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Bayesian filtering is a statistical approach that naturally appears in many signal processing problems. Ranging from Kalman filter to particle filters, there is a plethora of alternatives depending on model assumptions. With the exception of very few tractable cases, one has to resort to suboptimal methods due to the inability to analytically compute the Bayesian recursion in general dynamical systems. This is why it has attracted the attention of many researchers in order to develop efficient algorithms to implement it. We focus our interest into a recently developed algorithm known as the Quadrature Kalman filter (QKF). Under the Gaussian assumption, the QKF can tackle arbitrary nonlinearities by resorting to the Gauss-Hermite quadrature rules. However, its complexity increases exponentially with the state-space dimension. In this paper we study a complexity reduction technique for the QKF based on the partitioning of the state-space, referred to as the Multiple QKF. We prove that partitioning schemes can effectively be used to reduce the curse of dimensionality in the QKF. Simulation results are also provided to show that a nearly-optimal performance can be attained, while drastically reducing the computational complexity with respect to state-of-the-art algorithms that are able to deal with such nonlinear filtering problems. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the problem of direction of arrival (DOA) estimation in the presence of sensor gain-phase errors. Under some mild assumptions, we propose a new DOA estimation method based on the eigendecomposition of a covariance matrix which is constructed by the dot product of the array output vector and its conjugate. By combining the new DOA estimation with the conventional gain-phase error estimation, a method is proposed to simultaneously estimate the DOA and gain-phase errors without joint iteration. Theoretical analysis shows that the proposed method performs independently of phase errors and thus behaves well regardless of phase errors. However, the resolution capability of the proposed method is lower than that of the method in [A. J. Weiss and B. Friedlander, “Eigenstructure methods for direction finding with sensor gain and phase uncertainties,” Circuits Systems Signal Process., vol. 9, no. 3, pp. 271–300, 1990], named as the WF method. In order to improve the resolution capability and maintain phase error independence, a combined strategy is developed using the proposed and WF methods. The advantage of the proposed methods is that they are independent of phase errors, leading to the cancellation of phase error calibration during the operation life of an array. Moreover, the proposed methods avoid the problem of suboptimal convergence which occurs in the WF method. The drawbacks of the proposed methods are their high computational complexity and their requirement for the condition that at least two signals are spatially far from each other, and they are not applicable to a linear array. Simulation results verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this correspondence, we focus on blind estimation of the chip duration of time-hopping signals by introducing a cost function based on time-of-arrival (ToA) folding over multiple observation sets. An optimization algorithm that takes advantage of the highly oscillatory behavior in the nearby of the global minimum is proposed and a performance bound for the chip time estimate is derived. The pertinence of our approach is shown through numerical results, considering alternative methods like periodogram and separable least squares line search. The proposed technique enables a good tradeoff between statistical accuracy and computational complexity. [ABSTRACT FROM AUTHOR]

Consider the problem of estimating the parameters of multiple polynomial phase signals observed by a sensor array. In practice, it is difficult to maintain a precisely calibrated array. The array manifold is then assumed to be unknown, and the estimation is referred to as blind estimation. To date, only an approximated maximum likelihood estimator (AMLE) was suggested for blindly estimating the polynomial coefficients of each signal. However, this estimator requires a multidimensional search over the entire coefficient space. Instead, we propose an estimation approach which is based on two steps. First, the signals are separated using a blind source separation technique, which exploits the constant modulus property of the signals. Then, the coefficients of each polynomial are estimated using a least squares method applied to the unwrapped phase of the estimated signal. This estimator does not involve any search in the coefficient spaces. The computational complexity of the proposed estimator increases linearly with respect to the polynomial order, whereas that of the AMLE increases exponentially. Simulation results show that the proposed estimator achieves the Cramér-Rao lower bound at moderate or high signal to noise ratio. [ABSTRACT FROM PUBLISHER]

This correspondence investigates the Abel bound in order to predict the estimators mean square error (mse) threshold effect. A tractable and computationally efficient form of this bound is derived. This form combines the Chapman-Robbins and the Crameacuter-Rao bounds. This bound is applied to a data-aided carrier frequency estimation problem for which a closed-form expression is provided. An indicator of the signal-to-noise ratio threshold is proposed. A comparison with recent results on the Barankin bound (Chapman-Robbins version) shows the superiority of the Abel-bound version to predict the mse threshold without increasing the computational complexity [ABSTRACT FROM PUBLISHER]

The problem of estimating the frequency and carrier phase of a single sinusoid observed in additive, white, Gaussian noise is addressed. Much of the work in the literature considers maximum likelihood (ML) estimation. However, the ML estimator given by the location of the peak of a periodogram in the frequency domain shown in D.C. Rife and R. R. Boorstyn, ‘Single-tone parameter estimation from discrete-time observations,’ IEEE TRANSACTIONS ON INFORMATION THEORY, vol. IT-20, pp. 591–598, Sep. 1974, has a very high computational complexity. This paper derives the explicit structure of the ML estimator for data processing in the time domain, assuming only reasonably high signal-to-noise ratio (SNR). The result of this approximate ML estimator shows that both the phase and the magnitude of the noisy signal samples are utilized in the estimator, and the phase data alone as assumed in S. A. Tretter, ‘Estimating the frequency of a noisy sinusoid by linear regression,’ IEEE TRANSACTIONS ON INFORMATION THEORY, vol. IT-31, pp. 832–835, Nov. 1985 and S. Kay, ‘A fast and accurate single frequency estimator,’ IEEE TRANSACTIONS ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, vol. 39, pp. 1203-1205, May 1991, is not a sufficient statistic. The sample-by-sample iterative processing nature of the estimator enables us to propose a novel, recursive phase-unwrapping algorithm that allows the estimator to be implemented efficiently. To facilitate the performance analysis, a new, linearized observation model for the instantaneous signal phase that is more accurate than that of S. A. Tretter, ‘Estimating the frequency of a noisy sinusoid by linear regression,’ IEEE TRANSACTIONS ON INFORMATION THEORY, vol. IT-31, pp. 832–835, Nov. 1985 and of S. Kay, "A fast and accurate single frequency estimator," vol. 39, pp. 1203–1205, May 1991, is proposed. This new model explains physically why the phase data are weighted by the magnitude information in the ML estimator. Moreover, by incorporating a priori knowledge via the a priori probability density function of the unknown frequency and the carrier phase, the explicit structure of the approximate maximum a posteriori probability (MAP) estimator is derived, and the Bayesian Cramer-Rao lower bound (BCRLB) on the mean-square error (mse) is obtained. Our analysis shows that the mse performance of the MAP estimator can approach the BCRLB very closely. [ABSTRACT FROM AUTHOR]

In this paper, the computational complexity of the marginalized particle filter is analyzed and a general method to perform this analysis is given. The key is the introduction of the equivalent flop measure. In an extensive Monte Carlo simulation, different computational aspects are studied and compared with the derived theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with recursive estimation using augmented data. We study two recursive procedures closely linked with the well-known expectation and maximization (EM) and space alternating generalized EM (SAGE) algorithms. Unlike iterative methods, the recursive EM and SAGE-inspired algorithms give a quick update on estimates given new data. Under mild conditions, estimates generated by these procedures are strongly consistent and asymptotically normally distributed. These mathematical properties are valid for a broad class of problems. When applied to direction of arrival (DOA) estimation, the recursive EM and SAGE-inspired algorithms lead to a very simple and fast implementation of the maximum-likelihood (ML) method. The most complicated computation in each recursion is inversion of the augmented information matrix. Through data augmentation, this matrix is diagonal and easy to invert. More importantly, there is no search in such recursive procedures. Consequently, the computational time is much less than that associated with existing numerical methods for finding ML estimates. This feature greatly increases the potential of the ML approach in real-lime processing. Numerical experiments show that both algorithms provide good results with low computational cost. [ABSTRACT FROM AUTHOR]