Batch Nonlinear Continuous-Time Trajectory Estimation as Exactly Sparse Gaussian Process Regression

In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent variable. Our continuous-time prior can be defined by any nonlinear, time-varying stochastic differential equation driven by white noise; this allows the possibility of smoothing our trajectory estimates using a variety of vehicle dynamics models (e.g., `constant-velocity'). We show that this class of prior results in an inverse kernel matrix (i.e., covariance matrix between all pairs of measurement times) that is exactly sparse (block-tridiagonal) and that this can be exploited to carry out GP regression (and interpolation) very efficiently. When the prior is based on a linear, time-varying stochastic differential equation and the measurement model is also linear, this GP approach is equivalent to classical, discrete-time smoothing (at the measurement times); when a nonlinearity is present, we iterate over the whole trajectory to maximize accuracy. We test the approach experimentally on a simultaneous trajectory estimation and mapping problem using a mobile robot dataset.Comment: Submitted to Autonomous Robots on 20 November 2014, manuscript # AURO-D-14-00185, 16 pages, 7 figure

Millisecond and Binary Pulsars as Nature's Frequency Standards. II. Effects of Low-Frequency Timing Noise on Residuals and Measured Parameters

Pulsars are the most stable natural frequency standards. They can be applied to a number of principal problems of modern astronomy and time-keeping metrology. The full exploration of pulsar properties requires obtaining unbiased estimates of the spin and orbital parameters. These estimates depend essentially on the random noise component being revealed in the residuals of time of arrivals (TOA). In the present paper, the influence of low-frequency ("red") timing noise with spectral indices from 1 to 6 on TOA residuals, variances, and covariances of estimates of measured parameters of single and binary pulsars are studied. In order to determine their functional dependence on time, an analytic technique of processing of observational data in time domain is developed which takes into account both stationary and non-stationary components of noise. Our analysis includes a simplified timing model of a binary pulsar in a circular orbit and procedure of estimation of pulsar parameters and residuals under the influence of red noise. We reconfirm that uncorrelated white noise of errors of measurements of TOA brings on gradually decreasing residuals, variances and covariances of all parameters. On the other hand, we show that any red noise causes the residuals, variances, and covariances of certain parameters to increase with time. Hence, the low frequency noise corrupts our observations and reduces experimental possibilities for better tests of General Relativity Theory. We also treat in detail the influence of a polynomial drift of noise on the residuals and fitting parameters. Results of the analitic analysis are used for discussion of a statistic describing stabilities of kinematic and dynamic pulsar time scales.Comment: 40 pages, 1 postscript figure, 1 picture, uses mn.sty, accepted to Mon. Not. Roy. Astron. So

Model-Based Speech Enhancement

Abstract A method of speech enhancement is developed that reconstructs clean speech from a set of acoustic features using a harmonic plus noise model of speech. This is a significant departure from traditional filtering-based methods of speech enhancement. A major challenge with this approach is to estimate accurately the acoustic features (voicing, fundamental frequency, spectral envelope and phase) from noisy speech. This is achieved using maximum a-posteriori (MAP) estimation methods that operate on the noisy speech. In each case a prior model of the relationship between the noisy speech features and the estimated acoustic feature is required. These models are approximated using speaker-independent GMMs of the clean speech features that are adapted to speaker-dependent models using MAP adaptation and for noise using the Unscented Transform. Objective results are presented to optimise the proposed system and a set of subjective tests compare the approach with traditional enhancement methods. Threeway listening tests examining signal quality, background noise intrusiveness and overall quality show the proposed system to be highly robust to noise, performing significantly better than conventional methods of enhancement in terms of background noise intrusiveness. However, the proposed method is shown to reduce signal quality, with overall quality measured to be roughly equivalent to that of the Wiener filter

Noise behavior in CGPS position time series : the eastern North America case study

We analyzed the noise characteristics of 112 continuously operating GPS stations in eastern North America using the Spectral Analysis and the Maximum Likelihood Estimation (MLE) methods. Results of both methods show that the combination ofwhite plus flicker noise is the best model for describing the stochastic part of the position time series. We explored this further using the MLE in the time domain by testing noise models of (a) powerlaw, (b)white, (c)white plus flicker, (d)white plus randomwalk, and (e) white plus flicker plus random-walk. The results show that amplitudes of all noise models are smallest in the north direction and largest in the vertical direction. While amplitudes of white noise model in (c–e) are almost equal across the study area, they are prevailed by the flicker and Random-walk noise for all directions. Assuming flicker noise model increases uncertainties of the estimated velocities by a factor of 5–38 compared to the white noise model

System Identification Theory Approach to Cohesive Sediment Transport Modelling

Two aspects of the modelling sediment transport are investigated. One is the univariate time series modelling the current velocity dynamics. The other is the multivariate time series modelling the suspended sediment concentration dynamics. Cohesive sediment dynamics and numerical sediment transport model are reviewed and investigated. The system identification theory and time series analysis method are developed and applied to set up the time series model for current velocity and suspended sediment dynamics. In this thesis, the cohesive sediment dynamics is considered as an unknown stochastic system to be identified. The study includes the model structure determination, system order estimation and parameter identification based on the real data collected from relevant estuaries and coastal areas. The strong consistency and convergence rate of recursive least squares parameter identification method for a class of time series model are given and the simulation results show that the time series modelling of sediment dynamics is accurate both in data fitting and prediction in different estuarine and coastal areas. It is well known that cohesive sediment dynamics is a very complicated process and it contains a lot of physical, chemical, biological and ocean geographical factors which are still not very well understood. The numerical modelling techniques at present are still not good enough for quantitative analysis. The time series modelling is first introduced in this thesis to set up cohesive sediment transport model and the quantitative description and analysis of current velocity and suspended sediment concentration dynamics, which provides a novel tool to investigate cohesive sediment dynamics and to achieve a better understanding of its underlying character

Human robot interaction in a crowded environment

Human Robot Interaction (HRI) is the primary means of establishing natural and affective communication between humans and robots. HRI enables robots to act in a way similar to humans in order to assist in activities that are considered to be laborious, unsafe, or repetitive. Vision based human robot interaction is a major component of HRI, with which visual information is used to interpret how human interaction takes place. Common tasks of HRI include finding pre-trained static or dynamic gestures in an image, which involves localising different key parts of the human body such as the face and hands. This information is subsequently used to extract different gestures. After the initial detection process, the robot is required to comprehend the underlying meaning of these gestures [3]. Thus far, most gesture recognition systems can only detect gestures and identify a person in relatively static environments. This is not realistic for practical applications as difficulties may arise from people‟s movements and changing illumination conditions. Another issue to consider is that of identifying the commanding person in a crowded scene, which is important for interpreting the navigation commands. To this end, it is necessary to associate the gesture to the correct person and automatic reasoning is required to extract the most probable location of the person who has initiated the gesture. In this thesis, we have proposed a practical framework for addressing the above issues. It attempts to achieve a coarse level understanding about a given environment before engaging in active communication. This includes recognizing human robot interaction, where a person has the intention to communicate with the robot. In this regard, it is necessary to differentiate if people present are engaged with each other or their surrounding environment. The basic task is to detect and reason about the environmental context and different interactions so as to respond accordingly. For example, if individuals are engaged in conversation, the robot should realize it is best not to disturb or, if an individual is receptive to the robot‟s interaction, it may approach the person. Finally, if the user is moving in the environment, it can analyse further to understand if any help can be offered in assisting this user. The method proposed in this thesis combines multiple visual cues in a Bayesian framework to identify people in a scene and determine potential intentions. For improving system performance, contextual feedback is used, which allows the Bayesian network to evolve and adjust itself according to the surrounding environment. The results achieved demonstrate the effectiveness of the technique in dealing with human-robot interaction in a relatively crowded environment [7]

Identification of audio evoked response potentials in ambulatory EEG data

Electroencephalography (EEG) is commonly used for observing brain function over a period of time. It employs a set of invasive electrodes on the scalp to measure the electrical activity of the brain. EEG is mainly used by researchers and clinicians to study the brain’s responses to a specific stimulus - the event-related potentials (ERPs). Different types of undesirable signals, which are known as artefacts, contaminate the EEG signal. EEG and ERP signals are very small (in the order of microvolts); they are often obscured by artefacts with much larger amplitudes in the order of millivolts. This greatly increases the difficulty of interpreting EEG and ERP signals.Typically, ERPs are observed by averaging EEG measurements made with many repetitions of the stimulus. The average may require many tens of repetitions before the ERP signal can be observed with any confidence. This greatly limits the study and useof ERPs. This project explores more sophisticated methods of ERP estimation from measured EEGs. An Optimal Weighted Mean (OWM) method is developed that forms a weighted average to maximise the signal to noise ratio in the mean. This is developedfurther into a Bayesian Optimal Combining (BOC) method where the information in repetitions of ERP measures is combined to provide a sequence of ERP estimations with monotonically decreasing uncertainty. A Principal Component Analysis (PCA) isperformed to identify the basis of signals that explains the greatest amount of ERP variation. Projecting measured EEG signals onto this basis greatly reduces the noise in measured ERPs. The PCA filtering can be followed by OWM or BOC. Finally, crosschannel information can be used. The ERP signal is measured on many electrodes simultaneously and an improved estimate can be formed by combining electrode measurements. A MAP estimate, phrased in terms of Kalman Filtering, is developed using all electrode measurements.The methods developed in this project have been evaluated using both synthetic and measured EEG data. A synthetic, multi-channel ERP simulator has been developed specifically for this project.Numerical experiments on synthetic ERP data showed that Bayesian Optimal Combining of trial data filtered using a combination of PCA projection and Kalman Filtering, yielded the best estimates of the underlying ERP signal. This method has been applied to subsets of real Ambulatory Electroencephalography (AEEG) data, recorded while participants performed a range of activities in different environments. From this analysis, the number of trials that need to be collected to observe the P300 amplitude and delay has been calculated for a range of scenarios