Parameter Estimation in the Presence of Measurement Noise†

The parameter estimation problem is formulated for the situation in which the measurement of every variable is subject to noise. The method of maximum likelihood is shown to produce estimators for which the amount of computation is prohibitive but these estimators fire used as a standard against which the accuracy of more easily computed methods may be judged, A number of alternative methods are introduced, a form of weighted least squares being shown to require the least computation and to approximate the accuracy of the maximum likelihood estimators. An example of the appli-cation of this method is given.     

Lower Bound Estimation of Hardware Resources for Scheduling in High-Level Synthesis

In high-level synthesis of VLSI circuits,good lower bound prediction can efficiently narrow down the large space of possible designs.Previous approaches predict the lower bound by relaxing or even ignoring the precedence constraints of the data flow graph (DFG),and result in inaccuracy of the lower bound.The loop folding and conditional branch were also not considered,In this paper,a new stepwise refinement algorithm is proposed.which takes consideration of precedence constraints of the DFG to estimate the lower bound of hardware resources under time constratints,Processing techniques to handle multi-cycle,chaining,pipelining,as well as loop folding and mutual exclusion among conditional branches are also incorporated in the algorithm.Experimental results show that the algorithm can produce a very tight and close to optimal lower bound in reasonable computation time.     

State Estimation of a Class of Hybrid Systems in the Presence of Unknown Mode Transitions

Since the state of hybrid systems is determined by interacting continuous and discrete dynamics,the state estimation of hybrid systems becomes a challenging problem.It is more com- plicated when the discrete mode transition information is not available,and the modes of hybrid systems are nonlinear stochastic dynamic systems.To address this problem,this paper proposes a novel hybrid strong tracking filter (HSTF) for state estimation of a class of hybrid nonlinear stochas- tic systems with unknown mode transition,the method for designing HSTF is presented.The HSTF can estimate the continuous state and discrete mode accurately with unknown mode transition in- formation,and the estimation of hybrid states is robust against the initial state.Simulation results illustrate the effectiveness of the proposed approach.     

Estimation of squeeze film damping in artificial hair-sensor towards the detection-limit of crickets’ hairs

The filliform hairs of crickets are among the most sensitive flow sensing elements in nature. The high sensitivity of these hairs enables crickets in perceiving tiny air-movements which are only just distinguishable from noise. This forms our source of inspiration to design highly-sensitive array system made of artificial hair sensors for flow pattern observation i.e. flow camera. The realization of such high-sensitive hair sensor requires designs with low thermo-mechanical noise to match the detection-limit of crickets’ hairs. Here we investigate the damping factor in our artificial hair-sensor using different methods, as it is the source of the thermo-mechanical noise in MEMS structures. The theoretical analysis was verified with measurements in different conditions to estimate the damping factor. The results show that the damping factor of the artificial hair sensor as estimated in air is in the range of 10^?12 N m/rad s^?1, which translates into a 93 μm/s threshold airflow velocity.     

Energy and angular momentum densities in a Gödel-type universe in teleparallel geometry

The main scope of this research consists in evaluating the energy-momentum (gravitational field plus matter) and gravitational angular momentum densities in the universe with global rotation, considering the Gödel—Obukhov metric. To do that, we use the Hamiltonian formalism of the Teleparallel equivalent of general relativity (TEGR), which is justified for presenting covariant expressions for the quantities under consideration. We have found that the total energy density calculated by the TEGR method is in agreement with the results reported by other authors in the literature using pseudotensors. The result found for the angular momentum density depends on the rotational parameter, as expected. We also show explicitly the equivalence among the field equations of the TEGR and the Einstein equations (GR), considering a perfect fluid and the Gödel—Obukhov metric.     

On the use of Buchberger criteria in G2V algorithm for calculating Gröbner bases

It has been experimentally demonstrated by Faugère that his F₅ algorithm is the fastest algorithm for calculating Gröbner bases. Computational efficiency of F₅ is due to not only applying linear algebra but also using the new F₅ criterion for revealing useless zero reductions. At the ISSAC 2010 conference, Gao, Guan, and Volny presented G²V, a new version of the F₅ algorithm, which is simpler than the original version of the algorithm. However, the incremental structure of G²V used in the algorithm for applying the F₅ criterion is a serious obstacle from the point of view of application of Buchberger’s second criterion. In this paper, a modification of the G²V algorithm is presented, which makes it possible to use both Buchberger criteria. To experimentally study computational effect of the proposed modification, we implemented the modified algorithm in Maple. Results of comparison of G²V and its modified version on a number of test examples are presented.     

A refutation of Penrose's Gödelian case against artificial intelligence

Having, as it is generally agreed, failed to destroy the computational conception of mind with the Godelian attack he articulated in his The Emperor's New Mind, Penrose has returned, armed with a more elaborate and more fastidious Gödelian case, expressed in Chapters 2 and 3 of his Shadows of the Mind. The core argument in these chapters is enthymematic, and when formalized, a remarkable number of technical glitches come to light. Over and above these defects, the argument, at best, is an instance of either the fallacy of denying the antecedent, the fallacy of petitio principii, or the fallacy of equivocation. More recently, writing in response to his critics in the electronic journal Psyche, Penrose has offered a Gödelian case designed to improve on the version presented in SOTM. But this version is yet again another failure. In falling prey to the errors we uncover, Penrose's new Gödelian case is unmasked as the same confused refrain J. R. Lucas initiated 35 years ago.     

Estimation of Leaf Area Index in dry deciduous forests from IRS‐WiFS in central India

Leaf Area Index (LAI) is an important biophysical parameter necessary to infer vegetation vigour, seasonal vegetation variability and different physiological and biochemical processes of vegetation. Gap fraction analysis has been carried out to estimate plot‐wise LAI. Tropical dry deciduous forests of the study area can be categorized into two prominent phases—growing and senescent phases. Efforts have been made to observe the relationship between ground based LAI values and satellite derived parameters, such as radiance values and also different vegetation indices, namely the Normalized Difference Vegetation Index (NDVI), maximum, minimum, amplitude, sum and radiance NDVI values for both the phases. Multi‐temporal IRS 1C WiFS data have been used. WiFS provides information in two bands: red (0.62–0.68 µm) and near‐infrared (0.77–0.86 µm). All the images from the representative months have been corrected radiometrically and geometrically. NDVI values have been derived for all the representative months. Among various parameters maximum NDVI values showed better relationships with LAI for both the phases. For the growing phase R ² (coefficient of determination) was 0.79, whereas for the senescent phase it was 0.48. These empirical relationships have been used to estimate LAI at a regional level. The LAI estimate for growing and senescent phases ranged from <1 to 4.25.     

Estimation of chlorophyll‐a concentration in Lake Tai,China using in situ hyperspectral data

Reflectance spectra of water in Lake Tai of East China were measured at 28 monitoring stations with an ASD FieldSpec spectroradiometer at an interval of 1.58 nm over five days in each month from June to August of 2004. Water samples collected at these stations were analyzed in the laboratory to determine chlorophyll‐a (chl‐a) concentration. Twenty‐eight spectral reflectance curves were standardized and correlated with chl‐a concentration. Examination of these curves reveals a peak reflectance at 719 nm. Chl‐a concentration level in the Lake was most closely correlated with the reflectance near 700 nm. If regressed against the reflectance at the wavelength of 667 nm (R ₆₆₇), chl‐a concentration was not accurately estimated at R ² = 0.494. Accuracy of estimation was improved to R ² = 0.817 using the maximum reflectance. A higher accuracy of 0.837 was achieved using the peak reflectance at 719 nm (R ₇₁₉) because it does not drift with the level of chl‐a concentration. The highest accuracy of estimation was achieved at R ² = 0.868 using R ₇₁₉/R ₆₆₇.     

The mysterious optimality of Naive Bayes: Estimation of the probability in the system of “classifiers”

Bayes Classifiers are widely used currently for recognition, identification and knowledge discovery. The fields of application are, for example, image processing, medicine, chemistry (QSAR). However, by mysterious way the Naive Bayes Classifier usually gives a very nice and good presentation of recognition. More complex models of Bayes Classifier cannot improve it considerably. We demonstrate here a very nice and simple proof of the Naive Bayes Classifier optimality that can explain this interesting fact. The derivation in the current paper is based on a paper of the author written in 2002.     

Complexity-Theoretic Hierarchies Induced by Fragments of Gödel’s T

We introduce two hierarchies of unknown ordinal height. The hierarchies are induced by natural fragments of a calculus based on finite types and Gödel’s T, and all the classes in the hierarchies are uniformly defined without referring to explicit bounds. Deterministic complexity classes like logspace, p, pspace, linspace and exp are captured by the hierarchies. Typical subrecursive classes are also captured, e.g. the small relational Grzegorczyk classes ? _* ⁰ , ? _* ¹ and ? _* ² .     

Derivation of a parsing algorithm in martin-löf's theory of types

Type Theory is a mathematical language with computation rules developed by Per Martin-Löf. Type Theory was initially developed as a formalization of constructive mathematics but Martin-Löf has pointed out that it can also be viewed as a formal system for the development of provably correct programs. Here, a parser for a simple expression language is specified and a program derived from the proof of correctness of its specification using the formalism of Type Theory. The proof is compared with a proof of the same problem formalized in the Edinburgh LCF system.     

Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems

Problems with uniqueness and high parametric sensitivity of the solution of equations of motion, encountered in the static friction regime, are addressed. Friction in joints of a multibody system with closed-loop kinematic chains is discussed. Three different models of friction are studied: the discontinuous Coulomb model with stiction regime represented in terms of additional constraints; the approximate Coulomb model, smoothed in the vicinity of zero relative velocity; and the LuGre model with presliding displacements represented in terms of auxiliary state variables. Firstly, a rigid body model is investigated. It is shown that in the case of constraint addition approach, problems with uniqueness of solution emerge in the static friction regime. In the case of continuous models of friction, the solution in the stiction regime and its vicinity is highly sensitive to some hardly measurable or arbitrarily chosen parameters of the model of friction. Origins of nonuniqueness and high sensitivity are investigated, and the questionable credibility of the stiction regime simulation results is discussed. Secondly, a simplified model of body and joint elasticity is introduced to investigate the impact of flexibility on the mechanism frictional behavior. It is shown that taking the flexibility into consideration may eliminate the uniqueness and sensitivity problems. Moreover, the quantities that represent flexibility may be regarded as the key factors influencing the results of stiction regime simulation. Five examples are provided to illustrate the presented considerations.     

Efficiency Research of Planted Rice Area Estimation From NOAA一AVHRR Data in Taihu Domain

运用NOAA-AVHRR资料估算水稻种植面积，是遥感应用领域中一个新的研究方向，结合国家“八五”攻关项目“太湖地区遥感话产”的要求，在太湖地区进行了初步的尝试:(1)根据估产精度要求和NOAA一AVHRR资料校正精度，探讨了运用NOAA一AVHRR资料估产所需的最小区域范围。(2)针对太湖地区的具休地理环境设计了提取水稻种植曲积的技术方案，并在试验区取得了初步成果。     

On the estimation of stochastic sensitivity for non-linear dynamical systems in state estimation problems†

This paper consists of two main parts. Recognizing the existence of identification errors due to variations of system parameters, the first part is devoted to the verification of the existence of a unique continuous solution of a non-linear vector stochastic differential equation with a random parameter and to the establishment of the stochastic sensitivity equation. Both the a and β-stochastic sensitivity equations are established through the precise definition of stochastic sensitivity.

The remainder of this paper deals with evaluation of quantitative aspects of the sensitivity in the state estimation by using the stochastic sensitivity equation.