recursive relaxation identification of linear multivariable systems with its parallel algorithm in this paper we propose a new method for the identification of discrete time linear multivariable systems this method comprises three recursive computation schemes including two parameter estimate schemes for both state equation and observation equation respectively and the state estimate scheme via kalman filtering we call this method the recursive relaxation identification abbreviated as rri compared with the existing methods the rri algorithm has advantages of simplification fast computation and high efficiency and is suitable for fast real time on line adaptive identification of linear multivariable systems

state estimation with partially observed inputs a unified kalman filtering approach for linear stochastic time varying state space models with gaussian noises this paper investigates state estimation for the scenario where the input variables of the state equation are not fully observed but rather the input data are available only at an aggregate level unlike the existing filters for unknown inputs that are based on the approach of minimum variance unbiased estimation this paper does not impose the unbiasedness condition for state estimation instead it incorporates a bayesian approach to derive a modified kalman filter by pooling the prior knowledge about the state vector at the aggregate level with the measurements on the output variables at the original level of interest the estimated state vector is shown to be a minimum mean square error estimator the developed filter provides a unified approach to state estimation it includes the existing filters obtained under two extreme scenarios as its special cases i e the classical kalman filter where all the inputs are observed and the filter for unknown inputs

a robust observer for discrete time nonlinear systems abstract this paper extends the results developed in ciccarella et al 1993 and presents a robust observer for discrete time nonlinear systems a simple robust and easy to implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems combined parameter and state estimation is made for a numerical example which compares the robust observer to the observer given in ciccarella et al 1993

technical communique a modified extended kalman filter for linear discrete time systems with unknown parameters this technical communique presents a modified extended kalman filter for estimating the states and unknown parameters in discrete time multi input multi output linear systems the hyperstability of the filter is guaranteed by introducing a compensator into the estimation mechanism it is proved that the estimates for the states and unknown parameters converge to the exact values if some conditions are assumed to the estimation mechanism a numerical example shows that the proposed filter is much more effective than the extended kalman filter in the estimation of unknown parameters

an interlaced extended kalman filter an estimation algorithm for a class of discrete time nonlinear systems is proposed the system structure we deal with is partitionable into in subsystems each affine w r t the corresponding part of the state vector the algorithm consists of a bank of m interlaced kalman filters and each of them estimates a part of the state considering the remaining parts as known time varying parameters whose values are evaluated by the other filters at the previous step the procedure neglects the subsystem coupling terms in the covariance matrix of the state estimation error and counteracts the errors so introduced by suitably increasing the noise covariance matrices comparisons through numerical simulations with the extended kalman filter and its modified versions proposed in the literature illustrate the good trade off provided by the algorithm between the reduction of the computational load and the estimation accuracy

iterated posterior linearization smoother this note considers the problem of bayesian smoothing in nonlinear state space models with additive noise using gaussian approximations sigma point approximations to the general gaussian rauch tung striebel smoother are widely used methods to tackle this problem these algorithms perform statistical linear regression slr of the nonlinear functions considering only the previous measurements we argue that slr should be done taking all measurements into account we propose the iterated posterior linearization smoother ipls which is an iterated algorithm that performs slr of the nonlinear functions with respect to the current posterior approximation the algorithm is demonstrated to outperform conventional gaussian nonlinear smoothers in two numerical examples

observer design for nonlinear systems with discrete time measurements this paper focuses on the development of asymptotic observers for nonlinear discrete time systems it is argued that instead of trying to imitate the linear observer theory the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations in particular it is shown that the discrete newton method properly interpreted yields an asymptotic observer for a large class of discrete time systems while the continuous newton method may be employed to obtain a global observer furthermore it is analyzed how the use of broyden s method in the observer structure affects the observer s performance and its computational complexity an example illustrates some aspects of the proposed methods moreover it serves to show that these methods apply equally well to discrete time systems and to continuous time systems with sampled outputs

some fixed point theorems of the schauder and the krasnosel skii type and application to nonlinear transport equations abstract in j math phys 37 1996 1336 1348 the existence of solutions to the boundary value problem 1 1 1 2 was analyzed for isotropic scattering kernels on l p spaces for p 1 due to the lack of compactness in l 1 spaces the problem remains open for p 1 the purpose of this work is to extend this analysis to the case p 1 for anisotropic scattering kernels our strategy consists in establishing new variants of the schauder and the krasnosel skii fixed point theorems in general banach spaces involving weakly compact operators in l 1 context these theorems provide an adequate tool to attack the problem our analysis uses the specific properties of weakly compacts sets on l 1 spaces and the weak compactness results for one dimensional transport equations established in j math anal appl 252 2000 767 789

general two stage extended kalman filters a general two stage extended kalman filter gtsekf which extends the linear general two stage kalman filter to nonlinear systems is further proposed a new nonlinear two stage transformation is introduced to facilitate achieving this extension as in the linear one the gtsekf is derived mainly by applying the nonlinear two stage transformation to the well known extended kalman filter ekf and is shown to be equivalent to the ekf with a decoupled computing structure a nonlinear filter for estimating constant parameters in dynamic systems is presented to illustrate one application of the proposed gtsekf a literature example is also given to demonstrate the correctness and usefulness of the proposed results

convergence analysis of the extended kalman filter used as an observer for nonlinear deterministic discrete time systems in this paper convergence analysis of the extended kalman filter ekf when used as an observer for nonlinear deterministic discrete time systems is presented based on a new formulation of the first order linearization technique sufficient conditions to ensure local asymptotic convergence are established furthermore it is shown that the design of the arbitrary matrix plays an important role in enlarging the domain of attraction and then improving the convergence of the modified ekf significantly the efficiency of this approach compared to the classical version of the ekf is shown through a nonlinear identification problem as well as a state and parameter estimation of nonlinear discrete time systems

regularized extended estimation with stabilized exponential forgetting this technical note concerns the problem of variable regularized estimation of time varying nonlinear systems from the bayesian viewpoint the questions of how to impose the posterior information being variably regularized and how to forget this information are carefully discussed the estimator design adopts the strategy of the iterated kalman filter but differs in that instead of the separated moments of the linearized system only the augmented covariance matrix is updated to suppress obsolete information a decision problem involving the kullback leibler divergence is solved the decision provides the best combination of a pair of time evolution model hypotheses in terms of the geometric mean as a result exponential forgetting with the adaptively tuned factor is inserted into the estimation process the regularization of the investigated statistics is induced through the processing of externally supplied information the presented estimator allows for absolute discarding or conversely retention of external information produced in terms of the normal wishart distribution

simultaneous estimation of transmissivity values and zonation the extended kalmanfilter ekf has long been recognized as a powerful yet computationally intensive methodology for stochastic parameter estimation three improvements to traditional algorithms are presented and applied to heterogeneous transmissivity estimation first the costly ekf covariance updates are replaced by more efficient approximations second the zonation structure of the distributed parameterfield being estimated is dynamically determined and refined using a partitional clustering algorithm third a new method of mergingfirst and second moments of randomfields that have heterogeneous statistics is introduced we apply this method called random field union as an alternative to conventional randomfield averaging for the systematic shrinking of covariance matrices as the dimensionality of the parameter space is reduced the effects of these three improvements are examined in applications to steady state groundwaterflow test problems we show that thefirst and second improvements reduce the computational time requirements dramatically while the second and third can improve the accuracy and stability of the results the resulting integrated method is successfully applied to a larger more realistic calibration test case under steady and cyclostationary flow conditions similar to regular seasonalfluctuations whenflow is steady the method can be viewed as iterative whenflow is transient the method is fully recursive

observability of autonomous discrete time non linear systems a geometric approach in this paper the observability of autonomous discrete time systems is studied from a purely differential geometric point of view as with continuous time systems this approach leads to a local canonical form for an observable system a proposal for the generalization of an invariant subspace is made

information driven distributed maximum likelihood estimation based on gauss newton method in wireless sensor networks in this paper we develop an energy efficient distributed estimation method that can be used in applications such as the estimation of a diffusive source and the localization and tracking of an acoustic target in wireless sensor networks we first propose a statistical measurement model in which we separate the linear and nonlinear parameters this modeling strategy reduce the processing complexity we then study the distributed implementation of the gauss newton method in the maximum likelihood estimation after that we propose a fully distributed estimation approach based on an incremental realization of the gauss newton method we derive three modifications of the basic algorithm to improve the distributed processing performance while still considering the energy restriction we implement the idea of information driven collaborative signal processing and provide a sensor node scheduling scheme in which the cramer rao bound crb is used as the performance and information utility measure to select the next sensor node numerical examples are used to study the performance of the distributed estimation and we show that of the methods considered here the proposed multiple iteration kalman filtering method has the most advantages for wireless sensor networks

gaussian map filtering using kalman optimization this paper deals with the update step of gaussian map filtering in this framework we seek a gaussian approximation to the posterior probability density function pdf whose mean is given by the maximum a posteriori map estimator we propose two novel optimization algorithms which are quite suitable for finding the map estimate although they can also be used to solve general optimization problems these are based on the design of a sequence of pdfs that become increasingly concentrated around the map estimate the resulting algorithms are referred to as kalman optimization ko methods we also provide the important relations between these ko methods and their conventional optimization algorithms coas counterparts i e newton s and levenberg marquardt algorithms our simulations indicate that ko methods are more robust than their coa equivalents

fixed point theorems for the sum of two weakly sequentially continuous mappings abstract in the present paper we prove some krasnosel skii leray schauder type fixed point theorems for weak topology some fixed point theorems for the sum of two weakly sequentially continuous mappings are also presented our results extend and improve on ones from several earlier works

random matrix theory and higher genus integrability the quantum chiral potts model we perform a random matrix theory rmt analysis of the quantum fourstate chiral potts chain for different sizes of the chain up to size l 8 ou ra nalysis gives clear evidence of a gaussian orthogonal ensemble goe statistics suggesting the existence of a generalized time reversal invariance furthermore a change from the generic goe distribution to a poisson distribution occurs when the integrability conditions are met the chiral potts model is known to correspond to a star triangle integrability associated with curves of genus higher than zero or one therefore the rmt analysis can also be seen as a detector of higher genus integrability

strong tracking filtering of nonlinear time varying stochastic systems with coloured noise application to parameter estimation and empirical robustness analysis the strong tracking filter stf proposed by zhou et al in 1992 which was developed for nonlinear systems with white noise is extended to a class of nonlinear time varying stochastic systems with coloured noise a new concept of softening factor is introduced to make the state estimator much smoother its value can be preselected by computer simulations via a heuristic searching scheme the stf is then used to estimate the parameters of a class of nonlinear time varying stochastic systems in the presence of coloured noise the robustness against model uncertainty of the stf is thoroughly studied via monte carlo simulations the results show that the stf has strong robustness against model plant parameter mismatches in the statistics of the initial conditions the statistics of the process noise and the measurement noise the system parameters and the parameters in the measurement noise model to a great extent the stf can give bias free parameter estimations where the parameters may be randomly time

a class of nonlinear filtering problems arising from drifting sensor gains this paper considers a state estimation problem where the nominal system is linear but the sensor has a time varying gain component giving rise to a bilinear output equation this is a general sensor self calibration problem and is of particular interest in the problem of estimating wafer thickness and etch rate during semiconductor manufacturing using reflectometry we explore the use of a least squares estimate for this nonlinear estimation problem and give several approximate recursive algorithms for practical realization stability results for these algorithms are also given simulation results for comparing the new algorithms with the extended kalman filter and iterated kalman filter are given

a fast kalman filter for images degraded by both blur and noise in this paper a fast kalman filter is derived for the nearly optimal recursive restoration of images degraded in a deterministic way by blur and in a stochastic way by additive white noise straightforwardly implemented optimal restoration schemes for two dimensional images degraded by both blur and noise create dimensionality problems which in turn lead to large storage and computational requirements when the band toeplitz structure of the model matrices and of the distortion matrices in the matrix vector formulations of the original image and of the noisy blurred observation are approximated by circulant matrices these matrices can be diagonalized by means of the fft consequently a parallel set of n dynamical models suitable for the derivation of n low order vector kalman filters in the transform domain is obtained in this way the number of computations is reduced from the order of o n4 to that of o n 2 log 2 n for n n images

simultaneous input and state estimation for nonlinear systems with applications to flow field estimation this paper studies the problem of simultaneous input and state estimation sise for nonlinear dynamical systems with and without direct input output feedthrough we take a bayesian perspective to develop a sequential joint input and state estimation approach our scheme gives rise to a nonlinear maximum a posteriori optimization problem which we solve using the classical gauss newton method the proposed approach generalizes a number of sise methods presented in the literature we illustrate the effectiveness of the proposed scheme for nonlinear systems with direct feedthrough in an oceanographic flow field estimation problem involving submersible drogues that measure position intermittently and acceleration continuously

speed and rotor flux estimation of induction machines using a two stage extended kalman filter this paper presents an effective implementation of an extended kalman filter used for the estimation of both rotor flux and rotor velocity of an induction motor an algorithm proposed by hsieh and chen in hsieh c s chen f c 1999 optimal solution of the two stage kalman estimator ieee transactions on automatic control 44 1 194 199 for linear parameter estimation is extended to non linear estimation where parameters such as the velocity of an induction machine are present in the transition matrix and in the augmented state space compared to a straightforward implementation of an extended kalman filter our modified optimal two stage kalman estimator reduces the number of arithmetic operations by 25 allowing higher sampling rate or the use of a cheaper microcontroller

nonlinear estimation with state dependent gaussian observation noise we consider the problem of estimating the state of a system when measurement noise is a function of the system s state we propose generalizations of the extended kalman filter and the iterated extended kalman filter that can be utilized when the state estimate distribution is approximately gaussian the state estimate is computed by an iterative root searching method that maximizes a maximum likelihood function the new filter allows for the consistent treatment of a class of control problem involving nonlinear estimation from measurements with state dependent noise the effectiveness of the estimation algorithm is illustrated for a control problem with a mobile bearing only sensor

optimal solution of the two stage kalman estimator the two stage kalman estimator was originally proposed to reduce the computational complexity of the augmented state kalman filter it was also applied to the tracking of maneuvering targets by treating the target acceleration as a bias term except in certain restrictive conditions the conventional two stage estimators are suboptimal in the sense that they are not equivalent to the augmented state filter in this paper the authors propose a new two stage kalman estimator i e new structure which is an extension of friedland s estimator and is optimal in general conditions in addition we provide some analytic results to demonstrate the computational advantages of two stage estimators over augmented ones

spectral properties of statistical mechanics models the full spectrum of transfer matrices of the general eight vertex model on a square lattice is obtained by numerical diagonalization the eigenvalue spacing distribution and the spectral rigidity are analysed in non integrable regimes we have found eigenvalue repulsion as for the gaussian orthogonal ensemble in random matrix theory by contrast in integrable regimes we have found eigenvalue independence leading to a poissonian behaviour and for some points level clustering these first examples from classical statistical mechanics suggest that the conjecture of integrability successfully applied to quantum spin systems also holds for classical systems

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

extension of friedland s separate bias estimation to randomly time varying bias of nonlinear systems by extending b friedland s 1969 separate bias estimation algorithm for linear systems to nonlinear systems and combining the result with the suboptimal fading extended kalman filter proposed by d h zhou 1990 and by d h zhou et al a pseudo separate bias estimation algorithm for randomly time varying bias of a class of nonlinear time varying stochastic systems is obtained a simulation example is presented to illustrate the effectiveness of the algorithm

modified extended kalman filtering in this paper we compare the performance of the extended kalman filter ekf with that of a proposed filter called modified extended kalman filter mekf in terms of the actual state and the estimated state as a function of time and the integral squared error as a function of noise intensity both for dynamics and measurement noise all the simulation results indicate that the performance of the mekf is better than ekf for illustration numerical examples are presented using both ekf and mekf

estimating sudden changes of biases in linear dynamic systems a procedure is presented for estimating sudden changes in the bias vector in a linear dynamic system this procedure is the result of combining the recently developed method 1 2 of tracking a piecewise constant vector observed directly through additive noise with the method 3 for separating the estimation of the bias in a linear system from the estimation of the dynamic state variables the application of the procedure is illustrated by a second order dynamic system with two biases subject to transition its performance is demonstrated by a simulation

modified extended kalman filtering and a real time parallel algorithm for system parameter identification a modification of the extended kalman filter ekf algorithm which is called mekf for short it introduced the modification is achieved by an improved linearization procedure for this purpose a parallel computational scheme is recommended and it has immediate applications to identifying unknown system parameters of time varying linear stochastic state space models in real time it should be noted that just like the ekf the mekf is also ad hoc in the sense that it is a real time approximation method numerical examples with computer simulation are included to demonstrate the effectiveness of this procedure as compared to the ekf algorithm

recursive identification method for miso wiener hammerstein model a simple technique for recursive identification of the wiener hammerstein model with extension to the multi input single output miso case is presented we use a new transformation of the input output difference equation where parameters to be estimated are those of each subsystem of the initial and unique realization after that a weighted extended least squares method is employed to estimate recursively and separately parameters of the linear subsystems and the static nonlinear element the convergence analysis of the proposed procedure is also studied finally a numerical example is provided to show the efficiency of the algorithm

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

a reduced order extended kalman filter for sequential images containing a moving object the extended kalman filter ekf is applied to the reduction of noise in sequential images containing a moving object and to the estimation of the object s velocity a computationally tractable approximation of the ekf called the parallel extended kalman filter pekf is generated the pekf consists of a parallel bank of third order ekfs operating on the fourier coefficients of the image followed by a finite impulse response filter the pekf is shown to converge to the optimal in the mean square sense algorithm in the limit as the velocity estimation errors approach zero the performance of the pekf is demonstrated for very low signal to noise ratio snr images the pekf also provides a natural setting for tracking slow changes in the object real or apparent and its velocity since these variations are included in the model the relation of the pekf to another frequency domain algorithm for velocity estimation is discussed the algorithm is illustrated by application to an example and its performance is demonstrated in the presence of velocity estimation errors

a stochastic analysis of a modified gain extended kalman filter with applications to estimation with bearings only measurements a new globally convergent nonlinear observer called the modified gain extended kalman observer mgeko is developed for a special class of systems this observer structure forms the basis of a new stochastic filter mechanization called the modified gain extended kalman filter mgekf a sufficient condition for the estimation errors of the mgekf to be exponentially bounded in the mean square is obtained finally the mgeko and the mgekf are applied to the three dimensional bearings only measurement problem where the extended kalman filter often shows erratic behavior

krasnoselskii s fixed point theorem for weakly continuous maps abstract we consider the sum a b m x where m is a weakly compact and convex subset of a banach space x a m x is weakly continuous and b l x with bp 1 p 1 an alternative condition is given in order to guarantee the existence of fixed points in m for a b some illustrative applications are given

a prediction error method for recursive indentification of nonlinear systems abstract nonlinear systems can be identified with nonlinear filters by combined estimation of parameters and state often these methods are very complex or have convergence problems as for example the extended kalman filter in this paper a new algorithm for recursive nonlinear system identification is presented convergence problems are eliminated by an improved calculation of the gradient as the total derivative of the prediction error by separately estimating parameters and states computation time is reduced the efficacy of the new identification algorithm is illustrated by studying its performance in a gravimetric filling system

the iterated kalman filter update as a gauss newton method it is shown that the iterated kalman filter ikf update is an application of the gauss newton method for approximating a maximum likelihood estimate an example is presented in which the iterated kalman filter update and maximum likelihood estimate show correct convergence behavior as the observation becomes more accurate whereas the extended kalman filter update does not

image flow segmentation and estimation by constraint line clustering image flow is the velocity field in the image plane caused by the motion of the observer objects in the scene or apparent motion and can contain discontinuities due to object occlusion in the scene an algorithm that can estimate the image flow velocity field when there are discontinuities due to occlusions is described the constraint line clustering algorithm uses a statistical test to estimate the image flow velocity field in the presence of step discontinuities in the image irradiance or velocity field particular emphasis is placed on motion estimation and segmentation in situations such as random dot patterns where motion is the only cue to segmentation experimental results on a demanding synthetic test case and a real image are presented a smoothing algorithm for improving the velocity field estimate is also described the smoothing algorithm constructs a smooth estimate of the velocity field by approximating a surface between step discontinuities it is noted that the velocity field estimate can be improved using surface reconstruction between velocity field boundaries

a decoupled approach to filter design for stochastic systems abstractthis paper presents a new theorem to guarantee the almost sure exponential stability for a class of stochastic triangular systems by studying only the stability of each diagonal subsystems this result allows to solve the filtering problem of the stochastic systems with multiplicative noises by using the almost sure exponential stability concept two kinds of observers are treated the full order and reduced order cases

linearized reduced order filtering a reduced order version of extended kalman filtering is presented in which both the filtering equation and the associated riccati equation have been reduced in dimension to allow for real time processing the procedure for designing the reduced order filter is similar to that for designing the extended kalman filter the same approximations being applied one technique useful for limiting the computational burden in a linearized filter design problems is presented and illustrated by an example the primary limitation of the result is that the nonlinearity must be in terms of the vector to be estimated

recursive update filtering for nonlinear estimation nonlinear filters are often very computationally expensive and usually not suitable for real time applications real time navigation algorithms are typically based on linear estimators such as the extended kalman filter ekf and to a much lesser extent the unscented kalman filter this work proposes a novel nonlinear estimator whose additional computational cost is comparable to n 1 ekf updates where n is the number of recursions a tuning parameter the higher n the less the filter relies on the linearization assumption a second algorithm is proposed with a differential update which is equivalent to the recursive update as n tends to infinity

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

filtering predictive and smoothing cramer rao bounds for discrete time nonlinear dynamic systems cramer rao lower bounds for the discrete time nonlinear state estimation problem are treated the cramer rao bound for the mean square error matrix of a state estimate is particularly important for quality evaluation of nonlinear state estimators as it represents a limit of cognizability of the state recursive relations for filtering predictive and smoothing cramer rao bounds are derived to establish a unifying framework for several previously published derivation procedures and results lower bounds for systems with unknown parameters are newly provided computation of filtering predictive and smoothing cramer rao bounds their mutual comparison and utilization for quality evaluation of some nonlinear filters are shown in numerical examples

dynamic observers as asymptotic limits of recursive filters special cases a method for constructing observers for dynamical systems as asymptotic limits of filters is described the program is carried out in detail for linear systems and in addition an observer is obtai

estimating three dimensional motion parameters of a rigid planar patch we present a new direct method of estimating the three dimensional motion parameters of a rigid planar patch from two time sequential perspective views image frames first a set of eight pure parameters are defined these parameters can be determined uniquely from the two given image frames by solving a set of linear equations then the actual motion parameters are determined from these pure parameters by a method which requires the solution of a sixth order polynomial of one variable only and there exists a certain efficient algorithm for solving a sixth order polynomial aside from a scale factor for the translation parameters the number of real solutions never exceeds two in the special case of three dimensional translation the motion parameters can be expressed directly as some simple functions of the eight pure parameters thus only a few arithmetic operations are needed

random matrix theory in lattice statistical mechanics abstract in this short note we collect together known results on the use of random matrix theory rmt in lattice statistical mechanics the purpose here is two fold firstly the rmt analysis provides an intrinsic characterization of integrability and secondly it appears to be an effective tool to find new integrable models various examples from quantum and classical statistical mechanics are presented

existence results for a generalized nonlinear hammerstein equation on l1 spaces abstract in this paper we are concerned with existence results for a nonlinear hammerstein integral equation acting on l 1 vector valued functions making use of the de blasi measure of weak noncompactness we establish a variant of the topological fixed point theorem of krasnosel skii for the sum of two operators without requiring weak compactness or weak continuity assumptions such a result provides an adequate tool for deriving an existence theory for problem 1 1

robust estimation in non linear state space models with state dependent noise in this paper we present a robust estimation algorithm for non linear state space models driven by state dependent noise the algorithm is robust to outliers in the data we derive the algorithm step by step from first principles from theory to implementation the implementation is straightforward and consists mainly of two components 1 a slightly modified version of the rauch tung striebel recursions and 2 a backtracking line search strategy since it preserves the underlying chain structure of the problem its computational complexity grows linearly with the number of data the algorithm is iterative and is guaranteed to converge under mild assumptions to a local optimum from any starting point we validate our approach via experiments on synthetic data from a multi variate stochastic volatility model

convergence and applications of a gossip based gauss newton algorithm the gauss newton algorithm is a popular and efficient centralized method for solving non linear least squares nlls problems in this paper a multi agent distributed version of this algorithm is proposed to solve general nlls problems in a network named gossip based gauss newton ggn algorithm furthermore we analyze and present sufficient conditions for its convergence and show numerically that the ggn algorithm achieves performance comparable to the centralized algorithm with graceful degradation in case of network failures more importantly the ggn algorithm provides significant performance gains compared to other distributed first order methods

posterior linearization filter principles and implementation using sigma points this paper is concerned with gaussian approximations to the posterior probability density function pdf in the update step of bayesian filtering with nonlinear measurements in this setting sigma point approximations to the kalman filter kf recursion are widely used due to their ease of implementation and relatively good performance in the update step these sigma point kfs are equivalent to linearizing the nonlinear measurement function by statistical linear regression slr with respect to the prior pdf in this paper we argue that the measurement function should be linearized using slr with respect to the posterior rather than the prior to take into account the information provided by the measurement the resulting filter is referred to as the posterior linearization filter plf in practice the exact plf update is intractable but can be approximated by the iterated plf iplf which carries out iterated slrs with respect to the best available approximation to the posterior the iplf can be seen as an approximate recursive kullback leibler divergence minimization procedure we demonstrate the high performance of the iplf in relation to other gaussian filters in two numerical examples

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

the iterated kalman smoother as a gauss newton method the kalman smoother is known to be the maximum likelihood estimator when the measurement and transition functions are affine i e a linear function plus a constant a new proof of this result is presented that shows that the kalman smoother decomposes a large least squares problem into a sequence of much smaller problems the iterated kalman smoother is then presented and shown to be a gauss newton method for maximizing the likelihood function in the nonaffine case this method takes advantage of the decomposition obtained with the kalman smoother

filter order selection in adaptive maximum likelihood estimation the choice of the number of parameters is an important problem in adaptive filtering in the general ground of maximum likelihood ml parameter estimation akaike criterion has proved to be a very useful tool significant results and the importance of the kullback information measure as the implicit measure of distance associated with ml estimation are discussed application of these results to adaptive filtering is then considered for time invariant and time varying parametric models the corresponding practical forms of akaike criterion are given in the time varying case this criterion may be used as a way to fit the model into the nonstationarity of an exact filter the possible generalization of the akaike criterion to non ml estimation is discussed and application is made for weighted least squares estimation a more general approach to the nonstationary case is given by assuming a linear stochastic model for the vector of the filter coefficients in which case the ml estimate is computed recursively using the kalman filtering equation then the random sequence of kalman gains is close to a deterministic average sequence this sequence may be precomputed and gives an optimal choice for the gain matrices in an adaptive gradient type filter

krasnosel skii type fixed point theorems under weak topology features abstract in this paper we prove the following krasnosel skii type fixed point theorem let m be a nonempty bounded closed convex subset of a banach space x suppose that a m x and b x x are two weakly sequentially continuous mappings satisfying i a m is relatively weakly compact ii b is a strict contraction iii x b x a y y m x m then a b has at least one fixed point in m this result is then used to obtain some new fixed point theorems for the sum of a weakly compact and a nonexpansive mapping the results presented in this paper encompass several earlier ones in the literature

l sub 2 and l sub 1 beamformers recursive implementation and performance analysis studies array beamformers as optimal waveform estimators the authors apply an inverse problem formulation presenting an integrated design to quadratic l sub 2 and least absolute value l sub 1 beamformers the general solution of the l sub 2 beamformers is parameterized by a regularizing parameter that weights the confidence placed by the designer on prior knowledge versus the quality of the measurements this regularizing parameter is used to establish an equivalence between alternative l sub 2 beamformers the authors then develop time recursive implementations of the l sub 2 and l sub 1 beamformers the performance of these beamformers is studied next the authors show that 1 in the presence of correlated arrivals the mmse beamformer uses constructively the correlation between incoming signals in reconstructing the estimated field while rejecting the uncorrelated returns and 2 the l sub 1 beamformer has the ability to adjust itself to unexpected noise conditions because it is considerably more robust than the l sub 2 beamformers to unmodeled impulsive noise or to the occurrence of malfunctioning sensors the analysis is confirmed by simulated studies

a topological and geometric approach to fixed points results for sum of operators and applications abstract in this paper we establish a fixed point result of krasnoselskii type for the sum a b where a and b are continuous maps acting on locally convex spaces our results extend previous ones we apply such results to obtain strong solutions for some quasi linear elliptic equations with lack of compactness we also provide an application to the existence and regularity theory of solutions to a nonlinear integral equation modeled in a banach space in the last section we develop a sequentially weak continuity result for a class of operators acting on vector valued lebesgue spaces such a result is used together with a geometric condition as the main tool to provide an existence theory for nonlinear integral equations in l p e

a reduced order observer for non linear discrete time systems abstract in this note a simple and useful reduced order observer for a large class of non linear discrete time systems is presented neither detectability of the linear part nor resolution of the sylvester constraint is required from the stability analysis we show that the proposed state observer has strong tracking properties under very general conditions and generalizes results in m boutayeb et al ieee trans automat control 42 4 1997 581 586 high performances from the design and implementation point of view will be shown through three numerical examples of physical processes largely used in industrial applications

unbiased minimum variance estimation for systems with unknown exogenous inputs a new method is developed for the state estimation of linear discrete time stochastic systems in the presence of an unknown disturbance the filter obtained is optimal in the unbiased minimum variance sense the necessary and sufficient conditions for the existence and the stability of the filter are given

a strong tracking extended kalman observer for nonlinear discrete time systems the authors show how the extended kalman filter used as an observer for nonlinear discrete time systems or extended kalman observer eko becomes a useful state estimator when the arbitrary matrices namely r sub k and q sub k are adequately chosen as a first step we use the linearization technique given by boutayed et al 1997 which consists of introducing unknown diagonal matrices to take the approximation errors into account it is shown that the decreasing lyapunov function condition leads to a linear matrix inequality lmi problem which points out the connection between a good convergence behavior of the eko and the instrumental matrices r sub k and q sub k in order to satisfy the obtained lmi a particular design of q sub k is given high performances of the proposed technique are shown through numerical examples under the worst conditions

adaptive unscented gaussian likelihood approximation filter this paper focuses on the update step of bayesian nonlinear filtering we first derive the unscented gaussian likelihood approximation filter uglaf which provides a gaussian approximation to the likelihood by applying the unscented transformation to the inverse of the measurement function the uglaf approximation is accurate in the cases where the unscented kalman filter ukf is not and the other way round as a result we propose the adaptive uglaf auglaf which selects the best approximation to the posterior ukf or uglaf based on the kullback leibler divergence this enables auglaf to outperform both the ukf and uglaf

a polynomial approach to bias aware fixed lag smoothing problem in the present technical note a solution to the problem of fixed lag smoothing of siso systems in presence of a dynamical bias is presented in a polynomial framework the bias aware smoothing problem is solved in three steps namely the design of the general structure of the smoother the estimation of the dynamical bias by means of a deconvolution technique and then the combination of the previous results to obtain the bias aware fixed lag smoother applied to an example this approach shows its efficiency

generalized iterated kalman filter and its performance evaluation in this paper we present a generalized iterated kalman filter gikf algorithm for state estimation of a nonlinear stochastic discrete time system with state dependent multiplicative observation noise the gikf algorithm adopts the newton raphson iterative optimization steps to yield an approximate maximum a posteriori estimate of the states the mean square estimation error mse and the cramer rao lower bound crlb of the state estimates are also derived in particular the local convergence of mse of gikf is rigorously established it is also proved that the gikf yields a smaller mse than those of the generalized extended kalman filter and the traditional extended kalman filter the performance advantages and convergence of gikf are demonstrated using monte carlo simulations on a target tracking application in a range measuring sensor network

a fresh look at the kalman filter in this paper we discuss the kalman filter for state estimation in noisy linear discrete time dynamical systems we give an overview of its history its mathematical and statistical formulations and its use in applications we describe a novel derivation of the kalman filter using newton s method for root finding this approach is quite general as it can also be used to derive a number of variations of the kalman filter including recursive estimators for both prediction and smoothing estimators with fading memory and the extended kalman filter for nonlinear systems