a globally convergent estimator for n frequencies in this paper we propose a solution to the well known problem of ensuring a simultaneous globally convergent online estimation of the state and the frequencies of a sinusoidal signal composed of n sinusoidal terms we present an estimator which guarantees global boundedness and convergence of both the state estimation and the frequency estimation for all initial conditions and frequency values

several inequalities for the pan integral several inequalities for the pan integral are investigated it is shown that the chebyshev inequality holds for an arbitrary subadditive measure if and only if the integrands f g are comonotone thus we provide a new characterization for nonnegative comonotone functions it is also shown that the holder and minkowski inequalities for the pan integral hold if the monotone measure is subadditive since the pan integral coincides with the concave integral when is subadditive our results can also be applied to the concave integral

on the equality of integrals considering a finite space x several necessary conditions and one rather general sufficient condition describing when the choquet integral coincides with the pan integral with respect to the standard arithmetic operations are shown these conditions are characterized by using the minimal atoms of monotone measure under the introduced constraints the calculation of these coinciding two integrals is also given

a sufficient condition of equivalence of the choquet and the pan integral abstract in this note we continue to investigate the relationship between the choquet integral and the pan integral on infinite space we will show that the m property of monotone measures is a sufficient condition that the choquet integral coincides with the pan integral in this discussion the spaces are not restricted to be finite thus the previous results obtained in finite space are further generalized and developed a characteristic of the m property of monotone measures is also presented

on the comonotonic property for sugeno integral the so called comonotonic property for sugeno integral is introduced and investigated where 0 2 0 is a binary operation under the assumption that lim b a email protected a and lim a a email protected b we prove that sugeno integral possesses comonotonic property if and only if equals to one of the four operators minimum maximum pf the first projection and pl the last projection we also discuss comonotonic property when this assumption does not hold

on the equivalence of the choquet integral and the pan integrals from above abstract a monotone measure is said to have dual m property if for any a b there exists c with a c b such that c a and b c b c by using this concept we study the relationship of the choquet integral and the pan integral from above we prove that the choquet integral coincides with the pan integral from above if has dual m property when the underlying space is finite we prove that the dual m property is also necessary for the coincidence of these two integrals thus we provide a necessary and sufficient condition for the equivalence of the choquet integral and the pan integral from above on a finite space

a note on the coincidence of decomposition integrals and superdecomposition integrals abstract it is known that the decomposition integral i h and the superdecomposition integral i h related to the system h of all finite chains from a where a is a algebra of the subsets of a nonvoid set x coincide with each other for each monotone measure and for each nonnegative measurable function and they are equal to the choquet integral in this note we show that the converse is also true that is for a complete system h of finite set systems from a if i h i h holds for each monotone measure and for each nonnegative measurable function then the system h and the system of all finite chains from a are equivalent in some sense and the integrals involved are the choquet integral

on the equivalence of the choquet pan and concave integrals on finite spaces abstract in this paper we introduce the concept of maximal cluster of minimal atoms on monotone measure spaces and by means of this new concept we continue to investigate the relation between the choquet integral and the pan integral on finite spaces it is proved that the m property of a monotone measure is a sufficient condition that the choquet integral coincides with the pan integral based on the usual addition and multiplication thus combining our recent results we provide a necessary and sufficient condition that the choquet integral is equivalent to the pan integral on finite spaces meanwhile we also use the characteristics of minimal atoms of monotone measure to present another necessary and sufficient condition that these two kinds of integrals are equivalent on finite spaces the relationships among the choquet integral the pan integral and the concave integral are summarized

on the performance of the weighted linear predictor frequency estimator a statistical analysis of kay s 1989 weighted linear predictor frequency estimator was carried out using a different analysis technique to that employed in that paper the asymptotic variance of the weighted linear predictor frequency estimator is derived

general chebyshev type inequalities for sugeno integrals chebyshev type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the real line and product operation

superdecomposition integrals this study introduces and discusses a new class of integrals based on superdecompositions of integrated functions including an analysis of their relationship with decomposition integrals which were introduced recently by even and lehrer the proposed superdecomposition integrals have several properties that are similar or dual with respect to decomposition integrals but they also have some significant differences the convex integral is obtained by considering all possible superdecompositions with no constraints on the applied sets which can be treated as the greatest convex homogeneous functional that is bounded from above by the measure we consider the relationship with the universal integral of klement et al is also discussed finally some possible generalizations are outlined

amplitude and frequency estimator of a sinusoid a dynamic estimator with global convergence property is proposed to simultaneously reconstruct the unknown values of the amplitude frequency and offset of a sinusoidal signal which is measured several versions of the estimator along with illustrative simulations are presented

statistical analysis of pisarenko s method for sinusoidal frequency estimation statistical analysis is performed for pisarenko s method of sinusoidal frequency estimation by using the periodogram technique under the assumption that the data consist of several sinusoids plus white noise we give an asymptotic expression of the error variance of the sinusoidal frequency estimator also a modified method is proposed this is computationally efficient but the statistical property is not improved we also present simulation results and compare them to the theoretical ones lastly we point out that the pisarenko s method can be implemented as an on line bias compensated least squares algorithm thus avoiding the eigenvalue and eigenvector calculations

multitype spatial point patterns with hierarchical interactions multitype spatial point patterns with hierarchical interactions are considered here hierarchical interaction means directionality points on a higher level of hierarchy affect the locations of points on the lower levels but not vice versa such relations are common for example in ecological communities interacting point patterns are often modeled by gibbs processes with pairwise interactions however these models are inherently symmetric and the hierarchy can be acknowledged only when interpreting the results we suggest the following in allowing the inclusion of the hierarchical structure in the model instead of regarding the pattern as a realization of a stationary multivariate point process we build the pattern one type at a time according to the order of the hierarchy by using nonstationary univariate processes as interactions connected to points x on a certain level are considered the effect of the higher levels is interpreted as heterogeneity of the pattern x and the points on the lower levels are neglected because of the hierarchical structure

a universal integral as common frame for choquet and sugeno integral the choquet and the sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required however their applicability is restricted because of the special operations used in the construction of these integrals therefore we provide a concept of integrals generalizing both the choquet and the sugeno case for functions with values in the nonnegative real numbers universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures for a fixed pseudo multiplication on the nonnegative real numbers the smallest and the greatest universal integrals are given finally another construction method for obtaining universal integrals is introduced and the restriction to the unit interval i e to fuzzy integrals is considered

monotone set functions defined by choquet integral abstract given a nonnegative monotone set function and a nonnegative measurable function on a measurable space the choquet integral determines a new nonnegative monotone set function that is absolutely continuous with respect to the original one in a generalized sense for monotone set functions this new set function preserves almost all desirable structural characteristics of the original monotone set function such as continuity subadditivity superadditivity null additivity converse null additivity autocontinuity converse autocontinuity uniform autocontinuity uniform converse autocontinuity and fuzzy multiplicativity such a construction is a useful method to define sound fuzzy measures in various applications

an exact direct method of sinusoidal parameter estimation derived from finite fourier integral of differential equation in this paper we propose a novel method for estimating the parameters frequency amplitude and phase of real sinusoids to derive the estimator we start from the characteristic differential equation of a sinusoid to remove differentials and obtain an algebraic relation for frequency we introduce finite period weighted integrals of the differential equation which become equivalent to the differential equation when a sufficient number of weight functions are applied as weight functions we show that fourier kernels have excellent properties terms related to integral boundaries are readily eliminated observations are provided by fourier coefficients and the relation becomes independently accurate for multiple sinusoids if they are sufficiently spaced we solve the obtained equations in two ways one is for approaching to the cramer rao lower bound crlb and the other is for enhancing the interference rejection capability also methods are proposed to calculate the weighted integrals from sampled signals with an improved accuracy proposed algorithms are examined under noise and sinusoidal interference error variances are compared with the crlb and other fast fourier transform fft based methods

two families of fuzzy integrals abstract in this paper we present two definitions of fuzzy integrals arising from the t seminorm and the t semiconorm concepts we show that sugeno s fuzzy integral is a particular case of them and we study their principal properties finally we suggest some applications of these results

relationship between the concave integrals and the pan integrals on finite spaces a r t i c l e i n f o a b s t r a c t this study discusses the relationship between the concave integrals and the pan integrals on finite spaces the minimal atom of a monotone measure is introduced and some properties are investigated by means of two important structure characteristics related to minimal atoms minimal atoms disjointness property and subadditivity for minimal atoms a necessary and sufficient condition is given that the concave integral coincides with the pan integral with respect to the standard arithmetic operations a nd on finite spaces following this result we have shown that these two integrals coincide if the underlying monotone measure is sub additive

choquet like integrals abstract integrals based on a pseudo addition and a pseudo multiplication with properties similar to those of the choquet and the sugeno integral respectively are introduced the structure of convenient pseudo arithmetical operations leading to a choquet like integral is studied

an efficient two dimensional frequency estimator the problem of two dimensional frequency estimation of a sinusoid embedded in complex white gaussian noise is addressed a frequency estimator and its statistical performance are derived the estimator is demonstrated to be an efficient estimator it achieves the cramer rao bound for high signal to noise ratios the results of a computer simulator which compares the variance with that of the maximum likelihood estimator and the theoretical two dimensional cramer rao bound are presented

the concave integral over large spaces this paper investigates the concave integral for capacities defined over large spaces we characterize when the integral with respect to capacity v can be represented as the infimum over all integrals with respect to additive measures that are greater than or equal to v we introduce the notion of loose extendability and study its relation to the concave integral a non additive version for the levi theorem and the fatou lemma are proven finally we provide several convergence theorems for capacities with large cores

approximate maximum likelihood frequency estimation the high resolution frequency estimators most commonly used such as music esprit and yule walker determine estimates of the sinusoidal frequencies from the sample covariances of noise corrupted data in this paper a frequency estimation method termed approximate maximum likelihood aml is derived from the approximate likelihood function of sample covariances the statistical performance of aml is studied both analytically and numerically and compared with the cramer rao bound as well as the statistical performance corresponding to the aforementioned methods of frequency estimation aml is shown to provide the minimum asymptotic error variance in the class of all estimators based on a given set of covariances the implementation of the aml frequency estimator is discussed in detail the paper also introduces an aml based procedure for estimating the number of sinusoidal signals in the measured data which is shown to possess high detection performance

relationship between two types of superdecomposition integrals on finite spaces abstract this paper investigates the relationship between two types of superdecomposition integrals namely the convex integral and the pan integral from above on finite spaces to this end we introduce two new concepts related to monotone measures superadditivity with respect to singletons and minimal strictly subadditive set and discuss some of their properties in the case that the monotone measure is superadditive with respect to singletons we show that these two types of integrals are equivalent in other cases by means of the characteristics of minimal strictly subadditive sets we provide a set of necessary and sufficient conditions for which these two types of integrals coincide with each other