This thesis is concerned with retrodiction and measurement in quantum optics. The latter of these two concepts is studied in particular form with a general optical multiport device, consisting of an arbitrary array of beam-splitters and phase-shifters. I show how such an apparatus generalizes the original projection synthesis technique, introduced as an in principle technique to measure the canonical phase distribution. Just as for the original projection synthesis, it is found that such a generalised device can synthesize any general projection onto a state in a finite dimensional Hilbert space. One of the important findings of this thesis is that, unlike the original projection synthesis technique, the general apparatus described here only requires a classical, that is a coherent, reference field at the input of the device. Such an apparatus lends itself much more readily to practical implementation and would find applications in measurement and predictive state engineering. If we relax the above condition to allow for just a single non-classical reference field, we show that the apparatus is capable of producing a single-shot measure of canonical phase. That is, the apparatus can project onto any one of an arbitrarily large subset of phase eigenstates, with a probability proportional to the overlap of the phase state and the input field. Unlike the original projection synthesis proposal, this proposal requires a binomial reference state as opposed to a reciprocal binomial state. We find that such a reference state can be obtained, to an excellent approximation, from a suitably squeezed state. The analysis of these measurement apparatuses is performed in the less usual, but completely rigorous, retrodictive formalism of quantum mechanics.

no / This research explores the possibility that a person's (perceiver's) prospects of making a correct inference of another person's (target's) inner states depends on the personal characteristics of the target, potentially relating to how readable they are. Twenty-seven targets completed the Empathy Quotient (EQ) and were classified as having low, average or high EQ. They were unobtrusively videoed while thinking of an event of happiness, gratitude, anger and sadness. After observing targets thinking of such a past event, fifty-two perceivers (participants) in Study 1 were asked to infer what the target was thinking, and fifty perceivers in Study 2 were asked to rate the target's expression – positive or negative. Results suggested that (1) perceivers' accuracy in detecting targets' thoughts depended on which EQ group the target belonged to, and (2) target readability is not a proxy measure for level of target expressiveness. In other words, something about EQ status renders targets more or less easy to read in a way that is not simply explained by expressive people being more readable. We conclude with discussion of the importance of the target's trait as well as situation they experience in determining how accurately a perceiver might infer their inner states.

No / Past research tells us that individuals can infer information about a target’s emotional state and intentions from their facial expressions (Frith & Frith, 2012), a process known as mentalising. This extends to inferring the events that caused the facial reaction (e.g. Pillai, Sheppard, & Mitchell, 2012; Pillai et al., 2014), an ability known as retrodictive mindreading. Here, we enter new territory by investigating whether or not people (perceivers) can guess a target’s social context by observing their response to stimuli. In Experiment 1, perceivers viewed targets’ responses and were able to determine whether these targets were alone or observed by another person. In Experiment 2, another group of perceivers, without any knowledge of the social context or what the targets were watching, judged whether targets were hiding or exaggerating their facial expressions; and their judgments discriminated between conditions in which targets were observed and alone. Experiment 3 established that another group of perceivers’ judgments of social context were associated with estimations of target expressivity to some degree. In Experiments 1 and 2, the eye movements of perceivers also varied between conditions in which targets were observed and alone. Perceivers were thus able to infer a target’s social context from their visible response. The results demonstrate an ability to use other minds as a window onto a social context that could not be seen directly.

<p>Multi-Target Tracking (MTT), where the number of targets as well as their states are time-varying, concerns with the estimation of both the number of targets and the individual states from noisy sensor measurements, whose origins are unknown. Filtering typically produces the best estimates of the target state based on all measurements up to current estimation time. Smoothing or retrodiction, which uses measurements beyond the current estimation time, provides better estimation of target states. This thesis proposes smoothing methods for various estimation methods that produce delayer, but better, estimates of the target states.</p> <p>First, we propose a novel smoothing method for the Probability Hypothesis Density (PHD) estimator. The PHD filer, which propagates the first order statistical moment of the multitarget state density, a computationally efficient MTT algorithm. By evaluating the PHD, the number of targets as well as their individual states can be extracted. Recent Sequential Monte Carlo (SMC) implementations of the PHD filter have paved the way to its application to realistic nonlinear non-Gaussian problems. The proposed PHD smoothing method involves forward multitarget filtering using the standard PHD filter recursion followed by backward smoothing recursion using a novel recursive formula.</p> <p>Second, we propose a Multiple Model PH (MMPHD) smoothing method for tracking of maneuvering targets. Multiple model approaches have been shown to be effective for tracking maneuvering targets. MMPHD filter propagates mode-conditioned PHD recursively. The proposed backward MMPHD smoothing algorithm involves the estimation of a continuous state for target dynamic as well as a discrete state vector for the mode of target dynamics.</p> <p>Third, we present a smoothing method for the Gaussian Mixture PHD (GMPHD) state estimator using multiple sensors. Under linear Gaussian assumptions, the PHD filter can be implemented using a closed-form recursion, where the PHD is represented by a mixture of Gaussian functions. This can be extended to nonlinear systems by using the Extended Kalman Filter (EKF) or the Unscented Kalman Filter (UKF). In the case of multisenor systems, a sequential update of the PHD has been suggested in literature. However, this sequential update is susceptible to imperfections in the last sensor. In this thesis, a parallel update for GMPHD filter is proposed. The resulting filter outputs are further improved using a novel closed-form backward smoothing recursion.</p> <p>Finally, we propose a novel smoothing method for Kalman based Interacting Multiple Model (IMM) estimator for tracking agile targets. The new method involves forwarding filtering followed by backward smoothing while maintaining the fundamental spirit of the IMM. The forward filtering is performed using the standard IMM recursion, while the backward smoothing is performed using a novel interacting smoothing recursion. This backward recursion mimics the IMM estimator in the backward direction, where each mode conditioned smoother uses standard Kalman smoothing recursion.</p> / Thesis / Doctor of Philosophy (PhD)

Yes / It has been proposed that mentalising involves retrodicting as well as predicting behaviour, by inferring previous mental states of a target. This study investigated whether retrodiction is impaired in individuals with Autism Spectrum Disorders (ASD). Participants watched videos of real people reacting to the researcher behaving in one of four possible ways. Their task was to decide which of these four “scenarios” each person responded to. Participants’ eye movements were recorded. Participants with ASD were poorer than comparison participants at identifying the scenario to which people in the videos were responding. There were no group differences in time spent looking at the eyes or mouth. The findings imply those with ASD are impaired in using mentalising skills for retrodiction.

<p>In the field of Tracking and Data Fusion most, if not all, computations executed by a computer are carried out serially. The sole part of the process that is not entirely serial is the collection of data from multiple sensors, which can be executed in parallel. However, once the data is to be filtered the most likely candidate is a serial algorithm. This is due in large part to the algorithms themselves that have been developed over the last several decades for use on conventional computers that have been left void of parallel computing capabilities, until now. With the arrival of graphical processing units, or GPUs, the tracking community is in a favourable position to exploit the functionality of parallel processing in order to track a growing number of targets. The problem, however, begins with the sheer labour of having to convert all the pre-existing serial tracking algorithms into parallel ones. This is clearly a daunting task when one considers the extent to which the tracking community has gone to develop modern day filters such as Alpha Beta filters, Probabilistic Data Association filters, Interacting Multiple Model filters, and several dozen, if not hundred, variants of the aforementioned. It is most likely that these filters will find some kind of a parallelization in the near future as ever more sensors are dispersed throughout society and even more targets are monitored with these sensors. The volume of targets then becomes simply too unmanageable for a serial algorithm and more focus is placed iv on parallel ones. Yet, before the parallel algorithms can be utilized they have to be derived. It is the derivation of these parallel algorithms which is the focus of this thesis. However, it should be made clear that it would be impossible to formulate a parallelization for every filter found in the literature, and so the goal here is to direct the attention onto one filter in particular, the Kalman filter.</p> / Master of Applied Science (MASc)

<p>Prediction, tracking, and retrodiction for targets whose motion is constrained by external conditions (e.g., shipping lanes, roads) present many challenges to tracking systems. The targets are moving along a path, defined by way-points and segments. Measurements are obtained by sensors at low revisit rates (e.g., spaceborne). Existing tracking algorithms assume that the targets follow the same motion model between successive measurements, but in a low revisit rate scenario targets may change the motion model between successive measurements. A prediction algorithm is proposed here, which addresses this issue by considering possible motion model whenever targets move to a different segment. Further, when a target approaches a junction, it has the possibility to travel into one of the multiple segments connected to that junction. To predict the probable locations, multiple hypotheses for segments are introduced and a probability is calculated for each segment hypothesis. When measurements become available, segment hypothesis probability is updated based on a combined mode likelihood and a sequential probability ratio test is carried out to reject the hypotheses with low probability. Retrodiction for path constrained targets is also considered, because in some scenarios it is desirable to find out the target's exact location at some previous time (e.g., at the time of an oil leakage). A retrodiction algorithm is developed for path constrained targets so as to facilitate motion forensic analysis. Simulation results are presented to validate the proposed algorithms.</p> / Master of Applied Science (MASc)