UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.
More information is available at Theses and Dissertations at University of Maryland Libraries.
Browse
2 results
Search Results
Item Analysis of the Stochastic Stability and Asymptotically Stationary Statistics for a Class of Nonlinear Attitude Estimation Algorithms(2018) Galante, Joseph Marshall; Sanner, Robert M; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Attitude estimation algorithms are critical components of satellite control systems, aircraft autopilots, and other applications. Attitude estimation systems perform their task by fusing attitude and gyroscope measurements; however, such measurements are typically corrupted by random noise and gyroscopes may have significant bias. Variations of the extended Kalman filter are commonly used, but this technique relies on instantaneous linearization of the underlying nonlinear dynamics and global stability cannot be guaranteed. Nonlinear attitude observers with guaranteed global stability have been derived and experimentally demonstrated, but only for the deterministic setting where no stochastic effects are present. The first part of this thesis extends a deterministic nonlinear attitude estimator by introducing additional dynamics that allow learning variations of gyro bias as a function of operating temperature, a common source of bias variation in rate gyro readings. The remainder of the thesis formally addresses the problem of stochastic stability and asymptotic performance for this family of estimators when the measurements contain random noise. Analysis tools from stochastic differential equation theory and stochastic Lyapunov analysis are used together to demonstrate convergence of the filter states to a stationary distribution, and to bound the associated steady-state statistics as a function of filter gains and sensor parameters. In many cases these bounds are conservative, but solutions have been found for the associated stationary Fokker-Planck PDEs for two cases. When only the gyro measurement contains noise, the attitude estimation errors are shown to converge to a bipolar Bingham distribution. When the gyro measurement is further assumed to have constant bias, the estimation errors are shown to converge to a joint bipolar Bingham and multivariate Gaussian distribution. Knowledge of the stationary distributions allow for exact computation of steady-state statistics. Further, the analysis suggests a method for modeling a continuous quaternion noise process with specified statistics on SO(3); this model is used for analyzing estimator performance when both the gyro and the attitude measurements contain noise. Bounds and exact predictions for the different noise models are validated using a high fidelity numerical integration method for nonlinear stochastic differential equations.Item Response dynamics of integrate-and-fire neuron models(2008-07-02) Pressley, Joanna; Troyer, Todd W; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)One of the fundamental problems in neuroscience is characterizing the transfer function that converts noisy synaptic inputs into output firing rates. A common assumption is that the membrane time constant is the dominant factor governing the time course of firing rate responses. However, previous studies have shown that neural response times can be faster than expected from voltage dynamics alone. If the membrane time constant does not solely determine response time, what are the parameters that describe the transformation of inputs into output firing rates? We investigate this question using integrate-and-fire models (IF). Noisy synaptic inputs are modeled as a white noise process with drift, characterized by a time-varying mean and variance. We use linear perturbation techniques to analyze the response dynamics of several different IF models, for signals encoded in the mean and the variance of the input, and for models operating in two qualitatively different regimes of behavior. In the perfect integrate-and-fire model (PIF), the sub-threshold membrane dynamics perfectly mimic the integral of the input current. We show that the PIF produces a perfect replica of the time-varying input rate for Poisson distributed input. Next, we survey the response properties of the leaky integrate-and-fire model (LIF). Our survey covers a wide range of baseline input parameter values and studies perturbations in both the mean or variance of the input. We find that response dynamics are highly dependent on regime, as well as which input parameter encodes the signal. Additionally we investigate how synaptic dynamics affect LIF response. We find a striking reduction in the overall gain for variance-encoded signals. Mean encoded signals elicit responses with finite high-frequency gain across regimes, and reduced resonances. Finally, we focus on nonlinear responses, examining the time course of onset and offset responses for two different IF models, the LIF and the more realistic exponential integrate-and-fire model (EIF). The responses of the models differ in that the EIF shows a slight delay before responding to a step increase in input, a delay that is not found for the LIF nor for the response to step decreases in input for either model.