J.M.C. Clark

Measurement of myocardial blood flow with oxygen-15 labelled water: comparison of different administration protocols

Abstract Positron emission tomography (PET) in conjunction with C15O2 or H215O can be used to measure myocardial blood flow (MBF) and tissue fraction (TF), i.e. the fraction of the tissue mass in the volume of the region of interest. However, with C15O2 inhalation, the tissue fraction in the septum is overestimated. Bolus injection of H215O together with arterial cannulation gives very precise results but is invasive. The purpose of this study was to develop a method which circumvents these problems. A four-parameter model with parameters for MBF, TF and spill-over fractions from both left and right ventricular cavities was developed. This method was compared with a three-parameter model (no right ventricular cavity spill-over) in both septal and non-septal regions of interest for three different administration protocols: bolus injection of H215O, infusion of H215O and inhalation of C15O2. It was found that MBF can be measured with intravenous administration of H215O without the requirement for arterial cannulation. The four-parameter protocol with bolus injection was stable in clinical studies. The four-parameter model proved essential for the septum, where it gave highly significantly better fits than did the three-parameter model (P<0.00003 in each of 15 subjects). Administration of H215O together with this four-parameter model also circumvented the problem of overestimation of TF in the septum seen with C15O2 inhalation. In addition, the radiation dose of H215O protocols is lower than that of C15O2 inhalation. Using a left atrial input curve instead of a left ventricular cavity input curve gave the same mean MBF and TF.

The shifted Rayleigh filter for bearings only tracking

The recently introduced shifted Rayleigh filter is a moment matching algorithm that exploits the essential structure of the nonlinearities present in bearings-only tracking. The algorithm can befitted to a wide range of scenarios and places no restrictions on model dimensionality. The key feature is that it generates the exact updated conditional distribution of target motion, given a normal approximation to the prior. In this paper, two versions of the algorithm are applied to the problem of tracking a moving object from multiple, independently drifting sonobuoys that supply noisy bearings only measurements, corrupted by clutter. A separate moving sensor provides noisy bearings only measurements of sonobuoy motion. The shifted Rayleigh filter adapts well to this scenario. Simulations indicate that it give good estimates, even in adverse circumstances when the clutter probability is 67% and the standard deviation of sensor noise is 16/spl deg/.

A Gaussian Mixture Filter for Range-Only Tracking

Range-only tracking problems arise in extended data collection for inverse synthetic radar applications, robotics, navigation and other areas. For such problems, the conditional density of the state variable given the measurement history is multi-modal or exhibits curvature, even in seemingly benign scenarios. For this reason, the use of extended Kalman filter (EKF) and other nonlinear filtering techniques based on Gaussian approximations can result in inaccurate estimates. We introduce a new filter for such tracking problems in two dimensions called the Gaussian mixture range-only filter (GMROF), which generates Gaussian mixture approximations to the conditional densities. The filter equations are derived by analytic techniques based on the specific nonlinearities of range-only tracking. A slight modification of the standard measurement process model, “noise before nonlinearity,” is used to simplify the moment calculations. Implementation requires, at each step, the fitting of a low order Gaussian mixture to a simple exponentiated trigonometric function of a scalar variable. Simulations involving scenarios from earlier comparative studies indicate that the GMROF consistently outperformed the EKF, and achieved the accuracy of particle filters while significantly reducing the computational cost.

The simulation of pinned diffusions

The author presents a method for simulating those paths of an R/sup n/-valued diffusion dX/sub t/=b(t,X/sub t/)dt+dW/sub t/, X/sub 0/=x that are conditioned to pass through a point z at time T, where (W/sub t/) is an R/sup n/-valued Brownian motion. Conditioned diffusions of this sort arise in nonlinear filtering problems.<<ETX>>

On “predicted miss” stochastic control problems

For steering a linear stochastic system with bounded controls so as to be as close as possible to a given hyperplane at the terminal time, Benes proved that the controller that predicts which side of the hyperplane the state would be on with no further control, and then applies full “bang” in the appropriate direction, optimal, a result conjectured y Hilborn. In this paper a different proof of this result is presented, using martingale-based optimality criteria.

A New Gaussian Mixture Algorithm for GMTI Tracking Under a Minimum Detectable Velocity Constraint

This paper introduces a new methodology to account for Doppler blind zone constraints, arising, for example, in ground moving target indicator (GMTI) tracking applications. In such problems, target measurements are suppressed when the range rate (Doppler) of the target drops below a specified threshold in magnitude (the minimum detectable velocity). The proposed method, employing Gaussian mixture approximations to the filtering density, differs from earlier Gaussian mixture approaches in the way missed measurements are modelled. The distinctive feature of the algorithm, as compared with other Gaussian mixture filters, is that it is based on an exact calculation of the filtering density when a measurement is not recorded. Algorithms that result from applying this methodology are simple to implement and computationally undemanding. Simulation results indicate a uniform improvement in estimation accuracy over that of earlier proposed analytic techniques, and a tracking performance comparable to that of state-of-the-art particle filters.

Asymptotic behaviour of the optimal filter of jump and slope jump processes

A piecewise constant process is considered which may contain a jump of random magnitude at a random time. The conditional density of the jump magnitude given noisy observations of the signal is derived, and the conditional density when only noisy observations of its integral can be measured. These densities are then analysed using large deviations theory and the asymptotical distributions for vanishing observation noise are characterised for times after the jump. The results suggest a surprisingly complicated behaviour of the conditional laws, which may be of some importance when assessing the performance of approximations to the optimal filter.

Power absorption invariance for brownian spring forcing

In [5] it was shown that, for a standard quarter-car vehicle model and a road disturbance whose velocity profile is white noise of intensity A, the mean power dissipated in the suspension is equal to kA/2 where k is the tyre vertical stiffness. It is remarkable that the power dissipation turns out to be independent of all masses and suspension parameters. The proof in [5] makes use of a spectral formulation of white noise and is specific to linear systems. This paper casts the result in a more general form and shows that it follows from a simple application of Ito calculus.

Stochastic exit time problems arising in process control

This paper concerns the problem of controlling a stochastic system, with small noise parameter, to prevent it leaving a safe region of the state space. Such problems arise in flow control and other areas. We consider a formulation of the problem, in which a control is sought, to maximize a cost which is related to the expected exit time, but modified to reduce the probability of an early exit, according to a specified level of risk aversion (‘risk sensitive’ stochastic control). Formally letting the noise parameter tend to zero, we find that the optimal control strategy for this problem coincides with the optimal feedback control strategy for a differential game. We identify a class of differential games arising in this way, the so called decomposable differential games, for which the optimal control strategy can be easily obtained and illustrate the proposed solution technique by applying it to a flow control problem arising in process systems engineering.

The interpretation of discontinuous state feedback control laws as nonanticipative control strategies in differential games

In differential games, one player chooses a feedback strategy to maximize a payoff. The other player counters by applying a minimizing open loop control. Classical notions of feedback strategies, based on state feedback control laws for which the corresponding closed loop dynamics uniquely define a state trajectory, are too restrictive for many problems, owing to the absence of minimizing classical feedback strategies or because consideration of classical feedback strategies fails to define, in a useful way, the value of the game. A number of feedback strategy concepts have been proposed to overcome this difficulty. That of Elliot and Kalton, according to which a feedback strategy is a nonanticipative mapping between control functions for the two players, has been widely taken up because it provides a value of the game which connects, via the Hamilton-Jacobi-Isaacs equation, with other fields of systems science. Heuristic analysis of specific games problems often points to discontinuous optimal feedback strategies. These cannot be regarded as classical feedback control strategies because the associated state trajectories are not in general unique. We give general conditions under which they can be interpreted as generalized feedback strategies in the sense of Elliot and Kalton.