ABSTRACT
S. Nakamori^*), R. Caballerc/**)1, A. Hermoso^***), J. Jimenez^**) and J. LinarW***) (^Department of Technology, Faculty of Education, Kagoshima University,
1-20-6, Kohrimoto, Kagoshima 890-0065, Japan (**)Departamento de Estadistica e l . O., Universidad de Jaen,
Campus Las Lagunillas s/n, 23071 Jaen, Spain (***)Departamento de Estadistica e l . O., Universidad de Granada,
Campus Fuentenueva s/n, 18071 Granada, Spain
Received March, 2006; accepted in revised form - - , 2006
1 Introduction The least-squares (LS) optimal signal estimation problem in systems with uncertain observations presents a considerable complexity due to the fact that the optimal estimator, which is the conditional expectation of the signal given the observations, is not easily achievable since the joint distribution of the signal and the observations is not gaussian. For this reason, the research on the estimation problem in these systems is focused on the search of suboptimal estimators of the signal. The literature about this subject is very rich and the problem has been addressed under different hypotheses on the processes involved and using different approaches. For example, in [1] and [2] the signal estimation problem is considered assuming that the state-space model is known. When such model is not completely known, alternative information (such as covariance information) must be used to address the signal estimation problem ([3], [4], among others)
In this paper, we propose a suboptimal nonlinear filtering and fixed-point smoothing algorithm to estimate gaussian signals from uncertain observations without requiring the state-space model generating the signal, but only covariance information. The technique used to derive the algorithm consists of approximating the conditional distribution of the signal given the observations via successive approximations of mixtures of gaussian distributions; so, the proposed suboptimal estimators are obtained as the expectation of these approximate conditional distributions. A numerical simulation example shows the improvement of the proposed estimators over the linear ones deduced in [3].
