Efficient Approximate Maximum Likelihood Research Articles

Joint Azimuth, Elevation, and Delay Estimation for 3-D Indoor Localization

Accurate localization in harsh indoor environments has long been a challenging problem due to the presence of multipath. Since joint direction-of-arrival (DOA) and time delay (TD) estimation has the capability to separate the line-of-sight signal from multipath signals in the TD space, it has recently become a key technique for accurate indoor localization in next-generation WiFi and 5G networks. This paper addresses the problem of joint azimuth, elevation, and TD estimation of multiple reflections of a known signal. First, we propose an efficient approximate maximum likelihood algorithm for this problem, which updates the DOA and TD parameters alternatingly. This algorithm applies to arbitrarily distributed (planar or 3-D) arrays. Then, we present the closed-form Cramer–Rao bound for joint DOA and TD estimation, based on which we provide further analysis to show the benefit of joint DOA and TD estimation over DOA-only estimation. Although the benefit of joint estimation has been empirically shown long ago, our analysis is the first theoretical proof of it. Finally, simulation results have been provided to demonstrate the theoretical finding and the effectiveness of the new algorithm. Matlab code for the new algorithm is available at https://github.com/FWen/JADE.git .

Approximate maximum likelihood estimation of two closely spaced sources

The performance of the majority of high resolution algorithms designed for either spectral analysis or Direction-of-Arrival (DoA) estimation drastically degrades when the amplitude sources are highly correlated or when the number of available snapshots is very small and possibly less than the number of sources. Under such circumstances, only Maximum Likelihood (ML) or ML-based techniques can still be effective. The main drawback of such optimal solutions lies in their high computational load. In this paper we propose a computationally efficient approximate ML estimator, in the case of two closely spaced signals, that can be used even in the single snapshot case. Our approach relies on Taylor series expansion of the projection onto the signal subspace and can be implemented through 1D Fourier transforms. Its effectiveness is illustrated in complicated scenarios with very low sample support and possibly correlated sources, where it is shown to outperform conventional estimators.

Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics

Stochastic differential equations (SDEs) are assuming an important role in the definition of dynamical models allowing for explanation of internal variability (stochastic noise). SDE models are well established in many fields, such as investment finance, population dynamics, polymer dynamics, hydrology and neuronal models. The metabolism of glucose and insulin has not yet received much attention from SDE modellers, except from a few recent contributions, because of methodological and implementation difficulties in estimating SDE parameters. Here, we propose a new SDE model for the dynamics of glycemia during a euglycemic hyperinsulinemic clamp experiment, introducing system noise in tissue glucose uptake and apply for its estimation a closed-form Hermite expansion of the transition densities of the solution process. The present work estimates the new model parameters using a computationally efficient approximate maximum likelihood approach. By comparison with other currently used methods, the estimation process is very fast, obviating the need to use clusters or expensive mainframes to obtain the quick answers needed for everyday iterative modelling. Furthermore, it can introduce the demonstrably essential concept of system noise in this branch of physiological modelling.

An efficient approximate maximum likelihood signal detection for MIMO systems

This paper proposes an efficient approximate Maximum Likelihood (ML) detection method for Multiple-Input Multiple-Output (MIMO) systems, which searches local area instead of exhaustive search and selects valid search points in each transmit antenna signal constellation instead of all hyperplane. Both of the selection and search complexity can be reduced significantly. The method performs the tradeoff between computational complexity and system performance by adjusting the neighborhood size to select the valid search points. Simulation results show that the performance is comparable to that of the ML detection while the complexity is only as the small fraction of ML.

ESTIMATION OF THE LONG‐MEMORY PARAMETER, BASED ON A MULTIVARIATE CENTRAL LIMIT THEOREM

Abstract. Long memory is known to occur in many fields of statistical application. Stationary processes whose correlations decay asymptotically like ‖k‖2H‐2, where k is the lag and Hε (0.5, 1), provide useful parsimonious models with long memory. The parameter H characterizes the long‐memory features of the data. For long time series, maximum likelihood estimation of H can be costly in terms of CPU time. In this paper, we show that, for disjoint stretches of the data, estimates of H and other parameters that characterize the dependence structure are asymptotically independent. Averaging these estimates leads to a fast and efficient approximate maximum likelihood method.

Estimating the frequencies of two sinusoids using only the phase angles of complex-valued data

The problem of estimating the frequencies of two complex sinusoids using only the phase data is addressed. Under the assumption that the amplitudes of the two signals are not equal, a computationally efficient approximate maximum likelihood estimation (AMLE) is obtained. This AMLE uses only the phase angles of the complex-valued data to estimate frequencies and uses the envelope data to resolve an inherent algebraic sign ambiguity in the difference frequency. At moderately high SNRs, satisfactory results are obtained from computer simulations. The mean-square errors of the estimates are compared with the corresponding values of the Cramer-Rao lower bounds (CRLBs).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>