251 research outputs found

    Recursive joint CramĂ©r‐Rao lower bound for parametric systems with two‐adjacent‐states dependent measurements

    Get PDF
    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

    Get PDF
    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

    Get PDF
    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 Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ 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

    Get PDF
    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 Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ 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

    Get PDF
    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

    Spacecraft Attitude Determination:A Magnetometer Approach

    Get PDF

    Multivariate multiscale complexity analysis

    No full text
    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

    Get PDF
    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

    Get PDF
    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
    • 

    corecore