Joint Maximum Likelihood Research Articles

Blind high-resolution localization and tracking of multiple frequency hopped signals

This paper considers the problem of blind localization and tracking of multiple frequency-hopped spread-spectrum signals using a uniform linear antenna array without knowledge of hopping patterns or directions of arrival. As a preprocessing step, we propose to identify a hop-free subset of data by discarding high-entropy spectral slices from the spectrogram. High-resolution localization is then achieved via either quadrilinear regression of four-way data generated by capitalizing on both spatial and temporal shift invariance or a new maximum likelihood (ML)-based two-dimensional (2-D) harmonic retrieval algorithm. The latter option achieves the best-known model identifiability bound while remaining close to the Cramer-Rao bound even at low signal-to-noise ratios (SNRs). Following beamforming using the recovered directions, a dynamic programming approach is developed for joint ML estimation of signal frequencies and hop instants in single-user tracking. The efficacy of the proposed algorithms is illustrated in pertinent simulations.

Multidimensional Rasch Measurement via Item Component Models and Faceted Designs

A multidimensional Rasch model is presented here, which is a multidimensional extension of item component models. Relations to existing multidimensional item response theory models are discussed. Apart from other applications, it is also suitable for analyzing tests and questionnaires, which are designed according to two or more facets. An application to a 77-item questionnaire on students’ interest in physics with a two-facet structure demonstrates that the model parameters can even be estimated when 17 latent dimensions are to be measured simultaneously (by means of joint maximum likelihood methods).

Incomplete Data and Item Parameter Estimates Under JMLE and MML Estimation

Although nonrandomly missing data is readily accommodated by joint maximum likelihood estimation (JMLE), it can theoretically be problematic for marginal maximum likelihood (MML) estimation. One situation of nonrandomly missing data, vertical equating using an anchor test, was simulated for this study under several conditions. The items from two test forms were calibrated simultaneously using JMLE and MML methods. Under MML, when the different ability distributions of the students taking the forms were not taken into account, the item difficulty parameters were overestimated for the items on the less difficult form and underestimated for the items on the more difficult form.

Carrier-frequency estimation for space-diversity reception over selective channels

Carrier-frequency estimation for space-diversity reception over frequency-selective channels is discussed. Three estimation schemes based on training sequences are proposed. The first scheme employs arbitrary sequences and provides joint maximum likelihood (ML) estimates of the carrier frequency and the channel response. Its implementation is complex, but its accuracy achieves the Cramer-Rao bound. The second scheme is based on the ML criterion but employs periodic sequences to reduce the computational load. Periodic sequences are also used in the third scheme which is based on heuristic reasoning. Theoretical analysis and simulations are employed to assess the performance of the three estimation methods, and to show the improvements due to space diversity.

Joint versus separate estimation of state and change in category frequencies from repeat stratified two-phase sampling with a fallible classifier.

Joint maximum likelihood estimates (JML) of category frequencies and change from repeat stratified two-phase sampling surveys with a fallible classifier are often seriously biased and have large root mean square errors when they are obtained for small populations (<5,000) with three or more categories and a moderate to small phase II sample size (<1,000). JML estimates of state also depend on antecedent or posterior data, a recipe for inconsistency. In these situations, a separate maximum likelihood estimation (SML) of category frequencies at each survey date appears preferable. SML estimates of net change are obtained as the difference in states. SML standard errors of change are obtained via an estimate of the temporal correlation and variances of state. A bivariate binary logistic model of change provided the estimate of temporal correlation. SML generally outperformed JML significantly in terms of bias and root mean square errors in eight case studies.

An Evaluation of a Markov Chain Monte Carlo Method for the Rasch Model

The accuracy of the Gibbs sampling Markov chain monte carlo procedure was examined for estimating item and person ( .) parameters in the one-parameter logistic model. Four datasets were analyzed using the Gibbs sampling method, conditional maximum likelihood, marginal maximum likelihood, and joint maximum likelihood. Maximum likelihood and expected a posteriori. estimation methods were used with marginal maximum likelihood estimation of item parameters. Item parameter estimates from the four methods were almost identical;. estimates from Gibbs sampling were similar to those obtained from the expected a posteriori method.

Group-metric multiuser decoding

We propose the new group metric (GM) soft-decision decoder for convolutionally coded synchronous multiple-access channels. The GM decoder exploits the independently operating encoders of the multiuser channel by making decoding decisions for a subset of the users, but incorporating all the multiuser information in its metrics. For a single user, this decoder will have a reduced complexity that is exponential in the sum of encoder memory and the number of users. The soft-decision maximum-likelihood (ML) joint decoder is well known. This optimal decoder suffers from a high complexity requirement that is exponential in the product of encoder memory and the number of users. The size of the decoded subset is a design parameter which allows a tradeoff between complexity and performance. The performance of the GM decoder, once properly characterized, can be analyzed using standard techniques. In addition, a new analysis technique is presented which considers decomposable sequences for the fading channel. With this analysis, we have a new tool for bounding error probabilities for multiuser decoders. Applying this technique to the GM decoder, we can directly identify sequences that are decomposable some fraction of the time, and obtain a new upper bound. Further, this improved bound can be expressed in closed form. Numerical results show that the actual performance gap between the GM and ML decoders can be quite small.

A global estimation for multichannel time-delay and signal parameters via genetic algorithm

The joint maximum likelihood (ML) estimates time delays and the parameters of radiated signal, which is received by two or more spatially distributed receivers in the presence of additive noises, is a rather high nonlinear and complicated problem. The conventional algorithms are susceptible to local maximum problem that arises with multimodal (many peaks) likelihood function. This study presents an iterative algorithm based on genetic ones to estimate ML of multichannel time delays and signal parameters. Genetic algorithms are optimization of natural selection and evolutionary genetics. The proposed algorithm works in frequency domain and tends to find the global optimum solution without becoming trapped at local maximum. Finally, an example is given to illustrate the estimation of algorithm's performance.

Overloaded array processing with spatially reduced search joint detection

An antenna array is overloaded when the number of cochannel signals in its operating environment exceeds the number of elements. This paper proposes an iterative joint detection technique, spatially reduced search joint detection (SRSJD), that well approximates the joint maximum likelihood (JML) receiver, while reducing its computational complexity by several orders of magnitude. This complexity reduction is achieved by first exploiting the spatial separation between interfering signals with a linear preprocessing stage, and second, performing iterative joint detection with a reduced-state trellis formed over space instead of time. These novel joint detection trellises are possibly tail-biting and vary in structure from stage to stage. Through simulation, SRSJD is shown to demodulate over 2M synchronous quaternary phase-shift keying signals of zero excess bandwidth with an M element circular array. The channels of all users are assumed known.

On the loss of information in conditional maximum likelihood estimation of item parameters

In item response models of the Rasch type (Fischer & Molenaar, 1995), item parameters are often estimated by the conditional maximum likelihood (CML) method. This paper addresses the loss of information in CML estimation by using the information concept of F-information (Liang, 1983). This concept makes it possible to specify the conditions for no loss of information and to define a quantification of information loss. For the dichotomous Rasch model, the derivations will be given in detail to show the use of the F-information concept for making comparisons for different estimation methods. It is shown that by using CML for item parameter estimation, some information is almost always lost. But compared to JML (joint maximum likelihood) as well as to MML (marginal maximum likelihood) the loss is very small. The reported efficiency in the use of information of CML to JML and to MML in several comparisons is always larger than 93%, and in tests with a length of 20 items or more, larger than 99%.

Mean likelihood frequency estimation

Estimation of signals with nonlinear as well as linear parameters in noise is studied. Maximum likelihood estimation has been shown to perform the best among all the methods. In such problems, joint maximum likelihood estimation of the unknown parameters reduces to a separable optimization problem, where first, the nonlinear parameters are estimated via a grid search, and then, the nonlinear parameter estimates are used to estimate the linear parameters. We show that a grid search can be avoided by using the mean likelihood estimator for estimating the unknown nonlinear parameters and how its performance can be made equivalent to that of the maximum likelihood estimator (MLE). The mean likelihood estimator requires computation of a multidimensional integral. However, using the concepts of importance sampling, we obtain the mean likelihood estimate without using integration. The technique is computationally far less burdensome than the direct maximum likelihood method but performs just as well. Simulation examples for estimating frequencies of multiple sinusoids in noise are given. The general technique can be applied to a large class of nonlinear regression problems.

Maximum likelihood, ESPRIT, and periodogram frequency estimation of radar signals in K-distributed clutter

The contribution of this paper is the derivation of the joint maximum likelihood (ML) estimator of complex amplitude and Doppler frequency of a radar target signal embedded in correlated non-Gaussian clutter modelled as a compound-Gaussian process. The estimation accuracy of the ML frequency estimator is investigated and compared with that of the well-known periodogram and ESPRIT estimators under various operational scenarios. The hybrid Cramér–Rao lower bound (HCRLB) and a large sample closed-form expression for the mean square estimation error are also derived for Swerling I target signal. Finally, numerical results obtained by Monte Carlo simulation are checked by means of measured sea clutter data for the general case of fluctuating target amplitude.

Sunyaev‐Zeldovich Effect–derived Distances to the High‐Redshift Clusters MS 0451.6−0305 and Cl 0016+16

We determine the distances to the z approximately equal to 0.55 galaxy clusters MS 0451.6-0305 and CL 0016+16 from a maximum likelihood joint fit to interferometric Sunyaev-Zel'dovich effect (SZE) and X-ray observations. We model the intracluster medium (ICM) using a spherical isothermal beta-model. We quantify the statistical and systematic uncertainties inherent to these direct distance measurements, and we determine constraints on the Hubble parameter for three different cosmologies. For an OmegaM = 0.3, OmegaL = 0.7 cosmology, these distances imply a Hubble constant of 63(exp 12)(sub -9)(exp +21)(sub -21) km/s/Mpc, where the uncertainties correspond to statistical followed by systematic at 68% confidence. The best fit H(sub o) is 57 km/sec/Mpc for an open OmegaM = 0.3 universe and 52 km/s/Mpc for a flat Omega = 1 universe.

A Joint Maximum Likelihood Estimation Procedure for the Hyperbolic Cosine Model for Single-Stimulus Responses

Joint maximum likelihood estimation (JMLE) for the hyperbolic cosine model (Andrich &amp; Luo, 1993) is extended to the situation in which the units of items are allowed to vary. Four issues were considered in developing this JMLE procedure: (1) the indeterminacy caused by the unit parameter of each item, (2) a necessary constraint to eliminate this indeterminacy, (3) the initial estimates of the unit and location parameters of the items, and (4) a practical correction procedure to account for inconsistency in parameter estimates. Four estimation cycles were designed to address these issues. Results from two sets of simulation studies (ideal and non-ideal situations) indicated that the algorithm yielded reasonably accurate recovery of the parameters.

Carrier-frequency estimation for transmissions over selective channels

This paper deals with carrier-frequency estimation for burst transmissions over frequency-selective channels. Three estimation schemes are proposed, all based on the use of known training sequences. The first scheme employs an arbitrary sequence and provides joint maximum-likelihood (ML) estimates of the carrier frequency and the channel response. Its implementation complexity is relatively high but its accuracy achieves the Cramer-Rao bound. The second scheme is still based on the ML criterion, but the training sequence is periodic, which helps to reduce the computational load. The third scheme also employs periodic sequences, but its structure comes from heuristic reasoning. Theoretical analysis and simulations are employed to assess the performance of the three schemes.

Multiuser detectors with single-user parameter estimation on quasi-synchronous CDMA channels

We present simulated error rate and code delay/amplitude tracking performance for two recently developed detectors: the adaptive whitened matched filter, and the quasi-synchronous decorrelator. Rapid convergence (within 50 symbols) of the estimated amplitude and delay of the desired user is demonstrated based on an approximate joint maximum likelihood approach. The adaptive whitened matched filter exhibits better bit error rate performance than the decorrelator, but requires a complex eigenanalysis stage.

Adaptive simulated annealing for optimization in signal processing applications

Many signal processing applications pose optimization problems with multimodal and nonsmooth cost functions. Gradient methods are ineffective in these situations. The adaptive simulated annealing (ASA) offers a viable optimization tool for tackling these difficult nonlinear optimization problems. Three applications, maximum likelihood (ML) joint channel and data estimation, infinite-impulse-response (IIR) filter design and evaluation of minimum symbol-error-rate (MSER) decision feedback equalizer (DFE), are used to demonstrate the effectiveness of the ASA.

The JML estimation of the generalised unfolding model incorporating the latitude of acceptance parameter

Using the hyperbolic cosine model (Andrich & Luo, 1993) as the prototypic model for a single-peaked response process, Luo (in press) introduced a general form for all unidimensional probabilistic unfolding models. In addition to the person and statement location parameters, this general form has an explicit parameter characterising the latitude of acceptance, an important concept in attitude measurement. This general form employs a single operational function, and the difference between various unfolding models is a difference between their operational functions. Because all unfolding models are special cases of the general form, it is possible to develop a general algorithm for the estimation of parameters. With a brief introduction, this paper derives such an algorithm using the joint maximum likelihood principle, which is preferred among various algorithms because it does not require any assumptions about the distribution of person locations. The joint maximum likelihood estimates are not consistent, but a simple correction factor is introduced and shown to work excellently.

Independent component analysis in the presence of Gaussian noise by maximizing joint likelihood

We consider the estimation of the data model of independent component analysis when Gaussian noise is present. We show that the joint maximum likelihood estimation of the independent components and the mixing matrix leads to an objective function already proposed by Olshausen and Field using a different derivation. Due to the complicated nature of the objective function, we introduce approximations that greatly simplify the optimization problem. We show that the presence of noise implies that the relation between the observed data and the estimates of the independent components is non-linear, and show how to approximate this non-linearity. In particular, the non-linearity may be approximated by a simple shrinkage operation in the case of super-Gaussian (sparse) data. Using these approximations, we propose an efficient algorithm for approximate maximization of the likelihood. In the case of super-Gaussian components, this may be approximated by simple competitive learning, and in the case of sub-Gaussian components, by anti-competitive learning.

Maximum likelihood joint channel and data estimation using genetic algorithms

A batch blind equalization scheme is developed based on maximum likelihood joint channel and data estimation. In this scheme, the joint maximum likelihood optimization is decomposed into a two-level optimization loop. A micro genetic algorithm is employed at the upper level to identify the unknown channel model, and the Viterbi algorithm is used at the lower level to provide the maximum likelihood sequence estimation of the transmitted data sequence. As is demonstrated in simulation, the proposed method is much more accurate compared with existing algorithms for joint channel and data estimation.