251 research outputs found
Recursive joint CramĂ©râRao lower bound for parametric systems with twoâadjacentâstates dependent measurements
Joint Cramér-Rao lower bound (JCRLB) is very useful for the performance evaluation of joint state and parameter estimation (JSPE) of non-linear systems, in which the current measurement only depends on the current state. However, in reality, the non-linear systems with two-adjacent-states dependent (TASD) measurements, that is, the current measurement is dependent on the current state as well as the most recent previous state, are also common. First, the recursive JCRLB for the general form of such non-linear systems with unknown deterministic parameters is developed. Its relationships with the posterior CRLB for systems with TASD measurements and the hybrid CRLB for regular parametric systems are also provided. Then, the recursive JCRLBs for two special forms of parametric systems with TASD measurements, in which the measurement noises are autocorrelated or cross-correlated with the process noises at one time step apart, are presented, respectively. Illustrative examples in radar target tracking show the effectiveness of the JCRLB for the performance evaluation of parametric TASD systems
Kinematic GNSS Shadow Matching Using Particle Filters
Student Paper Award Winner. The poor performance of GNSS user equipment in urban canyons is a well-known problem and is particularly inaccurate in the cross-street direction. However, the accuracy in this direction greatly affects many applications, including vehicle lane identification and high-accuracy pedestrian navigation. Shadow matching was proposed to help solve this problem by using information derived from 3D models of buildings. Though users of GNSS positioning typically move, previous research has focused on static shadow-matching positioning. In this paper, for the first time, kinematic shadow-matching positioning is tackled. Kalman filter based shadow matching is proposed and also, in order to overcome some of its predicted limitations, a particle filter is proposed to better solve the problem
Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond
Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form MarkovâBayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed âGaussian conjugacyâ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity
Approximate Gaussian Conjugacy: Parametric Recursive Filtering Under Nonlinearity, Multimodal, Uncertainty, and Constraint, and Beyond
This is a post-peer-review, pre-copyedit version of an article published in Frontiers of Information Technology & Electronic Engineering. The final authenticated version is available online at: https://doi.org/10.1631/FITEE.1700379Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form MarkovâBayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed âGaussian conjugacyâ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity
Real time depth of anaesthesia monitoring through electroencephalogram (EEG) signal analysis based on Bayesian method and analytical technique
The electroencephalogram (EEG) signal from the brain is used for analysing brain abnormality, diseases, and monitoring patient conditions during surgery. One of the applications of the EEG signals analysis is real-time anaesthesia monitoring, as the anaesthetic drugs normally targeted the central nervous system.
Depth of anaesthesia has been clinically assessed through breathing pattern, heart rate, arterial blood pressure, pupil dilation, sweating and the presence of movement. Those assessments are useful but are an indirect-measurement of anaesthetic drug effects. A direct method of assessment is through EEG signals because most anaesthetic drugs affect neuronal activity and cause a changed pattern in EEG signals.
The aim of this research is to improve real-time anaesthesia assessment through EEG signal analysis which includes the filtering process, EEG features extraction and signal analysis for depth of anaesthesia assessment. The first phase of the research is EEG signal acquisition. When EEG signal is recorded, noises are also recorded along with the brain waves. Therefore, the filtering is necessary for EEG signal analysis.
The filtering method introduced in this dissertation is Bayesian adaptive least mean square (LMS) filter which applies the Bayesian based method to find the best filter weight step for filter adaptation. The results show that the filtering technique is able to remove the unwanted signals from the EEG signals.
This dissertation proposed three methods for EEG signal features extraction and analysing. The first is the strong analytical signal analysis which is based on the Hilbert transform for EEG signal features' extraction and analysis. The second is to extract EEG signal features using the Bayesian spike accumulation technique. The third is to apply the robust Bayesian Student-t distribution for real-time anaesthesia assessment.
Computational results from the three methods are analysed and compared with the recorded BIS index which is the most popular and widely accepted depth of anaesthesia monitor. The outcomes show that computation times from the three methods are leading the BIS index approximately 18-120 seconds. Furthermore, the responses to anaesthetic drugs are verified with the anaesthetist's documentation and then compared with the BIS index to evaluate the performance. The results indicate that the three methods are able to extract EEG signal features efficiently, improve computation time, and respond faster to anaesthetic drugs compared to the existing BIS index
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Bayesian Approaches to Tracking, Sensor Fusion and Intent Prediction
This thesis presents work on the development of model-based Bayesian approaches to object tracking and intent prediction. Successful navigation/positioning applications rely fundamentally on the choice of appropriate dynamic model and the design of effective tracking algorithms capable of maximising the use of the structure of the dynamic system and the information from sensors. While the tracking problem with frequent and accurate position data has been well studied, we push back the frontiers of current technology where an object can undergo fast manoeuvres and position fixes are limited. On the other hand, intent prediction techniques which extract higher level information such as the intended destination of a moving object can be designed, given the ability to perform successful tracking. Such techniques can play important roles in various application areas, including traffic monitoring, intelligent human computer interaction systems and autonomous route planning.
In the first part of this thesis Bayesian tracking methods are designed based on a standard fix-rate setting in which the dynamic system is formulated into a Markovian state space form. We show that the combination of an intrinsic coordinate dynamic model and sensors in the object's body frame leads to novel state space models according to which efficient proposal kernels can be designed and implemented by the sequential Monte Carlo (SMC) methods. Also, sequential Markov chain Monte Carlo schemes are considered for the first time to tackle the sequential batch inference problems due to the presence of infrequent position data. Performance evaluation on both synthetic and real-world data shows that the proposed algorithms are superior to simpler particle filters, implying that they can be favourable alternatives to tracking problems with inertial sensors.
The modelling assumption that leads to Markovian state space models can be restrictive for real-world systems as it stipulates that the state sequence has to be synchronised with the observations. In the second major part of this thesis we relax this assumption and work with a more natural class of models, termed variable rate models. We generalise the existing variable rate intrinsic model to incorporate acceleration, speed, distance and position data and introduce new variable rate particle filtering methods tailored to the derived model to accommodate multi-sensor multi-rate tracking scenarios. The proposed algorithms can achieve substantial improvements in terms of tracking accuracy and robustness over a bootstrap variable rate particle filter. Moreover, full Bayesian inference schemes for the learning of both the hidden state and system parameters are presented, with numerical results illustrating their effectiveness.
The last part of the thesis is about designing efficient intent prediction algorithms within a Bayesian framework. A pseudo-observation based approach to the incorporation of destination knowledge is introduced, making the mathematics of the dynamical model and the observation process consistent with the Markov state process. Based on the new interpretation, two algorithms are proposed to sequentially estimate the probability of all possible endpoints. Whilst the synthetic maritime surveillance data demonstrate that the proposed methods can achieve comparable prediction performance with reduced computational cost in comparison to the existing bridging distribution based methods, the results on an extensive freehand pointing database, which contains 95 three-dimensional pointing trajectories, show that the new algorithms can outperform other state-of-the-art techniques. Some sensitivity tests are also performed, confirming the good robustness of the introduced methods against model mismatches
Multivariate multiscale complexity analysis
Established dynamical complexity analysis measures operate at a single scale and thus fail
to quantify inherent long-range correlations in real world data, a key feature of complex
systems. They are designed for scalar time series, however, multivariate observations are
common in modern real world scenarios and their simultaneous analysis is a prerequisite for
the understanding of the underlying signal generating model. To that end, this thesis first
introduces a notion of multivariate sample entropy and thus extends the current univariate
complexity analysis to the multivariate case. The proposed multivariate multiscale entropy
(MMSE) algorithm is shown to be capable of addressing the dynamical complexity of such
data directly in the domain where they reside, and at multiple temporal scales, thus
making full use of all the available information, both within and across the multiple data
channels. Next, the intrinsic multivariate scales of the input data are generated adaptively
via the multivariate empirical mode decomposition (MEMD) algorithm. This allows for
both generating comparable scales from multiple data channels, and for temporal scales
of same length as the length of input signal, thus, removing the critical limitation on
input data length in current complexity analysis methods. The resulting MEMD-enhanced
MMSE method is also shown to be suitable for non-stationary multivariate data analysis
owing to the data-driven nature of MEMD algorithm, as non-stationarity is the biggest
obstacle for meaningful complexity analysis. This thesis presents a quantum step forward
in this area, by introducing robust and physically meaningful complexity estimates of
real-world systems, which are typically multivariate, finite in duration, and of noisy and
heterogeneous natures. This also allows us to gain better understanding of the complexity
of the underlying multivariate model and more degrees of freedom and rigor in the analysis.
Simulations on both synthetic and real world multivariate data sets support the analysis
Nonlinear bayesian filtering with applications to estimation and navigation
In principle, general approaches to optimal nonlinear filtering can be described
in a unified way from the recursive Bayesian approach. The central idea to this recur-
sive Bayesian estimation is to determine the probability density function of the state
vector of the nonlinear systems conditioned on the available measurements. However,
the optimal exact solution to this Bayesian filtering problem is intractable since it
requires an infinite dimensional process. For practical nonlinear filtering applications
approximate solutions are required. Recently efficient and accurate approximate non-
linear filters as alternatives to the extended Kalman filter are proposed for recursive
nonlinear estimation of the states and parameters of dynamical systems. First, as
sampling-based nonlinear filters, the sigma point filters, the unscented Kalman fil-
ter and the divided difference filter are investigated. Secondly, a direct numerical
nonlinear filter is introduced where the state conditional probability density is calcu-
lated by applying fast numerical solvers to the Fokker-Planck equation in continuous-
discrete system models. As simulation-based nonlinear filters, a universally effective
algorithm, called the sequential Monte Carlo filter, that recursively utilizes a set of
weighted samples to approximate the distributions of the state variables or param-
eters, is investigated for dealing with nonlinear and non-Gaussian systems. Recentparticle filtering algorithms, which are developed independently in various engineer-
ing fields, are investigated in a unified way. Furthermore, a new type of particle
filter is proposed by integrating the divided difference filter with a particle filtering
framework, leading to the divided difference particle filter. Sub-optimality of the ap-
proximate nonlinear filters due to unknown system uncertainties can be compensated
by using an adaptive filtering method that estimates both the state and system error
statistics. For accurate identification of the time-varying parameters of dynamic sys-
tems, new adaptive nonlinear filters that integrate the presented nonlinear filtering
algorithms with noise estimation algorithms are derived.
For qualitative and quantitative performance analysis among the proposed non-
linear filters, systematic methods for measuring the nonlinearities, biasness, and op-
timality of the proposed nonlinear filters are introduced. The proposed nonlinear
optimal and sub-optimal filtering algorithms with applications to spacecraft orbit es-
timation and autonomous navigation are investigated. Simulation results indicate
that the advantages of the proposed nonlinear filters make these attractive alterna-
tives to the extended Kalman filter
Pedestrian Navigation using Artificial Neural Networks and Classical Filtering Techniques
The objective of this thesis is to explore the improvements achieved through using classical filtering methods with Artificial Neural Network (ANN) for pedestrian navigation techniques. ANN have been improving dramatically in their ability to approximate various functions. These neural network solutions have been able to surpass many classical navigation techniques. However, research using ANN to solve problems appears to be solely focused on the ability of neural networks alone. The combination of ANN with classical filtering methods has the potential to bring beneficial aspects of both techniques to increase accuracy in many different applications. Pedestrian navigation is used as a medium to explore this process using a localization and a Pedestrian Dead Reckoning (PDR) approach. Pedestrian navigation is primarily dominated by Global Positioning System (GPS) based navigation methods, but urban and indoor environments pose difficulties for using GPS for navigation. A novel urban data set is created for testing various localization and PDR based pedestrian navigation solutions. Cell phone data is collected including images, accelerometer, gyroscope, and magnetometer data to train the ANN. The ANN methods are explored first trying to achieve a low root mean square error (RMSE) of the predicted and original trajectory. After analyzing the localization and PDR solutions they are combined into an extended Kalman Filter (EKF) to achieve a 20% reduction in the RMSE. This takes the best localization results of 35m combined with underperforming PDR solution with a 171m RMSE to create an EKF solution of 28m of a one hour test collect
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