subspace polynomials and limits to list decoding of reed solomon codes we show combinatorial limitations on efficient list decoding of reed solomon codes beyond the johnson guraswami sudan bounds in particular we show that for arbitrarily large fields fn fn n for any 0 1 and k n 1 existence there exists a received word wn fn fn that agrees with a super polynomial number of distinct degree k polynomials on n points each 2 explicit there exists a polynomial time constructible received word w n fn fn that agrees with a superpolynomial number of distinct degree k polynomials on 2 log n k points each in both cases our results improve upon the previous state of the art which was n points of agreement for the existence case proved by justesen and hoholdt and 2n points of agreement for the explicit case proved by guruswami and rudra furthermore for close to 1 our bound approaches the guruswami sudan bound which is n k and implies limitations on extending their efficient reed solomon list decoding algorithm to larger decoding radius our proof is based on some remarkable properties of sub space polynomials using similar ideas we then present a family of low rate codes that are efficiently list decodable beyond the johnson bound this leads to an optimal list decoding algorithm for the family of matrix codes

additive rank metric codes we give an infinite family of maximum rank distance mrd codes which covers properly the largest known linear mrd code family our family contains infinite families of non linear mrd codes which are the first non linear examples for most of the parameters we also give explicit examples and a table that demonstrates the proportion of linear and non linear families for some small parameters

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

stopping time resampling for sequential monte carlo methods summary motivated by the statistical inference problem in population genetics we present a new sequential importance sampling with resampling strategy the idea of resampling is key to the recent surge of popularity of sequential monte carlo methods in the statistics and engineering communities but existing resampling techniques do not work well for coalescent based inference problems in population genetics we develop a new method called stopping time resampling which allows us to compare partially simulated samples at different stages to terminate unpromising partial samples and to multiply promising samples early on to illustrate the idea we first apply the new method to approximate the solution of a dirichlet problem and the likelihood function of a non markovian process then we focus on its application in population genetics all our examples show that the new resampling method can significantly improve the computational efficiency of existing sequential importance sampling methods

bounds on list decoding of rank metric codes so far there is no polynomial time list decoding algorithm beyond half the minimum distance for gabidulin codes these codes can be seen as the rank metric equivalent of reed solomon codes in this paper we provide bounds on the list size of rank metric codes in order to understand whether polynomial time list decoding is possible or whether it works only with exponential time complexity three bounds on the list size are proven the first one is a lower exponential bound for gabidulin codes and shows that for these codes no polynomial time list decoding beyond the johnson radius exists second an exponential upper bound is derived which holds for any rank metric code of length n and minimum rank distance d the third bound proves that there exists a rank metric code over bbfqm of length n m such that the list size is exponential in the length for any radius greater than half the minimum rank distance this implies that there cannot exist a polynomial upper bound depending only on n and d similar to the johnson bound in hamming metric all three rank metric bounds reveal significant differences to bounds for codes in hamming metric

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

a class of fast exact bayesian filters in dynamical models with jumps we address the statistical filtering problem in dynamical models with jumps when a particular application is adequately modeled by linear and gaussian probability density functions with jumps a usual method consists in approximating the optimal bayesian estimate in the sense of the minimum mean square error mmse in a linear and gaussian jump markov state space system jmss practical solutions include algorithms based on numerical approximations or on sequential monte carlo smc methods in this paper we propose a class of alternative methods which consists in building statistical models which locally similarly model the problem of interest but in which the computation of the mmse estimate can be be computed exactly without numerical nor smc approximations and at a computational cost which is linear in the number of observations

on line inference for multiple changepoint problems we propose an on line algorithm for exact filtering of multiple changepoint problems this algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models the computational cost of this exact algorithm is quadratic in the number of observations we further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations at the expense of introducing small errors and propose two new optimum resampling algorithms for this problem one a version of rejection control allows the particle filter to automatically choose the number of particles required at each time step the new resampling algorithms substantially out perform standard resampling algorithms on examples we consider and we demonstrate how the resulting particle filter is practicable for segmentation of human gc content

galois extensions and subspaces of alternating bilinear forms with special rank properties abstract let k be a field admitting a cyclic galois extension of degree n the main result of this paper is a decomposition theorem for the space of alternating bilinear forms defined on a vector space of odd dimension n over k we show that this space of forms is the direct sum of n 1 2 subspaces each of dimension n and the non zero elements in each subspace have constant rank defined in terms of the orders of the galois automorphisms furthermore if ordered correctly for each integer k lying between 1 and n 1 2 the rank of any non zero element in the sum of the first k subspaces is at most n 2 k 1 slightly less sharp similar results hold for cyclic extensions of even degree

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

on approximate maximum likelihood methods for blind identification how to cope with the curse of dimensionality we discuss approximate maximum likelihood methods for blind identification and deconvolution these algorithms are based on particle approximation versions of the expectation maximization em algorithm we consider three different methods which differ in the way the posterior distribution of the symbols is computed the first algorithm is a particle approximation method of the fixed interval smoothing the two filter smoothing and the novel joined two filter smoothing involve an additional backward information filter because the state space is finite it is furthermore possible at each step to consider all the offsprings of any given particle it is then required to construct a novel particle swarm by selecting among all these offsprings particle positions and computing appropriate weights we propose here a novel unbiased selection scheme which minimizes the expected loss with respect to general distance functions we compare these smoothing algorithms and selection schemes in a monte carlo experiment we show a significant performance increase compared to the expectation maximization viterbi algorithm emva a fixed lag smoothing algorithm and the block constant modulus algorithm cma

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

a gaussian mixture filter for range only tracking range only tracking problems arise in extended data collection for inverse synthetic radar applications robotics navigation and other areas for such problems the conditional density of the state variable given the measurement history is multi modal or exhibits curvature even in seemingly benign scenarios for this reason the use of extended kalman filter ekf and other nonlinear filtering techniques based on gaussian approximations can result in inaccurate estimates we introduce a new filter for such tracking problems in two dimensions called the gaussian mixture range only filter gmrof which generates gaussian mixture approximations to the conditional densities the filter equations are derived by analytic techniques based on the specific nonlinearities of range only tracking a slight modification of the standard measurement process model noise before nonlinearity is used to simplify the moment calculations implementation requires at each step the fitting of a low order gaussian mixture to a simple exponentiated trigonometric function of a scalar variable simulations involving scenarios from earlier comparative studies indicate that the gmrof consistently outperformed the ekf and achieved the accuracy of particle filters while significantly reducing the computational cost

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

particle markov chain monte carlo methods summary markov chain monte carlo and sequential monte carlo methods have emerged as the two main tools to sample from high dimensional probability distributions although asymptotic convergence of markov chain monte carlo algorithms is ensured under weak assumptions the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and or if highly correlated variables are updated independently we show here how it is possible to build efficient high dimensional proposal distributions by using sequential monte carlo methods this allows us not only to improve over standard markov chain monte carlo schemes but also to make bayesian inference feasible for a large class of statistical models where this was not previously so we demonstrate these algorithms on a non linear state space model and a levy driven stochastic volatility model

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

brief paper detection and estimation for abruptly changing systems the problem of state estimation and system structure detection for discrete stochastic dynamical systems with parameters which may switch among a finite set of values is considered the switchings are modelled by a markov chain with known transition probabilities a brief survey and a unified treatment of the existing suboptimal algorithms are provided the optimal algorithms require exponentially increasing memory and computations with time simulation results comparing the various suboptimal algorithms are presented

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

on the number of roots of some linearized polynomials abstract linearized polynomials appear in many different contexts such as rank metric codes cryptography and linear sets and the main issue regards the characterization of the number of roots from their coefficients results of this type have been already proved in 7 10 24 in this paper we provide bounds and characterizations on the number of roots of linearized polynomials of this form a x b 0 x q s b 1 x q s n b 2 x q s 2 n b t 1 x q s n t 1 f q n t x with gcd s n 1 also we characterize the number of roots of such polynomials directly from their coefficients dealing with matrices which are much smaller than the relative dickson matrices and the companion matrices used in the previous papers furthermore we develop a method to find explicitly the roots of a such polynomial by finding the roots of a q n polynomial finally as an application of the above results we present a family of linear sets of the projective line whose points have a small spectrum of possible weights containing most of the known families of scattered linear sets in particular we carefully study the linear sets in pg 1 q 6 presented in 9

the shifted rayleigh mixture filter for bearings only tracking of maneuvering targets this paper introduces the shifted rayleigh mixture filter srmf which is based on jump markov linear systems the formulation permits the presence of clutter for bearings only tracking problems involving maneuvering targets the conditional density of the target state given the available measurements evolves as a growing mixture of probability density functions associated with a history of manoeuvre modes similar to other mixture algorithms the srmf approximates this conditional density by a gaussian mixture of fixed order unlike the extended or unscented kalman filters the shifted rayleigh filter incorporates an exact calculation of the posterior density when the prior is assumed to be gaussian given the latest bearings measurement computer simulations are provided to demonstrate the performance of the algorithm

multiuser spectrum optimization for discrete multitone systems with asynchronous crosstalk finding computationally efficient spectrum optimization methods for a multiuser digital subscriber line dsl environment is a key objective of dynamic spectrum management for dsl systems for synchronous discrete multitone dmt based dsl systems the computational complexity issue can be partially addressed using a dual optimization approach that decomposes the problem in the frequency domain however the decomposition approach fails whenever the dmt system is asynchronous in which case the power allocations in adjacent frequency tones interfere with each other this paper provides a mathematical model for intercarrier interference due to symbol misalignment and proposes ways to modify the dual method for spectrum optimization of asynchronous dsl systems the main ingredient of the algorithm is an efficient method to evaluate the minimum power required to support a given bit allocation using a power series approximation combined with a local gradient search

an efficient direct solution of cave filling problems waterfilling problems subjected to peak power constraints are solved which are known as cave filling problems cfp the proposed algorithm finds both the optimum number of positive powers and the number of resources that are assigned the peak power before finding the specific powers to be assigned the proposed solution is non iterative and results in a computational complexity which is of the order of m o m where m is the total number of resources which is significantly lower than that of the existing algorithms given by an order of m 2 o m 2 under the same memory requirement and sorted parameters the algorithm is then generalized both to weighted cfp wcfp and wcfp requiring the minimum power these extensions also result in a computational complexity of the order of m o m finally simulation results corroborating the analysis are presented

practical algorithms for a family of waterfilling solutions many engineering problems that can be formulated as constrained optimization problems result in solutions given by a waterfilling structure the classical example is the capacity achieving solution for a frequency selective channel for simple waterfilling solutions with a single waterlevel and a single constraint typically a power constraint some algorithms have been proposed in the literature to compute the solutions numerically however some other optimization problems result in significantly more complicated waterfilling solutions that include multiple waterlevels and multiple constraints for such cases it may still be possible to obtain practical algorithms to evaluate the solutions numerically but only after a painstaking inspection of the specific waterfilling structure in addition a unified view of the different types of waterfilling solutions and the corresponding practical algorithms is missing the purpose of this paper is twofold on the one hand it overviews the waterfilling results existing in the literature from a unified viewpoint on the other hand it bridges the gap between a wide family of waterfilling solutions and their efficient implementation in practice to be more precise it provides a practical algorithm to evaluate numerically a general waterfilling solution which includes the currently existing waterfilling solutions and others that may possibly appear in future problems

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

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

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

a new family of mrd codes abstract we introduce a family of linear sets of pg 1 q 2 n arising from maximum scattered linear sets of pseudoregulus type of pg 3 q n for n 3 4 and for certain values of the parameters we show that these linear sets of pg 1 q 2 n are maximum scattered and they yield new mrd codes with parameters 6 6 q 5 for q 2 and with parameters 8 8 q 7 for q odd

on line inference for hidden markov models via particle filters we consider the on line bayesian analysis of data by using a hidden markov model where inference is tractable conditional on the history of the state of the hidden component a new particle filter algorithm is introduced and shown to produce promising results when analysing data of this type the algorithm is similar to the mixture kalman filter but uses a different resampling algorithm we prove that this resampling algorithm is computationally efficient and optimal among unbiased resampling algorithms in terms of minimizing a squared error loss function in a practical example that of estimating break points from well log data our new particle filter outperforms two other particle filters one of which is the mixture kalman filter by between one and two orders of magnitude

an ell _ 1 laplace robust kalman smoother robustness is a major problem in kalman filtering and smoothing that can be solved using heavy tailed distributions e g l1 laplace this paper describes an algorithm for finding the maximum a posteriori map estimate of the kalman smoother for a nonlinear model with gaussian process noise and l1 laplace observation noise the algorithm uses the convex composite extension of the gauss newton method this yields convex programming subproblems to which an interior point path following method is applied the number of arithmetic operations required by the algorithm grows linearly with the number of time points because the algorithm preserves the underlying block tridiagonal structure of the kalman smoother problem excellent fits are obtained with and without outliers even though the outliers are simulated from distributions that are not l1 laplace it is also tested on actual data with a nonlinear measurement model for an underwater tracking experiment the l1 laplace smoother is able to construct a smoothed fit without data removal from data with very large outliers

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

sequential monte carlo samplers summary we propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space each distribution being known up to a normalizing constant these probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential monte carlo methods this methodology allows us to derive simple algorithms to make parallel markov chain monte carlo algorithms interact to perform global optimization and sequential bayesian estimation and to compute ratios of normalizing constants we illustrate these algorithms for various integration tasks arising in the context of bayesian inference

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

association pattern discovery via theme dictionary models summary discovering patterns from a set of text or more generally categorical data is an important problem in many disciplines such as biomedical research linguistics artificial intelligence and sociology we consider here the well known market basket problem that is often discussed in the data mining community and is also quite ubiquitous in biomedical research the data under consideration are a set of baskets where each basket contains a list of items our goal is to discover themes which are defined as subsets of items that tend to co occur in a basket we describe a generative model i e the theme dictionary model for such data structures and describe two likelihood based methods to infer themes that are hidden in a collection of baskets we also propose a novel sequential monte carlo method to overcome computational challenges using both simulation studies and real applications we demonstrate that the new approach proposed is significantly more powerful than existing methods such as association rule mining and topic modelling in detecting weak and subtle interactions in the data

a particle filtering scheme for processing time series corrupted by outliers the literature in engineering and statistics is abounding in techniques for detecting and properly processing anomalous observations in the data most of these techniques have been developed in the framework of static models and it is only in recent years that we have seen attempts that address the presence of outliers in nonlinear time series for a target tracking problem described by a nonlinear state space model we propose the online detection of outliers by including an outlier detection step within the standard particle filtering algorithm the outlier detection step is implemented by a test involving a statistic of the predictive distribution of the observations such as a concentration measure or an extreme upper quantile we also provide asymptotic results about the convergence of the particle approximations of the predictive distribution and its statistics and assess the performance of the resulting algorithms by computer simulations of target tracking problems with signal power observations

identifiers for mrd codes abstract for any admissible value of the parameters n and k there exist n k maximum rank distance f q linear codes indeed it can be shown that if field extensions large enough are considered almost all rank metric codes are mrd on the other hand very few families up to equivalence of such codes are currently known in the present paper we study some invariants of mrd codes and evaluate their value for the known families providing a new characterization of generalized twisted gabidulin codes

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

detecting change points for shifts in mean and variance using fuzzy classification maximum likelihood change point algorithms knowing the time of changes called change point cp in a process is crucial for engineers to recognize the root cause fast and accurately since special causes may induce simultaneous changes in mean and variance detecting changes in both at once is required many methodologies in quality control were developed for detecting changes in either mean or variance only and process parameters were assumed known often however they are rarely known exactly and a small estimation error may lead to unfavorable cp estimates fuzzy partitioning is better suited to cases of vague boundaries between two segments which appear very often in reality a new mechanism called fuzzy classification maximum likelihood change point fcml cp algorithm is proposed to detect shifts in mean and variance simultaneously a cp framework is transferred into a mixture model and then a fcml cp algorithm is created through fuzzy classification maximum likelihood procedures the proposed fcml cp can be applied to phase i and ii processes without knowledge of in control process parameters it can estimate multiple cps of process mean or and variance simultaneously the effectiveness and superiority of fcml cp are shown by extensive experiments with numerical and real data sets specifically the proposed fcml cp is superior to the commonly used statistical mixture likelihood approach using expectation maximization em algorithm it is much more time saving especially the remarkable performance of fcml cp in detecting cps for small changes is particularly important and helpful for engineers to recognize the special cause fast and correctly since an out of control signal resulted from small changes is usually delayed long we propose a new algorithm fcml cp to detect change points in a statistical process the mixture likelihood embedded fuzzy c partition is utilized to estimate the change points the method outperforms statistical likelihood approaches various experiments show the effectiveness and practicability of the proposed method excellent performance in detecting small changes is helpful for root cause analyses

on the list decodability of rank metric codes let k n m in mathbb z be integers such that k leq n leq m let mathrm g n k in mathbb f q m n be a delsarte gabidulin code recently wachter zeh proved that codes belonging to this family cannot be efficiently list decoded for any radius tau providing tau is large enough this achievement essentially relies on proving a lower bound for the list size of some specific words in mathbb f q m n some years later raviv and wachter zeh improved this bound in a special case i e when n mid m as a consequence they were able to detect infinite families of delsarte gabidulin codes that cannot be efficiently list decoded at all in this article we determine similar lower bounds for maximum rank distance codes belonging to a wider class of examples containing generalized gabidulin codes generalized twisted gabidulin codes and examples recently described by trombetti and zhou by exploiting arguments such as those used by raviv and wachter zeh when n mid m we also show infinite families of generalized gabidulin codes that cannot be list decoded efficiently at any radius greater than or equal to left lfloor frac d 1 2 right rfloor 1 where d is its minimum distance nonetheless in all the examples belonging to above mentioned class we detect infinite families that cannot be list decoded efficiently at any radius greater than or equal to left lfloor frac d 1 2 right rfloor 2 where d is its minimum distance in particular this leads to show infinite families of gabidulin codes with underlying parameters not already covered by the result of raviv and wachter zeh having this decodability defect finally relying on the properties of a set of subspace trinomials recently presented by mcguire and mueller we are able to prove our main result that is any rank metric code of mathbb f q m n of order q kn with n dividing m such that 4n 3 is a square in mathbb z and containing mathrm g n 2 is not efficiently list decodable at some values of the radius tau

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

a new gaussian mixture algorithm for gmti tracking under a minimum detectable velocity constraint this paper introduces a new methodology to account for doppler blind zone constraints arising for example in ground moving target indicator gmti tracking applications in such problems target measurements are suppressed when the range rate doppler of the target drops below a specified threshold in magnitude the minimum detectable velocity the proposed method employing gaussian mixture approximations to the filtering density differs from earlier gaussian mixture approaches in the way missed measurements are modelled the distinctive feature of the algorithm as compared with other gaussian mixture filters is that it is based on an exact calculation of the filtering density when a measurement is not recorded algorithms that result from applying this methodology are simple to implement and computationally undemanding simulation results indicate a uniform improvement in estimation accuracy over that of earlier proposed analytic techniques and a tracking performance comparable to that of state of the art particle filters

some gabidulin codes cannot be list decoded efficiently at any radius gabidulin codes can be seen as the rank metric equivalent of reed solomon codes it was recently proved using subspace polynomials that gabidulin codes cannot be list decoded beyond the so called johnson radius in another result cyclic subspace codes were constructed by inspecting the connection between subspaces and their subspace polynomials in this paper these subspace codes are used to prove two bounds on the list size in decoding certain gabidulin codes the first bound is an existential one showing that exponentially sized lists exist for codes with specific parameters the second bound presents exponentially sized lists explicitly for a different set of parameters both bounds rule out the possibility of efficiently list decoding several families of gabidulin codes for any radius beyond half the minimum distance such a result was known so far only for non linear rank metric codes and not for gabidulin codes using a standard operation called lifting identical results also follow for an important class of constant dimension subspace codes

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

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

convex separable problems with linear constraints in signal processing and communications in this work we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints the solution is given in closed form as a function of some lagrange multipliers that can be computed through an iterative procedure in a finite number of steps graphical interpretations are given casting valuable insights into the proposed algorithm and allowing to retain some of the intuition spelled out by the water filling policy it turns out that it is not only general enough to compute the solution to different instances of the problem at hand but also remarkably simple in the way it operates we also show how some power allocation problems in signal processing and communications can be solved with the proposed algorithm

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

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

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

optimal training design for channel estimation in decode and forward relay networks with individual and total power constraints in this paper we study the channel estimation and the optimal training design for relay networks that operate under the decode and forward df strategy with the knowledge of the interference covariance in addition to the total power constraint on all the relays we introduce individual power constraint for each relay which reflects the practical scenario where all relays are separated from one another considering the individual power constraint for the relay networks is the major difference from that in the traditional point to point communication systems where only a total power constraint exists for all colocated antennas two types of channel estimation are involved maximum likelihood ml and minimum mean square error mmse for ml channel estimation the channels are assumed as deterministic and the optimal training results from an efficient multilevel waterfilling type solution that is derived from the majorization theory for mmse channel estimation however the second order statistics of the channels are assumed known and the general optimization problem turns out to be nonconvex we instead consider three special yet reasonable scenarios the problem in the first scenario is convex and could be efficiently solved by state of the art optimization tools closed form waterfilling type solutions are found in the remaining two scenarios of which the first one has an interesting physical interpretation as pouring water into caves

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

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

blind deconvolution via sequential imputations abstract the sequential imputation procedure is applied to adaptively and sequentially reconstruct discrete input signals that are blurred by an unknown linear moving average channel and contaminated by additive gaussian noises a problem known as blind deconvolution in digital communication a rejuvenation procedure for improving the efficiency of sequential imputation is introduced and theoretically justified the proposed method does not require the channel to be nonminimum phase and can be used in real time signal restoration two simulated systems are studied to illustrate the proposed method our result shows that the ideas of multiple imputations and flexible simulation techniques are as powerful in engineering as in survey sampling

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

mixture kalman filters in treating dynamic systems sequential monte carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling importance sampling and weighted resampling to complete the on line filtering task we propose a special sequential monte carlo method the mixture kalman filter which uses a random mixture of the gaussian distributions to approximate a target distribution it is designed for on line estimation and prediction of conditional and partial conditional dynamic linear models which are themselves a class of widely used non linear systems and also serve to approximate many others compared with a few available filtering methods including monte carlo methods the gain in efficiency that is provided by the mixture kalman filter can be very substantial another contribution of the paper is the formulation of many non linear systems into conditional or partial conditional linear form to which the mixture kalman filter can be applied examples in target tracking and digital communications are given to demonstrate the procedures proposed

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

fuzzy change point algorithms for regression models change point cp regression models have been widely applied in various fields where detecting cps is an important problem detecting the location of cps in regression models could be equivalent to partitioning data points into clusters of similar individuals in the literature fuzzy clustering has been widely applied in various fields but it is less used in locating cps in cp regression models in this paper a new method called fuzzy cp fcp algorithm is proposed to detect the cps and simultaneously estimate the parameters of regression models the fuzzy c partitions concept is first embedded into the cp regression models any possible collection of all cps is considered as a partitioning of data with a fuzzy membership we then transfer these memberships into the pseudomemberships of data points belonging to each individual cluster and therefore we can obtain the estimates for model parameters by the fuzzy c regressions method subsequently we use the fuzzy c means clustering to obtain the new iterates of the cp collection memberships by minimizing an objective function concerning the deviations between the predicted response values and data values we illustrate the new approach with several numerical examples and real datasets experimental results actually show that the proposed fcp is an effective and useful cp detection algorithm for cp regression models and can be applied to various fields such as econometrics medicine quality control and signal processing