In digital transmission and storage systems, sequences must have attributes that comply with the physical characteristics of the channel. These channel constraints can often be satisfied through constrained sequence coding techniques which avoid use of sequences that violate the given channel constraints. In the design of a constrained code, it is usually helpful to consider the PSD of the encoded sequence in order to ensure that PSD requirements are met, and to obtain an indication of bandwidth, response at dc, average power peaks, and other spectral characteristics of interest. In this paper, we introduce an approach for the construction of finite-state sequential machine (FSSM) modeled encoders to satisfy spectral requirements. This approach involves construction of either a Mealy or a Moore FSSM to represent the encoder, and evaluation of the state transition probabilities and codeword values such that the PSD of the designed code meets a predefined spectral shape. Examples in this paper demonstrate the usefulness of this approach.

The modified covariance (MC) method provides a computationally attractive and closed-form solution for frequency estimation of a single real sinusoid. In this paper, the performance measures of the MC estimator, namely, mean and mean square error, are derived in closed-form and confirmed by computer simulations.

Localization of mobile terminals has received considerable attention in wireless communications. In this letter, we present a covariance shaping least squares (CSLS) estimator using time-of-arrival measurements of the signal from the mobile station received at three or more base stations. It is shown that the CSLS estimator yields better performance than the other LS estimators at low signal-to-noise ratio conditions.

This paper discusses the least-squares linear filtering and smoothing (fixed-point and fixed-interval) problems of discrete-time signals from observations, perturbed by additive white noise, which can be randomly delayed by one sampling time. It is assumed that the Bernoulli random variables characterizing delay measurements are correlated in consecutive time instants. The marginal distribution of each of these variables, specified by the probability of a delay in the measurement, as well as their correlation function, are known. Using an innovation approach, the filtering, fixed-point and fixed-interval smoothing recursive algorithms are obtained without requiring the state-space model generating the signal; they use only the covariance functions of the signal and the noise, the delay probabilities and the correlation function of the Bernoulli variables. The algorithms are applied to a particular transmission model with stand-by sensors for the immediate replacement of a failed unit.

This paper discusses the least-squares linear filtering and fixed-lag smoothing problems of discrete-time signals from uncertain observations when the random interruptions in the observation process are modelled by a sequence of not necessarily independent Bernoulli variables. It is assumed that the observations are perturbed by white noise and the autocovariance function of the signal is factorizable. Using an innovation approach we obtain the filtering and fixed-lag smoothing recursive algorithms, which do not require the knowledge of the state-space model generating the signal. Besides the observed values, they use only the matrix functions defining the factorizable autocovariance function of the signal, the noise autocovariance function, the marginal probabilities and the (2,2)-element of the conditional probability matrices of the Bernoulli variables. The algorithms are applied to estimate a scalar signal which may be transmitted through one of two channels.

This paper treats the least-squares linear filtering and smoothing problems of discrete-time signals from uncertain observations when the random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables. Using an innovation approach we obtain the filtering algorithm and a general expression for the smoother which leads to fixed-point, fixed-interval and fixed-lag smoothing recursive algorithms. The proposed algorithms do not require the knowledge of the state-space model generating the signal, but only the covariance information of the signal and the observation noise, as well as the probability that the signal exists in the observed values.

This paper considers the least-squares linear estimation problem of signals from randomly delayed observations when the additive white noise is correlated with the signal. The delay values are treated as unknown variables, modelled by a binary white noise with values zero or one; these values indicate that the measurements arrive in time or they are delayed by one sampling time. A recursive one-stage prediction and filtering algorithm is obtained by an innovation approach and do not use the state-space model of the signal. It is assumed that both, the autocovariance functions of the signal and the crosscovariance function between the signal and the observation noise are expressed in a semi-degenerate kernel form; using this information and the delay probabilities, the estimators are recursively obtained.

This paper presents recursive algorithms for the least mean-squared error linear filtering and fixed-interval smoothing estimators, from uncertain observations for the case of white and white plus coloured observation noises. The estimators are obtained by an innovation approach and do not use the state-space model, but only covariance information about the signal and the observation noises, as well as the probability that the signal exists in the observed values. Therefore the algorithms are applicable not only to signal processes that can be estimated by the conventional formulation using the state-space model but also to those for which a realization of the state-space model is not available. It is assumed that both the signal and the coloured noise autocovariance functions are expressed in a semi-degenerate kernel form. Since the semi-degenerate kernel is suitable for expressing autocovariance functions of non-stationary or stationary signal processes, the proposed estimators provide estimates of general signal processes.

The objective of this study was to explore suitable spatial filters for inverse estimation of cortical potentials from the scalp electroencephalogram. The effect of incorporating noise covariance into inverse procedures was examined by computer simulations. The parametric projection filter, which allows inverse estimation with the presence of information on the noise covariance, was applied to an inhomogeneous three-concentric-sphere model under various noise conditions in order to estimate the cortical potentials from the scalp potentials. The present simulation results suggest that incorporation of information on the noise covariance allows better estimation of cortical potentials, than inverse solutions without knowledge about the noise covariance, when the correlation between the signal and noise is low. The method for determining the optimum regularization parameter, which can be applied for parametric inverse techniques, is also discussed.

Least-squares second-order polynomial filter and fixed-point smoother are derived in systems with uncertain observations, when the variables describing the uncertainty are non-independent. The proposed estimators do not require the knowledge of the state-space model of the signal. The available information is only the moments, up to the fourth one, of the involved processes, the probability that the signal exists in the observations and the (2,2) element of the conditional probability matrices of the sequence describing the uncertainty.

We study the optimal transmission strategy of a multiple-input multiple-output (MIMO) communication system with covariance feedback. We assume that the receiver has perfect channel state information while the transmitter knows only the channel covariance matrix. We consider the common downlink transmission model where the base station is un-obstructed while the mobile station is surrounded by local scatterer. Therefore the channel matrix is modeled with Gaussian complex random entries with independent identically distributed rows and correlated columns. For this transmission scenario the capacity achieving eigenvectors of the transmit covariance matrix are known. The capacity achieving eigenvalues can not be computed easily. We analyze the optimal transmission strategy as a function of the transmit power. A MIMO system using only one eigenvalue performs beamforming. We derive a necessary and sufficient condition for when beamforming achieves capacity. The theoretical results are illustrated by numerical simulations.

This paper proposes new recursive fixed-point smoother and filter using covariance information in linear discrete-time stochastic systems. In this paper, to be able to treat the estimation of the stochastic signal, a performance criterion, extended from the criterion in the H estimation problem, is newly proposed. The criterion is transformed equivalently into a min-max principle in game theory, and an observation equation in a Krein space is obtained as a result. The estimation accuracy of the proposed estimators are compared with the recursive least-squares (RLS) Wiener estimators, the Kalman filter and the fixed-point smoother based on the state-space model.

In recent years, several inverse solutions of magnetoencephalography (MEG) have been proposed. Among them, the multiple signal classification (MUSIC) method utilizes spatio-temporal information obtained from magnetic fields. The conventional MUSIC method is, however, sensitive to Gaussian noise and a sufficiently large signal-to-noise ratio (SNR) is required to estimate the number of sources and to specify the precise locations of electrical neural activities. In this paper, a new algorithm for solving the inverse problem using the fourth order MUSIC (FO-MUSIC) method is proposed. We apply it to the MEG source estimation problem. Numerical simulations demonstrate that the proposed FO-MUSIC algorithm is more robust against Gaussian noise than the conventional MUSIC algorithm.

This paper proposes new recursive fixed-point smoother and filter using covariance information in linear continuous-time stochastic systems. To be able to treat the stochastic signal estimation problem, a performance criterion, extended from the criterion in the H filtering problem by introducing the stochastic expectation, is newly introduced in this paper. The criterion is transformed equivalently into a min-max principle in game theory, and an observation equation in the Krein spaces is obtained as a result. For γ2<, the estimation accuracies of the fixed-point smoother and the filter are superior to the recursive least-squares (RLS) Wiener estimators previously designed in the transient estimation state. Here, γ represents a parameter in the proposed criterion. This paper also presents the fixed-point smoother and the filter using the state-space parameters from the devised estimators using the covariance information.

It is an important problem in signal processing, system realization and system identification to find linear discrete-time systems which are consistent with given covariance parameters. This problem is formulated as a problem of finding discrete-time positive real functions which interpolate given covariance parameters. Various investigations have yielded several significant solutions to the problem, while there remains an important open problem concerning the McMillan degree. In this paper, we use more general input-output characteristics than covariance parameters and consider finding discrete-time positive real matrix functions which interpolate such characteristics. The input-output characteristics are given by the coefficients of the Taylor series at some complex points in the open unit disk. Thus our problem is a generalization of the interpolation problem of covariance parameters. We reduce the problem to a directional interpolation problem with a constraint and develop the solution by a state-space based new approach. The main results consist of the necessary and sufficient condition for the existence of the discrete-time positive real matrix function which interpolates the given characteristics and has a limited McMillan degree, and a parameterization of all such functions. These are a contribution to the open problem and a generalization of the previous result.

We present a minimal lattice realization of MIMO linear discrete-time systems which interpolate the desired Markov and covariance parameters. The minimal lattice realization is derived via a recursive construction algorithm based on the state space description and it parametrizes all the interpolants.

In the usual optical flow detection, the gradient constraint, which expresses the relationship between the gradient of the image intensity and its motion, is combined with the least-squares criterion. This criterion means assuming that only the time derivative of the image intensity contains noise. In this paper, we assume that all image derivatives contain noise and derive a new optical flow detection technique. Since this method requires the knowledge about the covariance matrix of the noise, we also discuss a method for its estimation. Our experiments show that the proposed method can compute optical flow more accurately than the conventional method.

The recursive least-squares filter and fixed-point smoother are designed in linear discrete-time systems. The estimators require the information of the system matrix, the observation vector and the variances of the state and white Gaussian observation noise in the signal generating model. By appropriate choices of the observation vector and the state variables, the state-space model corresponding to the ARMA (autoregressive moving average) model of order (n,m) is introduced. Here,some elements of the system matrix consist of the AR parameters. This paper proposes modified iterative technique to the existing one regarding the estimation of the variance of observation noise based on the estimation methods of ARMA parameters in Refs. [2],[3]. As a result, the system matrix, the ARMA parameters and the variances of the state and observation noise are estimated from the observed value and its sampled autocovariance data of finite number. The input noise variance of the ARMA model is estimated by use of the autocovariance data and the estimates of the AR parameters and one MA parameter.

We prove that the maximum likelihood estimator for estimating 3-D motion from noisy optical flow is not optimal", i.e., there is an unbiased estimator whose covariance matrix is smaller than that of the maximum likelihood estimator when a Gaussian noise distribution is assumed for a sufficiently large number of observed points. Since Gaussian assumption for the noise is given, the maximum likelihood estimator minimizes the mean square error of the observed optical flow. Though the maximum likehood estimator's covariance matrix usually reaches the Cramér-Rao lower bound in many statistical problems when the number of observed points is infinitely large, we show that the maximum likelihood estimator's covariance matrix does not reach the Cramér-Rao lower bound for the estimation of 3-D motion from noisy optical flow under such conditions. We formulate a superior estimator, whose covariance matrix is smaller than that of the maximum likelihood estimator, when the variance of the Gaussian noise is not very small.