markovian switching systems a suboptimal approach to the fixed interval smoothing problem for markovian switching systems is examined a smoothing algorithm is developed that uses two multiple model filters where one of the filters propagates in the forward time direction and the other one propagates in the backward time direction a backward time filtering algorithm based on the interacting multiple model concept is also developed results from a simulation example are given to illustrate the performance of the smoothing algorithm with respect to that of filtering the example involves radar tracking of a mach 1 aircraft

coupling deep correlation filter and online discriminative learning for visual object tracking advances in mathematical models and optimization introduce powerful tools for solving the visual object tracking problem but this fundamental problem remains unsolved due to various challenges such as illumination variation deformation and occlusion recent progress in correlation filter based models has provided an effective and efficient tracking solution this type of trackers exploits the property of convolution theorem to significantly speed up their computational processes however their scheme of training correlation filters restricts them to use only a few negative examples to train their model consequently lowers their performance therefore in this paper we propose to combine the fast calculation advantage of correlation filter with an online discriminative learning model which can fully exploit the negative examples in the context around the target the proposed tracker proceeds in a coarse to fine scheme the proposed tracker will first employ a correlation filter to generate a coarse estimation of the location of the target and then employ a translating model to refine its estimation and calculate the scale variation of the target via a scaling model both the translating model and the scaling model are formulated in the framework of our online discriminative model besides we also propose an effective offline representation learning method to generate robust image feature for our correlation filter extensive experiments on the online object tracking benchmark against the state of the art methods validate the effectiveness of the proposed tracker

a novel batch bayesian wiv estimator for three dimensional tma using bearing and elevation measurements in this paper we derive a novel batch bayesian weighted instrumental variable estimator for the three dimensional 3d target motion analysis tma problem using bearing and elevation measurements unlike most existing 3d estimators based on instrumental variables the proposed approach is able to incorporate a priori information into the estimation process and is proven to be approximately asymptotically unbiased an approximate asymptotic covariance matrix is also presented to evaluate the performance of the estimator simulation results show that the proposed estimator outperforms its non bayesian counterpart and has an estimation performance on par with the conventional iterative maximum a posteriori estimator while being orders of magnitude faster in a passive sonar tma problem moreover it was shown that the proposed approach can provide an accurate initialization for recursive estimators

convex saturated particle filter in many systems the state variables are defined on a compact set of the state space to estimate the states of such systems the constrained particle filters have been used with some success the performance of the standard particle filters can be improved if the measurement information is used during the importance sampling of the filtering phase it has been shown that the particles obtained in such a way approximate the true state of the system more accurately the measurement is incorporated into the filtering algorithm through a user specified detection function which aims to detect the saturation as it occurs the algorithm derived from the aforementioned principle is called the saturated particle filter spf in our previous work we have derived a complete spf framework for the class of systems with one dimensional constraints in this paper we derive a novel convex spf that extends our method to multidimensional systems with convex constraints the effectiveness of the new method is demonstrated using an illustrative example

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

on the use of binary programming for sensor scheduling in this paper we propose two myopic sensor scheduling algorithms for target tracking scenarios in which there is a tradeoff between tracking performance and sensor usage costs specifically we consider the problem of activating the lowest cost combination of at most l sensors that maintains a desired squared error accuracy in the target s position estimate for sensors that provide position information only we develop a binary 0 1 mixed integer programming formulation for the scheduling problem and solve it using a linear programming relaxation based branch and bound technique for sensors that provide both position and velocity information we pose the scheduling problem as a binary convex programming problem and solve it using the outer approximation algorithm we apply our scheduling procedures in a network of sensors where the sensor usage costs correspond to network energy consumption our simulation results demonstrate that scheduling using binary programming allows us to obtain optimal solutions to scheduling involving up to 50 70 sensors typically in the order of seconds

manoeuvring target tracking with coordinated turn motion using stochastic non linear filter allowing for perturbations in speed and turn rate of a target moving in a coordinated turn obeys a non linear stochastic differential equation existing algorithms for coordinated turn tracking avoid this problem by ignoring perturbations in the continuous time model and adding process noise only after discretisation the dynamic model used here adds small perturbations modelled as independent brownian motion processes to the speed and turn rate the target state is to be recursively estimated from noisy discrete time measurements of the target s range and bearing in particular this paper examines the effect of the perturbations in speed and turn rate on the coordinated turn motion of the aircraft and subsequently the stochastic algorithm is developed by deriving the evolutions of conditional means and variances for estimating the state of the aircraft by linearizing the stochastic differential equations about the mean of the state vector using first order approximation the mean trajectory of the r

performance evaluation of ukf based nonlinear filtering the performance of the modified unscented kalman filter ukf for nonlinear stochastic discrete time system with linear measurement equation is investigated it is proved that under certain conditions the estimation error of the ukf remains bounded furthermore it is shown that the design of noise covariance matrix plays an important role in improving the stability of the algorithm error behavior of the ukf is then derived in terms of mean square error mse and the cramer rao lower bound crlb is introduced as a performance measure the modified ukf is found to approach the crlb if the difference between the real noise covariance matrix and the selected one is small enough these results are verified by using monte carlo simulations on two example systems

parameter estimation by ensemble kalman filters with transformed data approach and application to hydraulic tomography 1 ensemble kalman filters enkfs are a successful tool for estimating state variables in atmospheric and oceanic sciences recent research has prepared the enkf for parameter estimation in groundwater applications enkfs are optimal in the sense of bayesian updating only if all involved variables are multivariate gaussian subsurface flow and transport state variables however generally do not show gaussian dependence on hydraulic log conductivity and among each other even if log conductivity is multi gaussian to improve enkfs in this context we apply nonlinear monotonic transformations to the observed states rendering them gaussian gaussian anamorphosis ga similar ideas have recently been presented by beal et al 2010 in the context of state estimation our work transfers and adapts this methodology to parameter estimation additionally we address the treatment of measurement errors in the transformation and provide several multivariate analysis tools to evaluate the expected usefulness of ga beforehand for illustration we present a first time application of an enkf to parameter estimation from 3 d hydraulic tomography in multi gaussian log conductivity fields results show that 1 ga achieves an implicit pseudolinearization of drawdown data as a function of log conductivity and 2 this makes both parameter identification and prediction of flow and transport more accurate combining enkfs with ga yields a computationally efficient tool for nonlinear inversion of data with improved accuracy this is an attractive benefit given that linearization free methods such as particle filters are computationally extremely demanding

calculus on arithmetic surfaces in a2 and a3 arakelov introduces an intersection calculus for arithmetic surfaces that is for stable models of curves over a number field in this paper we intend to show that his intersection product has a lot of useful properties more precisely we show that the following properties from the theory of algebraic surfaces have an analogue in our situation

filtering via simulation auxiliary particle filters this article analyses the recently suggested particle approach to filtering time series we suggest that the algorithm is not robust to outliers for two reasons the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution here we tackle the first of these problems

following a moving target monte carlo inference for dynamic bayesian models markov chain monte carlo mcmc sampling is a numerically intensive simulation technique which has greatly improved the practicality of bayesian inference and prediction however mcmc sampling is too slow to be of practical use in problems involving a large number of posterior target distributions as in dynamic modelling and predictive model selection alternative simulation techniques for tracking moving target distributions known as particle filters which combine importance sampling importance resampling and mcmc sampling tend to suffer from a progressive degeneration as the target sequence evolves we propose a new technique based on these same simulation methodologies which does not suffer from this progressive degeneration

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

efficient numerical approximation of maximum entropy estimates a class of algorithms for approximation of the maximum entropy estimate of probability density functions on the basis of a finite number of sampled data is introduced the algorithms are presented as a finite sequence in order of increasing accuracy and decreasing computational efficiency in which the last element of the sequence is the exact maximum entropy estimate numerical and applicative examples are reported

constructive method for detecting the information backflow of non markovian dynamics we investigate the relation between two approaches to the characterization of quantum markovianity divisibility and lack of information backflow we show that a bijective dynamical map is completely positive divisible if and only if a monotonic nonincrease of distinguishability is observed for two equiprobable states of the evolving system and an ancilla moreover our proof is constructive given any such map that is not completely positive divisible we give an explicit construction of two states that when taken with the same a priori probability exhibit information backflow finally while an ancilla is necessary for the equivalence to hold in general we show that it is always possible to witness the non markovianity of bijective maps without using any entanglement between the system and ancilla

optimized self localization for slam in dynamic scenes using probability hypothesis density filters in many applications sensors that map the positions of objects in unknown environments are installed on dynamic platforms as measurements are relative to the observer s sensors scene mapping requires accurate knowledge of the observer state however in practice observer reports are subject to positioning errors simultaneous localization and mapping addresses the joint estimation problem of observer localization and scene mapping state of the art approaches typically use visual or optical sensors and therefore rely on static beacons in the environment to anchor the observer estimate however many applications involving sensors that are not conventionally used for simultaneous localization and mapping slam are affected by highly dynamic scenes such that the static world assumption is invalid this paper proposes a novel approach for dynamic scenes called generalized motion gem slam based on probability hypothesis density filters the proposed approach probabilistically anchors the observer state by fusing observer information inferred from the scene with reports of the observer motion this paper derives the general theoretical framework for gem slam and shows that it generalizes existing probability hypothesis density phd based slam algorithms simulations for a model specific realization using range bearing sensors and multiple moving objects highlight that gem slam achieves significant improvements over three benchmark algorithms

a scalable algorithm for tracking an unknown number of targets using multiple sensors we propose an algorithm for tracking an unknown number of targets based on measurements provided by multiple sensors our algorithm achieves low computational complexity and excellent scalability by running belief propagation on a suitably devised factor graph a redundant formulation of data association uncertainty and the use of augmented target states including binary target indicators make it possible to exploit statistical independencies for a drastic reduction of complexity an increase in the number of targets sensors or measurements leads to additional variable nodes in the factor graph but not to higher dimensions of the messages as a consequence the complexity of our method scales only quadratically in the number of targets linearly in the number of sensors and linearly in the number of measurements per sensor the performance of the method compares well with that of previously proposed methods including methods with a less favorable scaling behavior in particular our method can outperform multisensor versions of the probability hypothesis density phd filter the cardinalized phd filter and the multi bernoulli filter

nonlinear kalman filtering with divergence minimization we consider the nonlinear kalman filtering problem using kullback leibler kl and alpha divergence measures as optimization criteria unlike linear kalman filters nonlinear kalman filters do not have closed form gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood in this paper we propose novel algorithms to approximate this posterior by optimizing the forward and reverse forms of the kl divergence as well as the alpha divergence that contains these two as limiting cases unlike previous approaches our algorithms do not make approximations to the divergences being optimized but use monte carlo techniques to derive unbiased algorithms for direct optimization we assess performance on radar and sensor tracking and options pricing showing general improvement over the extended unscented and ensemble kalman filters as well as competitive performance with particle filtering

an ensemble kushner stratonovich poisson filter for recursive estimation in nonlinear dynamical systems we propose a monte carlo filter for recursive estimation of diffusive processes that modulate the instantaneous rates of poisson measurements a key aspect is the additive update through a gain like correction term empirically approximated from the innovation integral in the time discretized kushner stratonovich equation the additive filter update scheme eliminates the problem of particle collapse encountered in many conventional particle filters through a few numerical demonstrations the versatility of the proposed filter is brought forth

high degree cubature kalman filter the cubature kalman filter ckf which is based on the third degree spherical radial cubature rule is numerically more stable than the unscented kalman filter ukf but less accurate than the gauss hermite quadrature filter ghqf to improve the performance of the ckf a new class of ckfs with arbitrary degrees of accuracy in computing the spherical and radial integrals is proposed the third degree ckf is a special case of the class the high degree ckfs of the class can achieve the accuracy and stability performances close to those of the ghqf but at lower computational cost a numerical integration problem and a target tracking problem are utilized to demonstrate the necessity of using the high degree cubature rules to improve the performance the target tracking simulation shows that the fifth degree ckf can achieve higher accuracy than the extended kalman filter the ukf the third degree ckf and the particle filter and is computationally much more efficient than the ghqf

operational characterization of divisibility of dynamical maps in this work we show the operational characterization to the divisibility of dynamical maps in terms of the distinguishability of quantum channels it is proven that the distinguishability of any pair of quantum channels does not increase under divisible maps in which the full hierarchy of divisibility is isomorphic to the structure of entanglement between system and environment this shows that i channel distinguishability is the operational quantity signifying detecting divisibility indivisibility of dynamical maps and ii the decision problem for the divisibility of maps is as hard as the separability problem in entanglement theory we also provide the information theoretic characterization to the divisibility of maps with conditional min entropy

implicit sampling for hierarchical bayesian inversion and applications in fractional multiscale diffusion models abstract this paper presents an implicit sampling method for hierarchical bayesian inverse problems a widely used approach for sampling posterior distribution is markov chain monte carlo mcmc however the samples generated by mcmc are usually strongly correlated which may lead to a small size of effective samples the implicit sampling method proposed in chorin and tu 2009 can generate independent samples and capture inherent non gaussian features of the posterior in implicit sampling method the posterior samples are generated by a map and distribution around the maximum a posterior map point for practical applications some parameters in prior density are often unknown and the hierarchical bayesian formulation is used to estimate the map point effectively it is applied to the bayesian inverse problems of multi term time fractional diffusion models in heterogeneous media to effectively capture the heterogeneity effect we present a mixed generalized multiscale finite element method mixed gmsfem to substantially speed up the bayesian inversion finally we carry out a few numerical examples to effectively identify various unknown inputs

observer design for stochastic nonlinear systems via contraction based incremental stability this paper presents a new design approach to nonlinear observers for ito stochastic nonlinear systems with guaranteed stability a stochastic contraction lemma is presented which is used to analyze incremental stability of the observer a bound on the mean squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of the contraction rate and maximum noise intensity the observer design is based on a non unique state dependent coefficient sdc form which parametrizes the nonlinearity in an extended linear form the observer gain synthesis algorithm called linear matrix inequality state dependent algebraic riccati equation lmi sdare is presented the lmi sdare uses a convex combination of multiple sdc parametrizations an optimization problem with state dependent linear matrix inequality sdlmi constraints is formulated to select the coefficients of the convex combination for maximizing the convergence rate and robustness against disturbances two variations of lmi sdare algorithm are also proposed one of them named convex state dependent riccati equation csdre uses a chosen convex combination of multiple sdc matrices and the other named fixed sdare uses constant sdc matrices that are pre computed by using conservative bounds of the system states while using constant coefficients of the convex combination pre computed by a convex lmi optimization problem a connection between contraction analysis and l 2 gain of the nonlinear system is established in the presence of noise and disturbances results of simulation show superiority of the lmi sdare algorithm to the extended kalman filter ekf and state dependent differential riccati equation sddre filter

fluctuation theorems for non markovian quantum processes exploiting previous results on markovian dynamics and fluctuation theorems we study the consequences of memory effects on single realizations of nonequilibrium processes within an open system approach the entropy production along single trajectories for forward and backward processes is obtained with the help of a recently proposed classical like non markovian stochastic unravelling which is demonstrated to lead to a correction of the standard entropic fluctuation theorem this correction is interpreted as resulting from the interplay between the information extracted from the system through measurements and the flow of information from the environment to the open system due to memory effects single realizations of a dynamical process are no longer independent and their correlations fundamentally affect the behavior of entropy fluctuations

thermodynamics of non markovian reservoirs and heat engines we show that non markovian effects of the reservoirs can be used as a resource to extract work from an otto cycle the state transformation under non markovian dynamics is achieved via a two step process namely an isothermal process using a markovian reservoir followed by an adiabatic process from second law of thermodynamics we show that the maximum amount of extractable work from the state prepared under the non markovian dynamics quantifies a lower bound of non markovianity we illustrate our ideas with an explicit example of non markovian evolution

a low complexity sequential monte carlo algorithm for blind detection in mimo systems in statistical signal processing the sequential monte carlo smc method is powerful and can approach the theoretical optima however its computational complexity is usually very high especially in multiple input multiple output mimo systems this paper presents a new low complexity smc lc smc algorithm for blind detection in mimo systems the main idea of which is to shrink the sampling space via channel estimation which is initialized using the first differentially modulated symbol and then updated using the monte carlo samples since the a posteriori probability of the transmitted symbols can be calculated separately by each transmit antenna the proposed lc smc algorithm is not only computationally efficient as compared to the original smc whose complexity grows exponentially with the number of transmit antennas but also makes blind turbo receiver more feasible for multilevel phase modulations simulation results are presented to demonstrate the effectiveness of the lc smc algorithm