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1.
A problem of estimation of states and parameters in stochastic dynamic systems of observation with discrete time containing
a Markovian chain is studied. Matrices of transient probabilities and observation plans are random with unknown distribution
with a given compact carrier. Observations, on the basis of which the estimation is made, are available at a fixed interval
of time [0, T]. As a loss function, we have a conditional mathematical expectation with respect to the available observations of ℓ
2-norm of the estimation error of a signal process on [0, T]. The problem is in constructing an estimate minimizing losses correspondent to the worst distribution of the pair “a matrix
of transient probabilities—a matrix of observation plan” form a set of allowable distributions. For a correspondent minimax
problem is demonstrated the existence of a saddle point and is obtained a form of the wanted minimax estimation. The applicability
of the obtained results is illustrated by a numerical example of the estimation of a state of TCP under the conditions of
uncertainty of communication channel parameters. 相似文献
2.
We consider the minimax estimation problem in a linear observation model under ellipsoidal constraints on the vector of unknown parameters. To solve the problem, we use dual optimization and semidefinite programming methods. The developed algorithms are applied to constructing motion parameter estimates for a maneuvering flying vehicle under constraints on the acceleration vector. 相似文献
4.
This paper presents a state estimation approach for an uncertain linear equation with a non-invertible operator in Hilbert space. The approach addresses linear equations with uncertain deterministic input and noise in the measurements, which belong to a given convex closed bounded set. A new notion of a minimax observable subspace is introduced. By means of the presented approach, new equations describing the dynamics of a minimax recursive estimator for discrete-time non-causal differential-algebraic equations (DAEs) are presented. For the case of regular DAEs it is proved that the estimator’s equation coincides with the equation describing the seminal Kalman filter. The properties of the estimator are illustrated by a numerical example. 相似文献
5.
A central issue in dimension reduction is choosing a sensible number of dimensions to be retained. This work demonstrates the surprising result of the asymptotic consistency of the maximum likelihood criterion for determining the intrinsic dimension of a dataset in an isotropic version of probabilistic principal component analysis (PPCA). Numerical experiments on simulated and real datasets show that the maximum likelihood criterion can actually be used in practice and outperforms existing intrinsic dimension selection criteria in various situations. This paper exhibits and outlines the limits of the maximum likelihood criterion. It leads to recommend the use of the AIC criterion in specific situations. A useful application of this work would be the automatic selection of intrinsic dimensions in mixtures of isotropic PPCA for classification. 相似文献
6.
Consideration was given to the minimax estimation in the observation system including a hidden Markov model for continuous and counting observations. The dynamic and observation equations depend on a random finite-dimensional parameter having an unknown distribution with the given support. The conditional expectation of the available observation of some generalized quadratic loss function was used as the risk function. Existence of the saddle point in the formulated minimax problem was proved, and the worst distribution and the minimax estimate as the solution of a simpler dual problem were characterized. 相似文献
7.
In this paper, we propose a method to test a probabilistic FSM. The testing process consists of two parts. First, we check if there are any output faults or transfer faults in transitions. In order to identify a state of a PFSM, the characterization set is extended such that states are identified not only by observing output sequences but also by comparing probabilities. Second, we test whether the transition probabilities are correctly implemented. Interval estimation is used to assert the correctness of transition probabilities where a test verdict is assigned with a given confidence level. From a given confidence level and confidence interval length, a method is presented to determine the test sequence repetition numbers for testing probabilities. Fault coverage evaluation is carried out based on extended fault types where probabilities are changed. As an application, we apply the proposed method to a probabilistic non-repudiation protocol. 相似文献
9.
概率符号有向图(probabilistic signed digraph,PSDG)模型通过在传统定性符号有向图(signed digraph,SDG)的模型结构中引入节点和支路的概率信息,改善了传统定性SDG故障诊断的性能,提高了故障诊断的分辨率.然而,在PSDG模型中,节点的概率分布通常是在给定其父节点条件下的条件... 相似文献
10.
A modification was proposed for the relations of the method of dynamic programming in the problems of optimal stochastic control of the discrete systems by the probabilistic performance criterion. It enabled one to simplify the process of finding the optimal Markov strategy and obtain a suboptimal solution. Its efficiency was verified by the examples of maneuver optimization of the stationary satellite in the neighborhood of a geostationary orbit. An explicit form of the optimal control for the bilinear system with probabilistic terminal criterion was determined using the results obtained. 相似文献
11.
The paper deals with the problem of parameter estimation using two different sources of information, namely a time series with dynamic data and steady-state data. The new estimator is based on a two-step procedure: first a multi-objective optimization is performed, leading to a set of Pareto-optimal vectors of parameter estimates and, second, a single model is chosen based on the free-run simulation error which is required to be minimally correlated with the model output. The procedure is general in nature and can be applied to any model representation, but for the sake of simplicity, the new procedure is illustrated using NARX polynomial models for which closed formulae for generating the Pareto-set are readily available. Monte Carlo simulation studies suggest that the new estimator, which does not assume any particular noise model, is fairly unbiased even when the conventional least-squares estimator is biased. 相似文献
14.
Consideration was given to some problems of estimation (filtering and identification) in the observation systems describing the Markov processes with finite state spaces. The transition intensity matrices and the observation plan are random and have unknown distributions of some class. The conditional expectations of the accessible observations of some quadratic functions of the estimate errors are used as the performance criteria. The estimation problems under study lie in constructing estimates minimizing the conditional mean losses corresponding to the least favorable distribution of the “transition intensity matrix-observation plan matrix” pair from the set of permissible distributions. For the corresponding minimax problems, existence of the saddle points was proved, and the form of the corresponding minimax estimates was established. 相似文献
15.
State-of-the-art in real-time simultaneous objects tracking through automated probabilistic estimation framework has been considered. The approach proposed here is dealt with in association with a novel self-correcting particle filter to track a number of moving objects. This idea is applicable to track most of simultaneous non-rigid objects, since 3D image is analyzed. Due to the fact that the captured frames are taken into account as two dimensional data matrices, some appropriate extracted features of the processed frames could be utilized to make the third dimension. The whole of suitable features of moving objects, which cannot directly be applied to the process of posterior probability calculation, need to be fed to a neural network for the purpose of making the third dimension. Subsequently, the probabilistic estimation of the present self-correcting particle filter in each frame is corrected through the neural network results to estimate each identified object, appropriately, in its current frame. The effectiveness of the proposed approach performance is guaranteed, once the results of three known particle filter-based procedures are taken into real consideration as benchmark approaches. Experimental results demonstrate that the proposed approach outperforms the traditional tracking systems for various challenging scenarios. It is shown that the accuracy of the proposed approach is improved, while its tracking error is correspondingly decreased. 相似文献
16.
Consideration was given to the Bayesian estimation in the multidimensional indefinite-stochastic observation model using the minimax criterion with the generalized probabilistic risk functionals. The sufficient conditions for minimax-optimality of the linear estimate in the class of all measurable estimates were formulated. The cases of the risk functionals in the form of expected losses, the probabilities of error exaltation over some level, as well as the quantiles of the error norm were discussed in detail. 相似文献
17.
An appropriate bid price is essential for winning a construction project contract. However, making an accurate cost estimate is both time-consuming and expensive. Thus, a method that does not take much time and can approximate a proper bid price can help a contractor in making bid-price decisions when the available bid-estimation time is insufficient. Such a method can also generate a target cost and provide a cross-check for their bid prices that were estimated using a detailed process. This study proposes a novel model for quickly making a bid-price estimation that integrates a probabilistic cost sub-model and a multi-factor evaluation sub-model. The cost sub-model, which is simulation-based, focuses on the cost divisions to save estimation time. At the same time, the multi-factor evaluation sub-model captures the specific factors affecting the cost of each cost division. The advantages of the proposed model are demonstrated by its application to three residential housing projects located in northern Taiwan. The steps for applying this model to other contractors are also provided. 相似文献
18.
A probabilistic discrete event system (PDES) is a nondeterministic discrete event system where the probabilities of nondeterministic transitions are specified. State estimation problems of PDES are more difficult than those of non-probabilistic discrete event systems. In our previous papers, we investigated state estimation problems for non-probabilistic discrete event systems. We defined four types of detectabilities and derived necessary and sufficient conditions for checking these detectabilities. In this paper, we extend our study to state estimation problems for PDES by considering the probabilities. The first step in our approach is to convert a given PDES into a nondeterministic discrete event system and find sufficient conditions for checking probabilistic detectabilities. Next, to find necessary and sufficient conditions for checking probabilistic detectabilities, we investigate the “convergence” of event sequences in PDES. An event sequence is convergent if along this sequence, it is more and more certain that the system is in a particular state. We derive conditions for convergence and hence for detectabilities. We focus on systems with complete event observation and no state observation. For better presentation, the theoretical development is illustrated by a simplified example of nephritis diagnosis. 相似文献
19.
#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of satisfiability modulo theories (SMT) there is a growing need for model counting solvers, coming from several application domains (quantitative information flow, static analysis of probabilistic programs). In this paper, we show a reduction from an approximate version of #SMT to SMT. We focus on the theories of integer arithmetic and linear real arithmetic. We propose model counting algorithms that provide approximate solutions with formal bounds on the approximation error. They run in polynomial time and make a polynomial number of queries to the SMT solver for the underlying theory, exploiting “for free” the sophisticated heuristics implemented within modern SMT solvers. We have implemented the algorithms and used them to solve the value problem for a model of loop-free probabilistic programs with nondeterminism. 相似文献
20.
This paper considers parameter estimation for nonlinear model using median squared error (MSE) criterion, which is limited
to linear model in the past. It is shown that applying MSE, the essence of estimating parameters for hinging hyperplanes (HH)
and linear model are the same. Motivated by this fact, MSE estimation is discussed for HH. A local optimality condition is
given and based on this condition, an algorithm using linear programming technique is proposed. Numerical experiments show
the good performance of the proposed estimation strategy and algorithm. 相似文献
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