Estimation of Radioactivity Release Activity Using Non-Linear Kalman Filter-Based Estimation Techniques

The estimation of radioactivity release following an accident in a nuclear power plant is crucial due to its short and long-term impacts on the surrounding population and the environment. In the case of any accidental release, the activity needs to be estimated quickly and reliably to effectively plan a rapid emergency response and design an appropriate evacuation strategy. The accurate prediction of incurred dose rate during normal or accident scenario is another important aspect. In this article, three different non-linear estimation techniques, extended Kalman filter, unscented Kalman filter, and cubature Kalman filter are proposed in order to estimate release activity and to improve the prediction of dose rates. Radionuclide release rate, average wind speed, and height of release are estimated using the dose rate monitors data collected in proximity of the release point. Further, the estimates are employed to improve the prediction of dose rates. The atmospheric dispersion phenomenon of radioactivity release is modelled using the Gaussian plume model. The Gaussian plume model is then employed for the calculation of dose rates. A variety of atmospheric and accident related scenarios for single source and multiple sources are studied in order to assess the efficacy of the proposed filters. Statistical measures have been used in order to validate the performance of the proposed approaches

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 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

Optimized Filter Design for Non-Differential GPS/IMU Integrated Navigation

The endeavours in improving the performance of a conventional non-differential GPS/MEMS IMU tightly-coupled navigation system through filter design, involving nonlinear filtering methods, inertial sensors' stochastic error modelling and the carrier phase implementation, are described and introduced in this thesis. The main work is summarised as follows. Firstly, the performance evaluation of a recently developed nonlinear filtering method, the Cubature Kalman filter (CKF), is analysed based on the Taylor expansion. The theoretical analysis indicates that the nonlinear filtering method CKF shows its benefits only when implemented in a nonlinear system. Accordingly, a nonlinear attitude expression with direction cosine matrix (DCM) is introduced to tightly-coupled navigation system in order to describe the misalignment between the true and the estimated navigation frames. The simulation and experiment results show that the CKF performs better than the extended Kalman filter (EKF) in the unobservable, large misalignment and GPS outage cases when attitude errors accumulate quickly, rendering the psi-angle expression invalid and subsequently showing certain nonlinearity. Secondly, the use of shaping filter theory to model the inertial sensors' stochastic errors in a navigation Kalman filter is also introduced. The coefficients of the inertial sensors' noises are determined from the Allan variance plot. The shaping filter transfer function is deduced from the power spectral density (PSD) of the noises for both stationary and non-stationary processes. All the coloured noises are modelled together in the navigation Kalman filter according to equivalence theory. The coasting performance shows that the shaping filter based modelling method has a similar and even smaller maximum position drift than the conventional 1st-order Markovian process modelling method during GPS outages, thus indicating its effectiveness. Thirdly, according to the methods of dealing with carrier phase ambiguities, tightly-coupled navigation systems with time differenced carrier phase (TDCP) and total carrier phase (TCP) as Kalman filter measurements are deduced. The simulation and experiment results show that the TDCP can improve the velocity estimation accuracy and smooth trajectories, but position accuracy can only achieve the single point positioning (SPP) level if the TDCP is augmented with the pseudo-range, while the TCP based method's position accuracy can reach the sub-meter level. In order to further improve the position accuracy of the TDCP based method, a particle filter (PF) with modified TDCP observation is implemented in the TDCP/IMU tightly-coupled navigation system. The modified TDCP is defined as the carrier phase difference between the reference and observation epochs. The absolute position accuracy is determined by the reference position accuracy. If the reference position is taken from DGPS, the absolute position accuracy can reach the sub-meter level. For TCP/IMU tightly-coupled navigation systems, because the implementation of TCP in the navigation Kalman filter introduces additional states to the state vector, a hybrid CKF+EKF filtering method with the CKF estimating nonlinear states and the EKF estimating linear states, is proposed to maintain the CKF's benefits while reducing the computational load. The navigation results indicate the effectiveness of the method. After applying the improvements, the performance of a non-differential GPS/MEMS IMU tightly-coupled navigation system can be greatly improved

A Level Set Kalman Filter Approach to Estimate the Circadian Phase and its Uncertainty from Wearable Data

Daily (~24hr) rhythms of behavior and physiology such as sleep and hormone secretion are coordinated by an endogenous timer, the circadian clock. The accurate estimation of the clock state (i.e., the circadian phase) outside of the laboratory has enormous potential for precision medicine. Several methods that predict the phase from measurements collected with wearables (e.g., Apple Watch) have been recently developed. However, computation of the uncertainty in the estimation remains an open problem. The uncertainty analysis is necessary because the estimation accuracy can largely change even by a small perturbation of daily routine. Here, we present a method to account for the uncertainty and estimate the circadian phase using a new extension of Kalman filtering named the level set Kalman filter. Using the newly proposed method, we study the relationship between phase uncertainty and process noise from various sources. This allows the identification of the magnitude of the noise in the circadian system, which is impossible with previous methods. Moreover, our study reveals how much the uncertainty of the phase estimate of the central clock that is inaccessibly located in the brain can be reduced when measurements of the peripheral clock phase are given from wearables. We also show that our method has a performance improvement over the previous methods. Finally, we apply our method to real-world data to further identify its usefulness. These results set the stage for systematically understanding the circadian dynamics in the real world

On the vehicle sideslip angle estimation: a literature review of methods, models and innovations

Typical active safety systems controlling the dynamics of passenger cars rely on real-time monitoring of the vehicle sideslip angle (VSA), together with other signals like wheel angular velocities, steering angle, lateral acceleration, and the rate of rotation about the vertical axis, known as the yaw rate. The VSA (aka attitude or “drifting” angle) is defined as the angle between the vehicle longitudinal axis and the direction of travel, taking the centre of gravity as a reference. It is basically a measure of the misalignment between vehicle orientation and trajectory therefore it is a vital piece of information enabling directional stability assessment, in transients following emergency manoeuvres for instance. As explained in the introduction the VSA is not measured directly for impracticality and it is estimated on the basis of available measurements like wheel velocities, linear and angular accelerations etc. This work is intended to provide a comprehensive literature review on the VSA estimation problem. Two main estimation methods have been categorised, i.e. Observer-based and Neural Network-based, focusing on the most effective and innovative approaches. As the first method normally relies on a vehicle model, a review of the vehicle models has been included. Advantages and limitations of each technique have been highlighted and discussed

Kalman Filtering and its Application to On-Line State Estimation of a Once-Through Boiler

This thesis contributes to non-linear continuous-discrete Kalman filtering of multiplex systems through the development of two main ideas, namely, integration of the unscented transforms with linearly implicit methods and incorporation of simulation errors in the state estimation problem. The newly developed techniques are then applied to the technically relevant problem of state estimation on the main components of a utility boiler. State estimators in industrial systems are used as soft-sensors in monitoring and control applications as the most cost effective and practical alternative to telemetering all variables of interest. One such example is in utility boilers where reliable and real-time data characterising its behaviour is used to detect faults and optimise performance. With respect to the state-of-the-art, state estimators display limitations in real-time applications to large-scale systems. This motivates theoretical developments in state estimation as a first part in this thesis. These developments are aimed at producing more practical and efficient algorithms in non-linear continuous discrete Kalman filtering for stiff large-scale industrial systems. This is achieved using two novel ideas. The first is to exploit the similarities between the extended and unscented Kalman filter in order to estimate the Jacobian required for linearly implicit schemes, thereby tightly coupling state propagation and continuous-time simulation. The second is to account for numerical integration error by appending a stochastic local error model to the system's stochastic differential equation. This allows for coarser integration time steps in systems that are otherwise only suited to relatively small step sizes, making the filter more computationally efficient without lowering its potential to construct accurate estimates. The second part of this thesis uses these algorithms to demonstrate the feasibility of on-line state estimation on the main components of a once-through utility power boiler that require in excess of a hundred state variables to capture its behaviour with adequate fidelity. Two separate models of the boiler are developed, a MATLAB® and a Flownex® model, comprising the economiser, evaporators, reheaters, superheaters and furnace. The mathematical MATLAB® model is better suited to real-time execution and is used in the filter. The more sophisticated model is based on a commercial thermal-hydraulic simulation environment, Flownex® , and is used to validate the mathematical modelling philosophies and construct filter observation data. After validating the performance of the filter against ground-truth data provided by the Flownex® model, the filter is demonstrated on historical plant data to illustrate its utility

Real Time Dynamic State Estimation: Development and Application to Power System

Since the state estimation algorithm has been firstly proposed, considerable research interest has been shown in adapting and applying the different versions of this algorithm to the power transmission systems. Those applications include power system state estimation (PSSE) and short-term operational planning. In the transmission level, state estimation offers various applications including, process monitoring and security monitoring. Recently, distribution systems experience a much higher level of variability and complexity due to the large increase in the penetration level of distributed energy resources (DER), such as distributed generation (DG), demand-responsive loads, and storage devices. The first step, for better situational awareness at the distribution level, is to adapt the most developed real time state estimation algorithm to distribution systems, including distribution system state estimation (DSSE). DSSE has an important role in the operation of the distribution systems. Motivated by the increasing need for robust and accurate real time state estimators, capable of capturing the dynamics of system states and suitable for large-scale distribution networks with a lack of sensors, this thesis introduces a three state estimators based on a distributed approach. The first proposed estimator technique is the square root cubature Kalman filter (SCKF), which is the improved version of cubature Kalman filter (CKF). The second one is based on a combination of the particle filter (PF) and the SCKF, which yields a square root cubature particle filter (SCPF). This technique employs a PF with the proposal distribution provided by the SCKF. Additionally, a combination of PF and CKF, which yields a cubature particle filter (CPF) is proposed. Unlike the other types of filters, the PF is a non-Gaussian algorithm from which a true posterior distribution of the estimated states can be obtained. This permits the replacement of real measurements with pseudo-measurements and allows the calculation to be applied to large-scale networks with a high degree of nonlinearity. This research also provides a comparison study between the above mentioned algorithms and the latest algorithms available in the literature. To validate their robustness and accuracy, the proposed methods were tested and verified using a large range of customer loads with 50 % uncertainty on a connected IEEE 123-bus system. Next, a developed foretasted aided state estimator is proposed. The foretasted aided state estimator is needed to increase the immunization of the state estimator against the delay and loss of the real measurements, due to the sensors malfunction or communication failure. Moreover, due to the lack of measurements in the electrical distribution system, the pseudo-measurements are needed to insure the observability of the state estimator. Therefore, the very short term load forecasting algorithm that insures the observability and provides reliable backup data in case of sensor malfunction or communication failure is proposed. The proposed very short term load forecasting is based on the wavelet recurrent neural network (WRNN). The historical data used to train the RNN are decomposed into low-frequency, low-high frequency and high frequency components. The neural networks are trained using an extended Kalman filter (EKF) for the low frequency component and using a square root cubature Kalman filter (SCKF) for both low-high frequency and high frequency components. To estimate the system states, state estimation algorithm based SCKF is used. The results demonstrate the theoretical and practical advantages of the proposed methodology. Finally, in recent years several cyber-attacks have been recorded against sensitive monitoring systems. Among them is the automatic generation control (AGC) system, a fundamental control system used in all power networks to keep the network frequency at its desired value and for maintaining tie line power exchanges at their scheduled values. Motivated by the increasing need for robust and safe operation of AGCs, this thesis introduces an attack resilient control scheme for the AGC system based on attack detection using real time state estimation. The proposed approach requires redundancy of sensors available at the transmission level in the power network and leverages recent results on attack detection using mixed integer linear programming (MILP). The proposed algorithm detects and identifies the sensors under attack in the presence of noise. The non-attacked sensors are then averaged and made available to the feedback controller. No assumptions about the nature of the attack signal are made. The proposed method is simulated using a large range of attack signals and uncertain sensors measurements. All the proposed algorithms were implemented in MATLAB to verify their theoretical expectations