estimation of amplitude and phase parameters of multicomponent signals this paper considers the problem of estimating signals consisting of one or more components of the form a t e sup j spl phi t where the amplitude and phase functions are represented by a linear parametric model the cramer rao bound crb on the accuracy of estimating the phase and amplitude parameters is derived by analyzing the crb for the single component case if is shown that the estimation of the amplitude and the phase are decoupled numerical evaluation of the crb provides further insight into the dependence of estimation accuracy on signal to noise ratio snr and the frequency separation of the signal components a maximum likelihood algorithm for estimating the phase and amplitude parameters is also presented its performance is illustrated by monte carlo simulations and its statistical efficiency is verified

a new kernel based approach for linear system identification this paper describes a new kernel based approach for linear system identification of stable systems we model the impulse response as the realization of a gaussian process whose statistics differently from previously adopted priors include information not only on smoothness but also on bibo stability the associated autocovariance defines what we call a stable spline kernel the corresponding minimum variance estimate belongs to a reproducing kernel hilbert space which is spectrally characterized compared to parametric identification techniques the impulse response of the system is searched for within an infinite dimensional space dense in the space of continuous functions overparametrization is avoided by tuning few hyperparameters via marginal likelihood maximization the proposed approach may prove particularly useful in the context of robust identification in order to obtain reduced order models by exploiting a two step procedure that projects the nonparametric estimate onto the space of nominal models the continuous time derivation immediately extends to the discrete time case on several continuous and discrete time benchmarks taken from the literature the proposed approach compares very favorably with the existing parametric and nonparametric techniques

analysis of polynomial phase signals by the integrated generalized ambiguity function the aim of this work is the performance analysis of a method for the detection and parameter estimation of mono or multicomponent polynomial phase signals pps embedded in white gaussian noise and based on a generalized ambiguity function the proposed method is shown to be asymptotically efficient for second order pps and nearly asymptotically efficient for third order ppss the method presents some advantages with respect to similar techniques like the polynomial phase transform for example in terms of i a closer approach to the cramer rao lower bounds ii a lower snr threshold iii a better capability of discriminating multicomponent signals

parameter estimation of chirp signals the problem of the parameter estimation of chirp signals is addressed several closely related estimators are proposed whose main characteristics are simplicity accuracy and ease of online or offline implementation for moderately high signal to noise ratios they are unbiased and attain the cramer rao bound monte carlo simulations verify the expected performance of the estimators it should be easy to extend this approach to signals having polynomials of any degree in the exponent all the derivations will be done under the assumption that the signal to noise ratio is sufficiently high

estimating parameters of multiple wideband polynomial phase sources in sensor arrays we consider the problem of estimating the parameters of multiple wideband polynomial phase signal pps sources in sensor arrays a new maximum likelihood ml direction of arrival doa estimator is introduced and the exact cramer rao bound crb is derived for the general case of multiple constant amplitude polynomial phase sources since the proposed exact ml estimator is computationally intensive an approximate solution is proposed originating from the analysis of the log likelihood ll function in the single chirp signal case as a result a new form of spatio temporal matched filter referred to as the chirp beamformer is derived which is applicable to well separated sources that have distinct time frequency or and spatial signatures this beamforming approach requires solving a three dimensional 3 d optimization problem and therefore enjoys essentially simpler implementation than that entailed by the exact ml simulation results are presented illustrating the performance of the estimators and validating our theoretical crb analysis

product high order ambiguity function for multicomponent polynomial phase signal modeling parameter estimation and performance analysis issues are studied for multicomponent polynomial phase signals ppss embedded in white gaussian noise identifiability issues arising with existing approaches are described first when dealing with multicomponent pps having the same highest order phase coefficients this situation is encountered in applications such as synthetic aperture radar imaging or propagation of polynomial phase signals through channels affected by multipath and is thus worthy of a careful analysis a new approach is proposed based on a transformation called product high order ambiguity function phaf the use of the phaf offers a number of advantages with respect to the high order ambiguity function haf more specifically it removes the identifiability problem and improves noise rejection capabilities performance analysis is carried out using the perturbation method and verified by simulation results

matchable observable linear models and direct filter tuning an approach to multivariable identification identification of linear time invariant multivariable systems can best be understood as comprising three separate problems selection of system model structure filter design and parameter estimation itself approaching the first using matchable observable models originally developed in the adaptive control literature and the second via direct or derivative free optimization effective least squares algorithms can be used for parameter estimation the accuracy robustness and moderate computational demands of the methods proposed are demonstrated via simulations with randomly generated models and applied to identification using real process data the results obtained are comparable or superior to the best results obtained using standard implementations of the algorithms described in the literature

robust em kernel based methods for linear system identification recent developments in system identification have brought attention to regularized kernel based methods this type of approach has been proven to compare favorably with classic parametric methods however current formulations are not robust with respect to outliers in this paper we introduce a novel method to robustify kernel based system identification methods to this end we model the output measurement noise using random variables with heavy tailed probability density functions pdfs focusing on the laplacian and the student s t distributions exploiting the representation of these pdfs as scale mixtures of gaussians we cast our system identification problem into a gaussian process regression framework which requires estimating a number of hyperparameters of the data size order to overcome this difficulty we design a new maximum a posteriori map estimator of the hyperparameters and solve the related optimization problem with a novel iterative scheme based on the expectation maximization em method in the presence of outliers tests on simulated data and on a real system show a substantial performance improvement compared to currently used kernel based methods for linear system identification

fast algorithms for polynomial time frequency transforms of real valued sequences this paper presents fast algorithms for computing the polynomial time frequency transform that deals with a real valued sequence of length apb where a b and p are positive integers in particular it shows that the polynomial time frequency transform has a conjugate symmetric property similar to that of the discrete fourier transform if the input sequence is real valued the computational complexities needed by these proposed algorithms are analyzed in terms of the numbers of real additions and real multiplications when a 3 4 and 8 comparisons show that the computational complexities required by the proposed algorithms are less than 60 of those needed by the fast algorithms for complex valued sequences

parameter estimation for locally linear fm signals using a time frequency hough transform an estimator for the phase parameters of mono and multicomponent fm signals with both good numerical properties and statistical performance is proposed the proposed approach is based on the hough transform of the pseudo wigner ville time frequency distribution pwvd it is shown that the numerical properties of the estimator can be improved by varying the pwvd window length the effect of the window time extent on the statistical performance of the estimator is delineated experimental data is used for validation of the statistical properties

prediction error identification of linear systems a nonparametric gaussian regression approach a novel bayesian paradigm for the identification of output error models has recently been proposed in which in place of postulating finite dimensional models of the system transfer function the system impulse response is searched for within an infinite dimensional space in this paper such a nonparametric approach is applied to the design of optimal predictors and discrete time models based on prediction error minimization by interpreting the predictor impulse responses as realizations of gaussian processes the proposed scheme describes the predictor impulse responses as the convolution of an infinite dimensional response with a low dimensional parametric response that captures possible high frequency dynamics overparameterization is avoided because the model involves only a few hyperparameters that are tuned via marginal likelihood maximization numerical experiments with data generated by armax and infinite dimensional models show the definite advantages of the new approach over standard parametric prediction error techniques and subspace methods both in terms of predictive capability on new data and accuracy in reconstruction of system impulse responses

the quest for the right kernel in bayesian impulse response identification the use of obfs kernel based regularization approaches for impulse response estimation of linear time invariant lti systems have received a lot of attention recently the reason is that regularized least squares estimators may achieve a favorable bias variance trade off compared with classical prediction error minimization pem methods to fully exploit this property the kernel function needs to capture relevant aspects of the data generating system at hand hence it is important to design automatic procedures for kernel design based on data or prior knowledge the kernel models so far introduced focus on encoding smoothness and bibo stability of the expected impulse response while other properties like oscillatory behavior or the presence of fast and slow poles have not been successfully implemented in kernel design inspired by the representation theory of dynamical systems we show how to build stable kernels that are able to capture particular aspects of system dynamics via the use of orthonormal basis functions obfs in particular desired dynamic properties can be easily encoded via the generating poles of obfs such poles are seen as hyperparameters which are tuned via marginal likelihood optimization special cases of our kernel construction include laguerre kautz and generalized obfs gobfs based kernel structures monte carlo simulations show that the obfs based kernels perform well compared with stable spline tc kernels especially for slow systems with dominant poles close to the unit circle moreover the capability of kautz basis to model resonating systems is also shown

the harmonic analysis of kernel functions abstract kernel based methods have been recently introduced for linear system identification as an alternative to parametric prediction error methods adopting the bayesian perspective the impulse response is modeled as a non stationary gaussian process with zero mean and with a certain kernel i e covariance function choosing the kernel is one of the most challenging and important issues in the present paper we introduce the harmonic analysis of this non stationary process and argue that this is an important tool which helps in designing such kernel furthermore this analysis suggests also an effective way to approximate the kernel which allows to reduce the computational burden of the identification procedure

estimation and classification of polynomial phase signals the measurement of the parameters of complex signals with constant amplitude and polynomial phase measured in additive noise is considered a novel new integral transform that is adapted for signals of this type is introduced this transform is used to derive estimation and classification algorithms that are simple to implement and that exhibit good performance the algorithms are extended to constant amplitude and continuous nonpolynomial phase signals

a computationally efficient technique for estimating the parameters of polynomial phase signals from noisy observations many real world applications are characterized by the presence of polynomial phase signals embedded in noise these applications include radar sonar telemetry communications and power systems in a significant number of these applications it is highly desirable to be able to accurately estimate the polynomial phase signal parameters this correspondence presents a computationally efficient method for estimating any or all of the parameters of polynomial phase signals in white gaussian noise and provides a first order statistical analysis of the technique simulations are also presented to support the theoretical analysis

bayes and empirical bayes semi blind deconvolution using eigenfunctions of a prior covariance we consider the semi blind deconvolution problem i e estimating an unknown input function to a linear dynamical system using a finite set of linearly related measurements where the dynamical system is known up to some system parameters without further assumptions this problem is often ill posed and ill conditioned we overcome this difficulty by modeling the unknown input as a realization of a stochastic process with a covariance that is known up to some finite set of covariance parameters we first present an empirical bayes method where the unknown parameters are estimated by maximizing the marginal likelihood posterior and subsequently the input is reconstructed via a tikhonov estimator with the parameters set to their point estimates next we introduce a bayesian method that recovers the posterior probability distribution and hence the minimum variance estimates for both the unknown parameters and the unknown input function both of these methods use the eigenfunctions of the random process covariance to obtain an efficient representation of the unknown input function and its probability distributions simulated case studies are used to test the two methods and compare their relative performance

estimation of multicomponent polynomial phase signals impinging on a multisensor array using state space modeling this contribution addresses the problem of estimating the parameters of multicomponent polynomial phase signals when impinging on a multisensor array an original approach is proposed based on a state space modelization of the signal and the application of an extended kalman filter for the state estimation the use of a multisensor array allows the exploitation of a spatial information and leads to the consideration of multiple filters with different observation equations computer simulations are used to demonstrate the effectiveness of the proposed algorithm

estimation of frequency in the presence of nonrandom interference this paper develops a method of error analysis for fourier transform based sinusoidal frequency estimation in the presence of nonrandom interferences a general error formula is derived and then specialized to the cases of additive and multiplicative interferences approximate error formulas are derived for the case of additive polynomial phase interference finally an application to error analysis in estimating the parameters of multiple polynomial phase signals is discussed in detail

performance analysis of preconditioners based on broyden method solving nonlinear equations is a problem often needed to be dealt with in the practical engineering application this paper discusses preconditioning methods based on block broyden method it first introduces the block broyden method and preconditioning technique then it presents four different preconditioners for the block broyden method and discusses the implementation process it also analyzes the time complexity of the four algorithms finally it solves the nonlinear systems arising from the bratu problem by the four preconditioning algorithms experimental results show that the preconditioning technique is effective for the block broyden method and that the preconditioner ssor has the fastest solving speed and the best performance among the four preconditioners therefore it can be used in the large scale problems arising from scientific and engineering computing

system identification via sparse multiple kernel based regularization using sequential convex optimization techniques model estimation and structure detection with short data records are two issues that receive increasing interests in system identification in this paper a multiple kernel based regularization method is proposed to handle those issues multiple kernels are conic combinations of fixed kernels suitable for impulse response estimation and equip the kernel based regularization method with three features first multiple kernels can better capture complicated dynamics than single kernels second the estimation of their weights by maximizing the marginal likelihood favors sparse optimal weights which enables this method to tackle various structure detection problems e g the sparse dynamic network identification and the segmentation of linear systems third the marginal likelihood maximization problem is a difference of convex programming problem it is thus possible to find a locally optimal solution efficiently by using a majorization minimization algorithm and an interior point method where the cost of a single interior point iteration grows linearly in the number of fixed kernels monte carlo simulations show that the locally optimal solutions lead to good performance for randomly generated starting points

on kernel design for regularized lti system identification abstract there are two key issues for the kernel based regularization method one is how to design a suitable kernel to embed in the kernel the prior knowledge of the lti system to be identified and the other one is how to tune the kernel such that the resulting regularized impulse response estimator can achieve a good bias variance tradeoff in this paper we focus on the issue of kernel design depending on the type of the prior knowledge we propose two methods to design kernels one is from a machine learning perspective and the other one is from a system theory perspective we also provide analysis results for both methods which not only enhances our understanding for the existing kernels but also directs the design of new kernels

on the estimation of transfer functions regularizations and gaussian processes revisited intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques we revisit the old problem of transfer function estimation from input output measurements we formulate a classical regularization approach focused on finite impulse response fir models and find that regularization is necessary to cope with the high variance problem this basic regularized least squares approach is then a focal point for interpreting other techniques like bayesian inference and gaussian process regression the main issue is how to determine a suitable regularization matrix bayesian prior or kernel several regularization matrices are provided and numerically evaluated on a data bank of test systems and data sets our findings based on the data bank are as follows the classical regularization approach with carefully chosen regularization matrices shows slightly better accuracy and clearly better robustness in estimating the impulse response than the standard approach the prediction error method maximum likelihood pem ml approach if the goal is to estimate a model of given order as well as possible a low order model is often better estimated by the pem ml approach and a higher order model is often better estimated by model reduction on a high order regularized fir model estimated with careful regularization moreover an optimal regularization matrix that minimizes the mean square error matrix is derived and studied the importance of this result lies in that it gives the theoretical upper bound on the accuracy that can be achieved for this classical regularization approach

on estimating the amplitude of harmonic vibration from the doppler spectrum of reflected signals the doppler spectrum of echoes from a sinusoidally vibrating scatterer has discrete spectral lines weighted by bessel functions of the first kind because the signal and spectrum are complicated functions of the vibration amplitude a number of different approaches have been tried in the past to estimate the vibration amplitude given a received signal here a new and simple relationship between the spread or variance of the doppler spectrum and the vibration amplitude is derived a method of estimating the vibration amplitude is proposed based on this relation and a noise compensation procedure is also demonstrated the performance of the estimators is studied through simulations high accuracy is predicted under proper sampling conditions even when the signal to noise ratio is poor slight deviations from single frequency oscillation as would be caused by nonlinear or nonideal medium or source effects are found to have little contribution to the total estimation error

estimating multiple frequency hopping signal parameters via sparse linear regression frequency hopping fh signals have well documented merits for commercial and military applications due to their near far resistance and robustness to jamming estimating fh signal parameters e g hopping instants carriers and amplitudes is an important and challenging task but optimum estimation incurs an unrealistic computational burden the spectrogram has long been the starting non parametric estimator in this context followed by line spectra refinements the problem is that hop timing estimates derived from the spectrogram are coarse and unreliable thus severely limiting performance a novel approach is developed in this paper based on sparse linear regression slr using a dense frequency grid the problem is formulated as one of under determined linear regression with a dual sparsity penalty and its exact solution is obtained using the alternating direction method of multipliers admom the slr based approach is further broadened to encompass polynomial phase hopping pph signals encountered in chirp spread spectrum modulation simulations demonstrate that the developed estimator outperforms spectrogram based alternatives especially with regard to hop timing estimation which is the crux of the problem

ssor and assor preconditioners for block broyden method solving nonlinear equations is a problem that needs to be dealt with in the practical engineering application this paper uses block broyden method for solving large scale nonlinear systems and two preconditioners are applied for solving the underlying linear systems including ssor preconditioner as well as assor method which is based on ssor it discusses their implementation processes and compares the two algorithms from different aspects finally it solves the nonlinear systems arising from the bratu problem experimental results show that the preconditioning technique is effective for the block broyden method and that the preconditioner assor has better performance as a whole therefore it can be used in the large scale problems arising from scientific and engineering computing

the discrete polynomial phase transform the discrete polynomial phase transform dpt is a new tool for analyzing constant amplitude polynomial phase signals the main properties of the dpt are its ability to identify the degree of the phase polynomial and to estimate its coefficients the transform is robust to deviations from the ideal signal model such as slowly varying amplitude additive noise and nonpolynomial phase the authors define the dpt derive its basic properties and use it to develop computationally efficient estimation and detection algorithms a statistical accuracy analysis of the estimated parameters is also presented

moving target parameters estimation in noncoherent mimo radar systems the problem of estimating the parameters of a moving target in multiple input multiple output mimo radar is considered and a new approach for estimating the moving target parameters by making use of the phase information associated with each transmit receive path is introduced it is required for this technique that different receive antennas have the same time reference but no synchronization of initial phases of the receive antennas is needed and therefore the estimation process is noncoherent we model the target motion within a certain processing interval as a polynomial of general order the first three coefficients of such a polynomial correspond to the initial location velocity and acceleration of the target respectively a new maximum likelihood ml technique for estimating the target motion coefficients is developed it is shown that the considered ml problem can be interpreted as the classic overdetermined nonlinear least squares problem the proposed ml estimator requires multidimensional search over the unknown polynomial coefficients the cramer rao bound crb for the proposed parameter estimation problem is derived the performance of the proposed estimator is validated by simulation results and is shown to achieve the crb

regularized lti system identification in the presence of outliers a variational em approach abstract regularized system identification of linear time invariant systems in the presence of outliers is investigated the finite impulse response fir model and the gaussian scale mixture are chosen to be the system model and the noise model respectively two special cases of the noise model are considered the well known student s t distribution and a proposed g confluent distribution both the fir model parameter and the latent variables in the noise model are treated as parameters of our statistical model and moreover the scale of the noise variance is treated as a hyper parameter besides the hyper parameters used to parameterize the priors of the impulse response and the latent variables then a variational expectation maximization algorithm is proposed for inference of the parameters and hyper parameters of the statistical model and the algorithm is guaranteed to converge to a stationary point monte carlo numerical simulations show that when the relative size of outliers is small the proposed approach performs comparably to a state of the art method and when the relative size of outliers and or the occurrence probability of outliers is large the proposed approach outperforms the state of the art method

a scaled gradient projection method for bayesian learning in dynamical systems a crucial task in system identification problems is the selection of the most appropriate model class and is classically addressed resorting to cross validation or using order selection criteria based on asymptotic arguments as recently suggested in the literature this can be addressed in a bayesian framework where model complexity is regulated by a few hyperparameters which can be estimated via marginal likelihood maximization it is thus of primary importance to design effective optimization methods to solve the corresponding optimization problem if the unknown impulse response is modeled as a gaussian process with a suitable kernel the maximization of the marginal likelihood leads to a challenging nonconvex optimization problem which requires a stable and effective solution strategy in this paper we address this problem by means of a scaled gradient projection algorithm in which the scaling matrix and the steplength parameter play a crucial role to provide a meaningful solution in a computatio

nonlinear analysis of cyclically correlated spectral spreading in modulated signals this paper examines the mapping from the cohen class of bilinear time evolutionary spectral estimators tes to a conjoint frequency cycle frequency signal description for modulated acoustic signals the transform mapping provides a cycle spectrum estimation that is used to identify cyclostationarity in modulated acoustic signals that often remains undetected in the one dimensional time history and power spectral density psd the wigner distribution wd tes is derived as the case for which the psd used in stationary analysis of acoustic signals is preserved in the fourier transform mapping to a conjoint frequency frequency correlation signal representation for modulated signals fourier transformation over temporal window centers of a pseudo wd tes of modulated acoustic signals is shown to equate to the time variant cyclic spectrum defined for cyclostationary signals evaluated along the center of a moving average estimate a pseudo wd tes based function mapping procedure for cycle frequency estimatio

quantifying the error in estimated transfer functions with application to model order selection previous results on estimating errors or error bounds on identified transfer functions have relied on prior assumptions about the noise and the unmodeled dynamics this prior information took the form of parameterized bounding functions or parameterized probability density functions in the time or frequency domain with known parameters it is shown that the parameters that quantify this prior information can themselves be estimated from the data using a maximum likelihood technique this significantly reduces the prior information required to estimate transfer function error bounds the authors illustrate the usefulness of the method with a number of simulation examples how the obtained error bounds can be used for intelligent model order selection that takes into account both measurement noise and under modeling is shown another simulation study compares the method to akaike s well known fpe and aic criteria

the achievable accuracy in estimating the instantaneous phase and frequency of a constant amplitude signal the approach is based on modeling the signal phase by a polynomial function of time on a finite interval the phase polynomial is expressed as a linear combination of the legendre basis polynomials first the cramer rao bound crb of the instantaneous phase and frequency of constant amplitude polynomial phase signals is derived then some properties of the crbs are used to estimate the order of magnitude of the bounds the analysis is extended to signals whose phase and frequency are continuous but not polynomial the crb can be achieved asymptotically if the estimation of the phase coefficients is done by maximum likelihood the maximum likelihood estimates are used to show that the achievable accuracy in phase and frequency estimation is determined by the crb of the polynomial coefficients and the deviation of true phase and frequency from the polynomial approximations

statistical analysis of the product high order ambiguity function the high order ambiguity function haf was introduced for the estimation of polynomial phase signals pps embedded in noise since the haf is a nonlinear operator it suffers from noise masking effects and from the appearance of undesired cross terms and possibly spurious harmonics in the presence of multicomponent mc signals the product haf phaf was then proposed as a way to improve the performance of the haf in the presence of noise and to solve the ambiguity problem in this correspondence we derive a statistical analysis of the phaf in the presence of additive white gaussian noise awgn valid for high signal to noise ratio snr and a finite number of data samples the analysis is carried out in detail for single component pps but the multicomponent case is also discussed error propagation phenomena implicit in the recursive structure of the phaf based estimator are explicitly taken into account the analysis is validated by simulation results for both single and multicomponent ppss

maximum entropy properties of discrete time first order stable spline kernel the first order stable spline ss 1 kernel also known as the tuned correlated tc kernel is used extensively in regularized system identification where the impulse response is modeled as a zero mean gaussian process whose covariance function is given by well designed and tuned kernels in this paper we discuss the maximum entropy properties of this kernel in particular we formulate the exact maximum entropy problem solved by the ss 1 kernel without gaussian and uniform sampling assumptions under general sampling assumption we also derive the special structure of the ss 1 kernel e g its tridiagonal inverse and factorization have closed form expression also giving to it a maximum entropy covariance completion interpretation

a new flexible approach to estimate the ia and if of nonstationary signals of long time duration in this paper we propose an original strategy for estimating and reconstructing monocomponent signals having a high nonstationarity and long time duration we locally apply to short time duration intervals the strategy developed in our previous work about nonstationary short time signals this paper describes a nonsequential time segmentation that provides segments whose lengths are suitable for modeling both the instantaneous amplitude and frequency locally with low order polynomials parameter estimation is done independently for each segment by maximizing the likelihood function by means of the simulated annealing technique the signal is then reconstructed by merging the estimated segments the strategy proposed is sufficiently flexible for estimating a large variety of nonstationarity and specifically applicable to high order polynomial phase signals the estimation of a high order model is not necessary the error propagation phenomenon occurring with the known approach the higher ambiguity function haf based method is avoided the proposed strategy is evaluated using monte carlo noise simulations and compared with the cramer rao bounds crbs the signal of a songbird is used as a real example of its applicability

inexact block jacobi broyden methods for solving nonlinear systems of equations we describe a parallelizable jacobi type block broyden algorithm for solving nonlinear systems of equations we study the conditions under which the algorithm is locally convergent basically the jacobian matrix in a newton algorithm is replaced by a block broyden like matrix which can be easily calculated by a recurrence relation a family of nonlinear solvers could be generated combining it with some iterative or direct linear solvers different initializations for the block broyden matrix are proposed as well as several partitioning schemes producing an effective block partitioning of the jacobian matrix coupled with the restarted version of the linear gmres m algorithm the method parallelizes very well and gives good cpu time savings which are shown by several numerical tests

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

estimating the frequency of a noisy sinusoid by linear regression corresp the estimation of the parameters of a sinusoid from observations of signal samples corrupted by additive noise is investigated at high signal to noise ratios the additive noise is viewed as an equivalent phase noise suggesting frequency and phase estimation by linear regression on the signal phase the variances of the regression estimates are shown to achieve the cramer rao bounds a formula for the variance of the regression frequency estimator is derived in terms of the noise power spectrum a simple formula for the variance with 1 f 2 phase noise is presented

analysis of multicomponent lfm signals by a combined wigner hough transform the aim of the paper is the performance evaluation of a method for the analysis of mono or multicomponent linear frequency modulation lfm signals based on the hough transform of the wigner ville distribution of the signals a closed form expression is found for the signal to noise ratio and the parameter estimation accuracy the overall method as any nonlinear method exhibits a threshold effect nevertheless it is shown to be asymptotically efficient and offers a good rejection capability of the cross terms

maximum entropy kernels for system identification bayesian nonparametric approaches have been recently introduced in system identification scenario where the impulse response is modeled as the realization of a zero mean gaussian process whose covariance kernel has to be estimated from data in this scheme quality of the estimates crucially depends on the parametrization of the covariance of the gaussian process a family of kernels that have been shown to be particularly effective in the system identification framework is the family of diagonal correlated dc kernels maximum entropy properties of a related family of kernels the tuned correlated tc kernels have been recently pointed out in the literature in this technical note we show that maximum entropy properties indeed extend to the whole family of dc kernels the maximum entropy interpretation can be exploited in conjunction with results on matrix completion problems in the graphical models literature to shed light on the structure of the dc kernel in particular we prove that the dc kernel admits a closed form factorization inverse and determinant these results can be exploited both to improve the numerical stability and to reduce the computational complexity associated with the computation of the dc estimator

on polynomial phase signals with time varying amplitudes we address the parameter estimation problem for a class of nonstationary signals modeled as polynomial phase signals with time varying amplitudes exponentially damped polynomial phase signals are treated as a special case and are analyzed in detail high order instantaneous moments provide the basic analytical tool but links are shown to exist with either the usually employed fft based technique or the high resolution kumaresan tufts 1982 music and matrix pencil methods asymptotic properties of the relevant estimators are established cramer rao lower bounds on the amplitude and phase parameter estimates are derived and computer simulations are carried out to evaluate the performance of various schemes we focus on parametric modeling of am fm signals mainly because parametric techniques offer parsimony and allow for theoretically unlimited resolution

on the performance of cyclic moments based parameter estimators of amplitude modulated polynomial phase signals parameter estimation of amplitude modulated polynomial phase signals embedded in additive white gaussian noise is considered the amplitude modulation is modeled as the sum of a real valued deterministic function and a zero mean correlated stationary random process it is shown that cyclic moments based estimators previously proposed for parameter estimation of polynomial phase signals modulated by stationary random processes can be adapted to the more general signal model considered here the covariance matrices of the cyclic moments based amplitude and phase parameter estimators are derived for large sample lengths using this result it is shown how the lags can be chosen to minimize the large sample variances of the cyclic moments based phase parameter estimators comparisons with the cramer rao bounds are performed under the assumption of a gaussian modulating process the theoretical derivations are confirmed by simulation results

multicomponent polynomial phase signal analysis using a tracking algorithm we describe an efficient technique analyzing signals that comprise a number of polynomial phase components the technique is based on a previously proposed multiple frequency tracker which is an algorithm for recursive estimation of parameters of multiple sine waves in noise it has a relatively low snr threshold and moderate computational complexity

a regularized snpom for stable parameter estimation of rbf ar x model recently the radial basis function rbf network style coefficients autoregressive with exogenous inputs rbf ar x model identified by the structured nonlinear parameter optimization method snpom has attracted considerable interest because of its significant performance in nonlinear system modeling however this promising technique may occasionally confront the problem that the parameters are divergent in the optimization process which may be a potential issue ignored by most researchers in this paper a regularized snpom together with the regularization parameter detection technique is presented to estimate the parameters of rbf ar x models this approach first separates the parameters of an rbf ar x model into a linear parameters set and a nonlinear parameters set and then combines a gradient based nonlinear optimization algorithm for estimating the nonlinear parameters and the regularized least squares method for estimating the linear parameters several examples demonstrate that the proposed approach is effective to cope with the potential unstable problem in the parameters search process and may also yield better or similar multistep forecasting accuracy and better robustness than the previous method

implementation of algorithms for tuning parameters in regularized least squares problems in system identification there has been recently a trend to study linear system identification with high order finite impulse response fir models using the regularized least squares approach one key of this approach is to solve the hyper parameter estimation problem that is usually nonconvex our goal here is to investigate implementation of algorithms for solving the hyper parameter estimation problem that can deal with both large data sets and possibly ill conditioned computations in particular a qr factorization based matrix inversion free algorithm is proposed to evaluate the cost function in an efficient and accurate way it is also shown that the gradient and hessian of the cost function can be computed based on the same qr factorization finally the proposed algorithm and ideas are verified by monte carlo simulations on a large data bank of test systems and data sets

inexact overlapped block broyden methods for solving nonlinear equations in this paper a parallelizable overlapped block broyden method is presented for solving large systems of nonlinear equations the basic idea is to perform the block broyden iteration described in siam j sci comput 18 1997 1367 for the overlapped blocks and then assemble the overlapping solutions in a weighted average manner at each iteration a family of nonlinear overlapped solvers could be generated combining it with some iterative or direct linear solvers the conditions under which the algorithm is locally convergent are studied and many useful techniques regarding the implementation are also considered

model selection of random amplitude polynomial phase signals procedures for selecting the amplitude and phase models of a polynomial phase signal pps modulated by a nonstationary random process are presented the model selection is performed by using nonlinear least squares type phase and amplitude parameter estimators with sequential generalizations of the bonferroni test simulation results are used to analyze the performance of the procedures an application to modeling of real passive acoustic data is presented

hybrid fm polynomial phase signal modeling parameter estimation and cramer rao bounds parameter estimation for a class of nonstationary signal models is addressed the class contains combination of a polynomial phase signal pps and a frequency modulated fm component of the sinusoidal or hyperbolic type such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components a novel approach is proposed that allows us to decouple estimation of the fm parameters from those of the pps relying on properties of the multilag high order ambiguity function ml haf the accuracy achievable by any unbiased estimator of the hybrid fm pps parameters is investigated by means of the cramer rao lower bounds crlbs both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on monte carlo simulations

asymptotic statistical analysis of the high order ambiguity function for parameter estimation of polynomial phase signals the high order ambiguity function haf is a nonlinear operator designed to detect estimate and classify complex signals whose phase is a polynomial function of time the haf algorithm introduced by peleg and porat 1991 estimates the phase parameters of polynomial phase signals measured in noise the purpose of this correspondence is to analyze the asymptotic accuracy of the haf algorithm in the case of additive white gaussian noise it is shown that the asymptotic variances of the estimates are close to the cramer rao bound crb for high snr however the ratio of the asymptotic variance and the crb has a polynomial growth in the noise variance

estimating random amplitude polynomial phase signals a cyclostationary approach modeling of a class of nonstationary signals with randomly time varying amplitude and parametric polynomial phase is addressed a novel approach is proposed for the estimation of the time varying phase by exploiting the higher order cyclostationarity of these signals the method does not require nonlinear search is easy to implement and yields consistent estimates for the parameters the resulting algorithms are theoretically tolerant to a large class of noises including additive stationary non gaussian noise and any gaussian noise simulation examples supporting the theory are provided

improving polynomial phase parameter estimation by using nonuniformly spaced signal sample methods this paper investigates the computationally efficient parameter estimation of polynomial phase signals embedded in noise many authors have previously proposed multilinear analysis methods which operate on uniformly spaced samples of the signal such methods include the higher order ambiguity functions hafs the polynomial wigner ville distributions pwvds and the higher order phase hp functions this paper investigates the use of multilinear methods which operate on nonuniformly spaced signal samples it is seen that the relaxation of the requirement to use uniformly spaced samples in the analysis can lead to significant performance improvements a theoretical analysis and simulations are presented in support of these claims

a hybrid cpf haf estimation of polynomial phase signals detailed statistical analysis in this paper we consider parameter estimation of high order polynomial phase signals ppss we propose an approach that combines the cubic phase function cpf and the high order ambiguity function haf and is referred to as the hybrid cpf haf method in the proposed method the phase differentiation is first applied on the observed pps to produce a cubic phase signal whose parameters are in turn estimated by the cpf the performance analysis carried out in the paper considers up to the tenth order ppss and is supported by numerical examples revealing that the proposed approach outperforms the haf in terms of the accuracy and signal to noise ratio threshold extensions to multicomponent and multidimensional ppss are also considered all supported by numerical examples specifically when multicomponent ppss are considered the product version of the cpf haf outperforms the product haf phaf that fails to estimate parameters of components whose pps order exceeds three