Optimal observers for ARMA models

A polynomial-based ARMA model, when posed in a state-space framework can be regarded in many different ways. In this paper two particular state-space forms of the ARMA model are considered, and although both are canonical in structure they differ in respect of the mode in which disturbances are fed into the state and output equations. For both forms a solution is found to the optimal discrete-time observer problem and algebraic connections between the two optimal observers are shown. The purpose of the paper is to highlight the fact that the optimal observer obtained from the first state-space form, commonly known as the innovations form, is not that employed in an optimal controller, in the minimum-output variance sense, whereas the optimal observer obtained from the second form is. Hence the second form is a much more appropriate state-space description to use for controller design, particularly when employed in self-tuning control schemes.

The state estimation of flow demands in gas networks from sparse pressure telemetry

This paper presents novel observer-based techniques for the estimation of flow demands in gas networks, from sparse pressure telemetry. A completely observable model is explored, constructed by incorporating difference equations that assume the flow demands are steady. Since the flow demands usually vary slowly with time, this is a reasonable approximation. Two techniques for constructing robust observers are employed: robust eigenstructure assignment and singular value assignment. These techniques help to reduce the effects of the system approximation. Modelling error may be further reduced by making use of known profiles for the flow demands. The theory is extended to deal successfully with the problem of measurement bias. The pressure measurements available are subject to constant biases which degrade the flow demand estimates, and such biases need to be estimated. This is achieved by constructing a further model variation that incorporates the biases into an augmented state vector, but now includes information about the flow demand profiles in a new form.

Self-ratings and observer-ratings of social skill: a manipulation of state social anxiety in anxious and non-anxious children

The role of state and trait anxiety on observer ratings of social skill and negatively biased self-perception of social skill was examined. Participants were aged between 7 and 13 years (mean=9.65; sd=1.77; N=102), 47 had a current anxiety diagnosis and 55 were non-anxious controls. Participants were randomly allocated to a high or low anxiety condition and asked to complete social tasks. Task instructions were adjusted across conditions to manipulate participants’ state anxiety. Observers rated anxious participants as having poorer social skills than non-anxious controls but there was no evidence that anxious participants exhibited a negative self-perception bias, relative to controls. However, as participants’ ratings of state anxiety increased, their perception of their performance became more negatively biased. The results suggest that anxious children may exhibit real impairments in social skill and that high levels of state anxiety can lead to biased judgements of social skills in anxious and non-anxious children.