Profile-based Maximum Penalised Likelihood Trajectory Estimation from Space-borne LOS Measurements

Estimating the boost-phase trajectory of a ballistic missile using line of sight measurements from space-borne passive sensors is an important issue in missile defense. A well-known difficulty of this issue is the poor-observability of the target motion. A profile-based maximum penalised likelihood estimator is presented, which is expected to work in poor-observability scenarios. Firstly, a more adaptable boost-phase profile is proposed by introducing unknown parameters. Then, the estimator is given based on the Bayesian paradigm. After that, a special penalty for box constraint is constructed based on a mixed distribution. Numerical results for some typical scenarios and sensitivity with respect to a priori information are reported to show that the proposed estimator is promising

New Viewpoints about Pseudo Measurements Method in Equality-Constrained State Estimation

We discuss the pseudo measurement method which is one of the main approaches to equality-constrained state estimation for a dynamic system. We demonstrate by the fundamental theory of Kalman filtering that reviewing the equality constraint as a pseudo measurement seems questionable. The main reason is that the additional pseudo measurement is actually a constant here which cannot help to estimate the state. More specifically, when the states in an unconstrained dynamic system model have already satisfied the equality constraint, the extra constraint is obviously not necessary. When the true equality-constrained states do not satisfy the unconstrained dynamic process equation, the effect of pseudo measurement is projecting the estimate which is not optimal onto the constraint set. However, since the performance of a projected estimate is also certainly influenced by its original estimate, we show through a numerical example that the pseudo measurement method is not always a good choice, especially when the process equation mismatch is large

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

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

Processamento do status de dispositivos chaveáveis como informação a priori na estimação integrada de estados e topologia em sistemas elétricos de potência

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Elétrica, Florianópolis, 2015.Este trabalho apresenta uma proposta para a estimação simultânea das variáveis de estado e da topologia da rede no contexto da modelagem em tempo real do sistema elétrico de potência. O método considera a modelagem no nível de seção de barra para parte do sistema, de modo que as subestações selecionadas são representadas de forma explícita pelos disjuntores, chaves e conexões que as formam. A metodologia proposta é baseada nas informações disponíveis sobre os \emph{status} de tais dispositivos, que são tratadas como informação \emph{a priori} da topologia para ser processada por um estimador especializado. O resultado abrange não somente estimativas para os estados convencionais do sistema, mas também para a topologia da rede. Desta maneira, a topologia presumida é, ao final do processo, validada ou corrigida com base nas informações contidas nas medidas analógicas disponíveis ao estimador de estados. Para resolver o problema de Estimação Integrada de Estados e Topologia, utiliza-se neste trabalho a formulação pelo método dos mínimos quadrados ponderados, cuja solução é obtida mediante um algoritmo baseado na versão rápida das rotações ortogonais de Givens. Entretanto, a dissertação também aborda o processamento de erros grosseiros tendo por base outros algoritmos de estimação de estados fundamentados no método dos mínimos quadrados ponderados. O desempenho da estimação integrada de estados e topologia é avaliado e validado através da sua aplicação aos sistemas-teste IEEE 14, 30 e 57 barras.Abstract : This research addresses the simultaneous estimation of state variables and network topology in the context of power system real-time modeling. The proposed method assumes that selected substations are modeled at the bus section level, so that the corresponding circuit breakers and disconnects are explicitly represented. Available information on the statuses of such switching branches are then treated as a priori topology information to be processed by a specialized estimator. Its outcome comprises estimates not only for the conventional states, but also for the network topology. Therefore, the initially assumed topology will eventually be either validated or corrected, on the basis of the information conveyed by real-time measurements to the state estimator. To solve the integrated state and topology estimation problem, the problem is formulated by using the weighted least-squares method and an algorithm based on a fast version of orthogonal Givens rotations is employed. Furthermore, it is shown that the bad data processing capabilities of weighted least-squares state estimators are preserved. The performance and validation of the joint estimator is assessed through its application to IEEE 14-bus, 30-bus and 57-bus test systems