9:30, SPTM-P5.1
MAXIMUM LIKELIHOOD BINARY SHIFT-REGISTER SYNTHESIS FROM NOISY OBSERVATIONS
T. MOON
We consider the problem of estimating the feedback coefficients of a linear feedback shift register (LFSR) based on noisy observations. In the current approach, the coefficients are endowed with a probabilistic model. Gradient ascent updates to coefficient probabilities are computable using recursions developed by means of the EM algorithm. Reduced-complexity approximations are also developed by reducing the number of coefficients propagated at each stage. Applications of this method may include soft decision decoding and blind spread spectrum interception.

9:30, SPTM-P5.2
THE NORMAL INVERSE GAUSSIAN DISTRIBUTION: A VERSATILE MODEL FOR HEAVY-TAILED STOCHASTIC PROCESSES
A. HANSSEN, T. ØIGÅRD
The normal inverse Gaussian (NIG) distribution is a recent flexible closed form distribution that may be applied as a model of heavy-tailed processes. The NIG distribution is completely specified by four real valued parameters that have natural interpretations in terms of the shape of the resulting probability density function. By choosing the parameters appropriately, one can describe a wide range of shapes of the distribution. In this paper, we discuss several of the desirable properties of the NIG distribution. In particular, we discuss the cumulant generating function and the cumulants of the NIG-variables. A particularly important property is that the NIG distribution is closed under convolution. Finally, we derive a set of very simple yet accurate estimators of the NIG parameters. Our estimators differ fundamentally from estimators suggested by other authors in that our estimators take advantage of the surprisingly simple structure of the cumulant generating function.

9:30, SPTM-P5.3
IMPROVEMENT OF CUMULANT-BASED PARAMETER ESTIMATION
D. KOUAME, J. GIRAULT, J. GIRAULT
This paper presents a improvement of high order cumulant-based parameter estimation using delta operator applied to instrumental variable algorithm. It is based on a modification of the classical least squares estimation and the utilization of the delta operator and the introduction of an additional term in the parameter estimates. Computer simulation results are given to illustrate the behavior of this method.

9:30, SPTM-P5.4
ENTROPY MINIMIZATION FOR PARAMETER ESTIMATION PROBLEMS WITH UNKNOWN DISTRIBUTION OF THE OUTPUT NOISE
L. PRONZATO, E. THIERRY
We consider the situation where the parameters of a linear regression model have to be estimated from observations corrupted by an additive noise with unknown distribution f. Since maximum likelihood estimation cannot be used, we estimate the parameters by minimizing the entropy of a kernel estimate of f, constructed from the residuals. The asymptotic behaviour of this estimator is considered. An example of parameter estimation in the presence of interference with random binary signal is presented.

9:30, SPTM-P5.5
MONTE CARLO SMOOTHING FOR NON-LINEARLY DISTORTED SIGNALS
W. FONG, S. GODSILL
We develop methods for Monte Carlo filtering and smoothing for estimating an unobserved state given a non-linearly distorted signal. Due to the lengthy nature of real signals, we suggest processing the data in blocks and a block-based smoother algorithm is developed for this purpose. In particular, we describe algorithms for de-quantisation and de-clipping in detail. Both algorithms are tested with real audio data which is either heavily quantised or clipped and the results are shown.

9:30, SPTM-P5.6
CONVOLUTIVE REDUCED RANK WIENER FILTERING
J. MANTON, Y. HUA
If two wide sense stationary time series are correlated then one can be used to predict the other. The reduced rank Wiener filter is the rank constrained linear operator which maps the current value of one time series to an estimate of the current value of the other time series in an optimal way. A closed form solution exists for the reduced rank Wiener filter. This paper studies the problem of determining the reduced rank FIR filter which optimally predicts one time series given the other. This optimal FIR filter is called the convolutive reduced rank Wiener filter, and it is proved that determining it is equivalent to solving a weighted low rank approximation problem. In certain cases a closed form solution exists, and in general, the iterative optimisation algorithm derived here can be used to converge to a locally optimal convolutive reduced rank Wiener filter.

9:30, SPTM-P5.7
PERFORMANCE BREAKDOWN OF SUBSPACE-BASED METHODS: PREDICTION AND CURE
M. HAWKES, A. NEHORAI
The performance breakdown of subspace-based parameter estimation methods can be naturally related to a switch of vectors between the estimated signal and noise subspaces (a ``subspace swap''). In this paper we derive a lower bound for the probability of such an occurrence and use it to obtain a simple data-based indicator of whether or not the probability of a performance breakdown is significant. We also present a conceptually simple technique to determine from the data whether or not a subspace swap has actually occurred, and to extend the range of SNR values or data samples in which a given subspace method produces accurate estimates.

9:30, SPTM-P5.8
REVISITING ADAPTIVE SIGNAL SUBSPACE ESTIMATION BASED ON RAYLEIGH'S QUOTIENT
S. ATTALLAH
In this paper, we propose a new adaptive algorithm for subspace estimation and tracking that is based on Rayleigh's quotient. This algorithm allows the estimation of the signal subspace of a vector sequence. It has a number of interesting properties such as a low computational complexity, a fast convergence, orthogonality of the subspace vectors which is ensured at each iteration and a good numerical stability. As will be shown, the proposed algorithm outperforms Oja's algorithm.

9:30, SPTM-P5.9
FINITE DIMENSIONAL ALGORITHMS FOR OPTIMAL SCHEDULING OF HIDDEN MARKOV MODEL SENSORS
V. KRISHNAMURTHY, B. WAHLBERG
Consider the Hidden Markov model estimation problem where the realization of a single Markov chain is observed by a number of noisy sensors. The sensor scheduling problem for the resulting Hidden Markov model is as follows: Design an optimal algorithm for selecting at each time instant, one of the many sensors to provide the next measurement. Each measurement has an associated measurement cost. The problem is to select an optimal measurement scheduling policy, so as to minimize a cost function of estimation errors and measurement costs. The problem of determining the optimal measurement policy is solved via stochastic dynamic programming. An optimal finite dimensional scheduling algorithm is presented along with numerical results for an aircraft tracking problem.

9:30, SPTM-P5.10
NONPARAMETRIC ESTIMATION OF INTERACTION FUNCTIONS FOR TWO-TYPE PAIRWISE INTERACTION POINT PROCESSES
J. GUBNER, W. CHANG
Nonparametric estimation of interaction functions for two-type pairwise interaction point processes is addressed. Such a problem is known to be challenging due to the intractable normalizing constant present in the density function. It is shown that the means of the marked interpoint distance functions embedded in the two-type pairwise interaction point process converge to the means of an inhomogeneous Poisson processes. This suggests a simple and effective nonparametric estimation method. An example is presented to illustrate the efficacy of our method. Our results can be generalized to multitype point processes in a straightforward manner, although the notation is more involved.