guaranteed robust nonlinear minimax estimation minimax parameter estimation aims at characterizing the set of all values of the parameter vector that minimize the largest absolute deviation between the experimental data and the corresponding model outputs it is well known however to be extremely sensitive to outliers in the data resulting e g of sensor failures in this paper a new method is proposed to robustify minimax estimation by allowing a prespecified number of absolute deviations to become arbitrarily large without modifying the estimates by combining tools of interval analysis and constraint propagation it becomes possible to compute the corresponding minimax estimates in an approximate but guaranteed way even when the model output is nonlinear in its parameters the method is illustrated on a problem where the parameters are not globally identifiable which demonstrates its ability to deal with the case where the minimax solution is not unique

hierarchical labeler in a speech recognition system a speech coding apparatus and method uses a hierarchy of prototype sets to code an utterance while consuming fewer computing resources the value of at least one feature of an utterance is measured during each of a series of successive time intervals to produce a series of feature vector signals representing the feature values a plurality of level subsets of prototype vector signals is computed wherein each prototype vector signal in a higher level subset is associated with at least one prototype vector signal in a lower level subset each level subset contains a plurality of prototype vector signals with lower level subsets containing more prototypes than higher level subsets the closeness of the feature value of the first feature vector signal is compared to the parameter values of prototype vector signals in the first level subset of prototype vector signals to obtain a ranked list of prototype match scores for the first feature vector signal and each prototype vector signal in the first level subset the closeness of the feature value of the first feature vector signal is compared to the parameter values of each prototype vector signal in a second lower level subset that is associated with the highest ranking prototype vectors in the first level subset to obtain a second ranked list of prototype match scores the identification value of the prototype vector signal in the second ranked list having the best prototype match score is output as a coded utterance representation signal of the first feature vector signal

normalization of speech by adaptive labelling in a speech processor system in which prototype vectors of speech are generated by an acoustic processor under reference noise and known ambient conditions and in which feature vectors of speech are generated during varying noise and other ambient and recording conditions normalized vectors are generated to reflect the form the feature vectors would have if generated under the reference conditions the normalized vectors are generated by a applying an operator function a i to a set of feature vectors x occurring at or before time interval i to yield a normalized vector y i a i x b determining a distance error vector e i by which the normalized vector is projectively moved toward the closest prototype vector to the normalized vector y i c up dating the operator function for next time interval to correspond to the most recently determined distance error vector and d incrementing i to the next time interval and repeating steps a through d wherein the feature vector corresponding to the incremented i value has the most recent up dated operator function applied thereto with successive time intervals successive normalized vectors are generated based on a successively up dated operator function for each normalized vector the closest prototype thereto is associated therewith the string of normalized vectors or the string of associated prototypes or respective label identifiers thereof or both provide output from the acoustic processor

speech recognition system using markov models having independent label output sets a speech recognition system measures the values of at least two classes of features of an utterance 1 a first class whose value is related to the frequency spectrum of the utterance and 2 a second class whose value is related to the variation with time of the first class value of the utterance word baseforms are constructed from markov model baseform units each output producing transition of a baseform unit produces outputs from both classes however for each output producing transition the probabilities of producing outputs from the first class are independent of the probabilities of producing outputs from the second class

a speaker independent label coding apparatus the present invention is related to speech recognition and particularly to a new type of vector quantizer and a new vector quantization technique in which the error rate of associating a sound with an incoming speech signal is drastically reduced to achieve this end the present invention technique groups the feature vectors in a space into different prototypes at least two of which represent a class of sound each of the prototypes may in turn have a number of subclasses or partitions each of the prototypes and their subclasses may be assigned respective identifying values to identify an incoming speech feature vector at least one of the feature values of the incoming feature vector is compared with the different values of the respective prototypes or the subclasses of the prototypes the class of sound whose group of prototypes or at least one of the prototypes whose combined value most closely matches the value of the feature value of the feature vector is deemed to be the class corresponding to the feature vector the feature vector is then labeled with the identifier associated with that class

using interval arithmetic to prove that a set is path connected in this paper we give a numerical algorithm able to prove whether a set s described by nonlinear inequalities is path connected or not to our knowledge no other algorithm numerical or symbolic is able to deal with this type of problem the proposed approach uses interval arithmetic to build a graph which has exactly the same number of connected components as s examples illustrate the principle of the approach

guaranteed characterization of exact non asymptotic confidence regions as defined by lscr and sps in parameter estimation it is often desirable to supplement the estimates with an assessment of their quality a new family of methods proposed by campi et al for this purpose is particularly attractive as it makes it possible to obtain exact non asymptotic confidence regions under mild assumptions on the noise distribution a bottleneck of this approach however is the numerical characterization of these confidence regions so far it has been carried out by gridding which provides no guarantee as to its results and is only applicable to low dimensional spaces this paper shows how interval analysis can contribute to removing this bottleneck

set membership state and parameter estimation for systems described by nonlinear differential equations this paper investigates the use of guaranteed methods to perform state and parameter estimation for nonlinear continuous time systems in a bounded error context a state estimator based on a prediction correction approach is given where the prediction step consists in a validated integration of an initial value problem for an ordinary differential equation ivp for ode using interval analysis and high order taylor models while the correction step uses a set inversion technique the state estimator is extended to solve the parameter estimation problem an illustrative example is presented for each part

classification of semigroups of linear fractional maps in the unit ball we give a complete classiflcation up to conjugation of continuous semigroups of linear fractional self maps of the unit ball

guaranteed nonlinear estimation using constraint propagation on sets bounded error estimation is the estimation of the parameter or state vector of a model from experimental data under the assumption that some suitably de ned errors should belong to some prior feasible sets when the model outputs are linear in the vector to be estimated a number of methods are available to enclose all estimates that are consistent with the data into simple sets such as ellipsoids orthotopes or parallelotopes thereby providing guaranteed set estimates in the nonlinear case the situation is much less developed and there are very few methods that produce such guaranteed estimates in this paper the discrete time problem is cast into the more general framework of constraint satisfaction problems algorithms rather classical in the area of interval constraint propagation are extended by replacing intervals by more general subsets of real vector spaces this makes it possible to propose a new algorithm that contracts the feasible domains for each uncertain variable optimally i e no smaller domain could be obtained and e ciently the resulting methodology is illustrated on discrete time nonlinear state estimation the state at time k is estimated either from past measurement only or from all measurements assumed to be available from the start even in the causal case prior information on the future value of the state and output vectors due for instance to physical constraints is readily taken into account

on the application of a hybrid ellipsoidal rectangular interval arithmetic algorithm to interval kalman filtering for state estimation of uncertain systems modelling uncertainty is a key limitation to the applicability of the classical kalman filter for state estimation of dynamic systems for such systems with bounded modelling uncertainty the interval kalman filter ikf is a direct extension of the former to interval systems however its usage is not yet widespread owing to the over conservatism of interval arithmetic bounds in this paper the ikf equations are adapted to use an ellipsoidal arithmetic that in some cases provides tighter bounds than direct rectangular interval arithmetic in order for the ikf to be useful it must be able to provide reasonable enclosures under all circumstances to this end a hybrid ellipsoidal rectangular enclosure algorithm is proposed and its robustness is evidenced by its application to two characteristically different systems for which it provides stable estimate bounds whereas the rectangular and ellipsoidal approaches fail to accomplish this in either one or the other case

state estimation for markovian jump linear systems with bounded disturbances in this paper we investigate the state estimation problem for a class of markovian jump linear systems mjlss in the presence of bounded polyhedral disturbances a set membership estimation algorithm is first proposed to find the smallest consistent set of all possible states which is shown to be expressed by a union of multiple polytopes the posterior probabilities of the system jumping modes are then estimated by introducing the lebesgue measure based on which the optimal point estimate is further provided moreover a similarity relationship for polytopes is defined and an approximate method is presented to calculate the minkowski sum of polytopes which can help reduce the computational complexity of the overall estimation algorithm

high gain observer for a class of non triangular systems this paper presents a high gain observer for a class of mimo nonlinear systems involving some uncertainties the latter is particularly composed of cascade subsystems where each subsystem is associated with a subset of the output variables and assumes a triangular dependence on its own state variables and may depend on the state variables of all other subsystems the main contribution consists in extending the available results to allow more interconnections between the subsystems of fundamental interest it is shown that the underlying observation error exponentially converges to zero in the absence of uncertainties moreover the observation error can be made as small as desired by properly specifying the observer design parameter in the case where uncertainties are considered

solving over constrained systems of non linear interval equations and its robotic application abstract this paper presents and describes in details an original method developed to solve over constrained systems of non linear interval equations that arise namely in parameter identification problems deriving from physical models and uncertain measurements our approach consists of computing an interval enclosure of the least square solution set and an inner box of tolerable solution set this method is applied in a detailed example and some interesting results obtained for the calibration of a cable driven robot are shown

valiron s theorem in the unit ball and spectra of composition operators abstract we prove a version of valiron s conjugacy theorem for schur class mappings of the unit ball of c n as an application we obtain a formula for the spectral radius of composition operators on the ball with schur class symbols

speech recognition apparatus having a speech coder outputting acoustic prototype ranks a speech coding and speech recognition apparatus the value of at least one feature of an utterance is measured over each of a series of successive time intervals to produce a series of feature vector signals the closeness of the feature value of each feature vector signal to the parameter value of each of a set of prototype vector signals is determined to obtain prototype match scores for each vector signal and each prototype vector signal for each feature vector signal first rank and second rank scores are associated with the prototype vector signals having the best and second best prototype match scores respectively for each feature vector signal at least the identification value and the rank score of the first ranked and second ranked prototype vector signals are output as a coded utterance representation signal of the feature vector signal to produce a series of coded utterance representation signals for each of a plurality of speech units a probabilistic model has a plurality of model outputs and output probabilities for each model output each model output comprises the identification value of a prototype vector and a rank score for each speech unit a match score comprises an estimate of the probability that the probabilistic model of the speech unit would output a series of model outputs matching a reference series comprising the identification value and rank score of at least one prototype vector from each coded utterance representation signal in the series of coded utterance representation signals

speech coding apparatus and method using classification rules a speech coding apparatus and method uses classification rules to code an utterance while consuming fewer computing resources the value of at least one feature of an utterance is measured during each of a series of successive time intervals to produce a series of feature vector signals representing the feature values the classification rules comprise at least first and second sets of classification rules the first set of classification rules map each feature vector signal from a set of all possible feature vector signals to exactly one of at least two disjoint subsets of feature vector signals the second set of classification rules map each feature vector signal in a subset of feature vector signals to exactly one of at least two different classes of prototype vector signals each class contains a plurality of prototype vector signals according to the classification rules a first feature vector signal is mapped to a first class of prototype vector signals the closeness of the feature value of the first feature vector signal is compared to the parameter values of only the prototype vector signals in the first class of prototype vector signals to obtain prototype match scores for the first feature vector signal and each prototype vector signal in the first class at least the identification value of at least the prototype vector signal having the best prototype match score is output as a coded utterance representation signal of the first feature vector signal

brief paper robust set membership state estimation application to underwater robotics this paper proposes a new observer for estimating the state vector of a nonlinear system this observer which is robust with respect to outliers assumes that the measurement errors as well as the number of outliers that could occur within a given time window are bounded the principle of the approach is to use interval analysis to deal properly with the nonlinearities involved in the system without any linearization or approximation and to propagate through the time in a forward and backward manner the assumptions made about outliers a test case related to the localization and control of an underwater robot is also proposed to illustrate the efficiency of the approach

norms and spectral radii of linear fractional composition operators on the ball abstract we give a new proof that every linear fractional map of the unit ball induces a bounded composition operator on the standard scale of hilbert function spaces on the ball and obtain new norm bounds analogous to the standard one variable estimates we also show that cowen s one variable spectral radius formula extends to these operators the key observation underlying these results is that every linear fractional map of the ball belongs to the schur agler class