Active sensors, such as radar, lidar, and sonar, emit signals into the environment and analyze the reflections to gather information such as distance, bearing, and, with more complex processing, shape and material. Conversely, passive sensors such as microphones and cameras, rely on signals produced by objects in the environment to collect data. This deprives the sensors of the ability to directly detect distance unless used in arrays, but affords them the benefits of being concealed and saving energy. In modern applications, we see active sensors filtering out any signals not originating from their transducers as if they were noise. However, contemporary research has shown that echolocating bats have the capability of taking advantage of both active and passive echolocation. By fusing the information a bat can gather from a conspecific's echoes with their own, it is suggested that more data may become available to the eavesdropping bat. Taking bioinspiration from these suggested abilities, we seek to explore the question of how fusing active and passive ultrasonic sensing may effect the information available to a robotic vehicle. Our first investigation was an experimental verification of the capabilities of a stereo sensor for passively tracking an ultrasonic sound source using limited a priori information about the target being tracked. Our results pos- itively supported a previous simulation study and showed that the Bayesian estimator was further able to recover from divergences due to hardware and software limitations. Break- ing from the limited assumptions of the previous work, we began a full investigation of the fusion of active and passive sensing with a numerical investigation of the effects of these sensing techniques on a robotic vehicle performing simultaneous localization and mapping (SLAM). The SLAM problem consists of robot that is placed in an unknown environment, which it proceeds to map and localize itself within. By ensonifying the environment with a stationary beacon, we compared the performance of the vehicle when using active, passive, and fused sensing strategies. Building upon previous numerical simulations, we found supporting evidence that, when information available through active sensing is limited, incorporating passive measurements improves the information available to the vehicle and may also improve the accuracy of its map and localization. Finally, we took the first step to fully realizing our initial goal by numerically investigating robotic eavesdropping on two dynamics vehicles. This work showed promising results for the continued investigation of fused sensing strategies and also highlighted the importance of formation control and landmark initialization. / Doctor of Philosophy / While the stereotype of bats being blind is a fallacy, it is true many species rely on their abilities of echolocation to navigate their surrounding environment. It has been observed that bats not only use the echoes of their own vocalizations to gather this information but also may eavesdrop on the echoes of other bats in their immediate area. This suggests that bats have the ability to effectively use two types of sensing at once, which are categorized as active and passive sensing. Active sensors are defined by their need to create signals that are sent out to the environment while passive sensors rely on signals they can collect from the environment to understand it. In this work we investigate the question: can robots that combine active and passive sensing capabilities into a single sensor gain more effective information about their environment? The first problem we investigate is an experimental proof of concept that it is possible to passively track an acoustic emitter without direct knowledge of how it is moving. Using a simple two microphone sensor we show support for previously tested numerical results that this form of tracking is possible. Moving away from this constrained system our later work uses modeling and simulation of the simultaneous localization and mapping (SLAM) problem in robotics to gain more understanding of the question above.

In this work, we propose a depth estimation system based on image sequence and odometry information. The key idea is that depth estimation is decoupled from pose estimation. Such approach results in multipurpose system applicable on different robot platforms and for different depth estimation related problems. Our implementation uses various filtration techniques, operates real-time and provides appropriate results. Although the system was aimed at and tested on drone platform, it can be well used on any other type of autonomous vehicle that provides odometry information and video output.

Derivative pricing, and in particular the pricing of options, is an important area of current research in financial mathematics. Experts debate on the best method of pricing and the most appropriate model of a price process to use. In this thesis, a ``Switching Black-Scholes'' model of a price process is proposed. This model is based on the standard geometric Brownian motion (or Black-Scholes) model of a price process. However, the drift and volatility parameters are permitted to vary between a finite number of possible values at known times, according to the state of a hidden Markov chain. This type of model has been found to replicate the Black-Scholes implied volatility smiles observed in the market, and produce option prices which are closer to market values than those obtained from the traditional Black-Scholes formula. As the Markov chain incorporates a second source of uncertainty into the Black-Scholes model, the Switching Black-Scholes market is incomplete, and no unique option pricing methodology exists. In this thesis, we apply the methods of mean-variance hedging, Esscher transforms and minimum entropy in order to price options on assets which evolve according to the Switching Black-Scholes model. C programs to compute these prices are given, and some particular numerical examples are examined. Finally, filtering techniques and reference probability methods are applied to find estimates of the model parameters and state of the hidden Markov chain. / Thesis (Ph.D.)--Applied Mathematics, 2003.

Derivative pricing, and in particular the pricing of options, is an important area of current research in financial mathematics. Experts debate on the best method of pricing and the most appropriate model of a price process to use. In this thesis, a ``Switching Black-Scholes'' model of a price process is proposed. This model is based on the standard geometric Brownian motion (or Black-Scholes) model of a price process. However, the drift and volatility parameters are permitted to vary between a finite number of possible values at known times, according to the state of a hidden Markov chain. This type of model has been found to replicate the Black-Scholes implied volatility smiles observed in the market, and produce option prices which are closer to market values than those obtained from the traditional Black-Scholes formula. As the Markov chain incorporates a second source of uncertainty into the Black-Scholes model, the Switching Black-Scholes market is incomplete, and no unique option pricing methodology exists. In this thesis, we apply the methods of mean-variance hedging, Esscher transforms and minimum entropy in order to price options on assets which evolve according to the Switching Black-Scholes model. C programs to compute these prices are given, and some particular numerical examples are examined. Finally, filtering techniques and reference probability methods are applied to find estimates of the model parameters and state of the hidden Markov chain. / Thesis (Ph.D.)--Applied Mathematics, 2003.