Adaptive and robust fractional gain based interpolatory cubature Kalman filter

In this study, we put forward the robust fractional gain based interpolatory cubature Kalman filter (FGBICKF) and the adaptive FGBICKF (AFGBICKF) for the development of the state estimators for stochastic nonlinear dynamics system. FGBICKF introduces a fractional gain to interpolatory cubature Kalman filter to increase the robustness of state estimation. AFGBICKF is developed to enhance the state estimation adaptive to stochastic nonlinear dynamics system with unknown process noise covariance through recursive estimation. The simulations on re-entry target tracking system have shown that the performance of FGBICKF is superior to that of cubature Kalman filter and interpolatory cubature Kalman filter, and standard deviation of FGBICKF is closer to posterior Cramér-Rao lower bound. Moreover, our simulations have also demonstrated that AFGBICKF remains stable even when the initial process noise covariance increase, proving its adaptiveness, robustness, and effectiveness on state estimation

Robusni algoritam praćenja mjerenjem smjera pomoću strukturiranog potpunog Kalmanovog filtra zasnovanog na metodi najmanjih kvadrata

A nonlinear approach called the robust structured total least squares kalman filter (RSTLS-KF) algorithm is proposed for solving tracking inaccuracy caused by outliers in bearings-only multi-station passive tracking. In that regard, the robust extremal function is introduced to the weighted structured total least squares (WSTLS) location criterion, and then the improved Danish equivalent weight function is built on the basis, which can identify outliers automatically and reduce the weight of the polluted data. Finally, the observation equation is linearized according to the RSTLS location result with the structured total least norm (STLN) solution. Hence location and velocity of the target can be given by the Kalman filter. Simulation results show that tracking performance of the RSTLS-KF is comparable or better than that of conventional algorithms. Furthermore, when outliers appear, the RSTLS-KF is accurate and robust, whereas the conventional algorithms become distort seriously.U ovome radu predložen je nelinearni pristup za rješavanje netočnosti uzrokovanih netipčnim vrijednostima kod praćenja mjerenjem smjera pasivnim senzorima s više stanica. Pristup je zasnovan na robusnom strukturiranom potpunom Kalmanovom filtru zasnovanom na metodi najmanjih kvadrata. Pomoću predložene metode moguće je estimirati položaj i brzinu praćenog objekta. Simulacijski rezultati pokazuju da je učinkovitost predloženog algoritma jednaka ili bolja od konvencionalnih algoritama. Nadalje, u prisustvu netipčnih vrijednosti mjerenja, predloženi algoritam zadržava točnost i robusnost, dok konvencionalni algoritmi pokazuju pogreške u estimaciji

Enhanced GMM-based Filtering with Measurement Update Ordering and Innovation-based Pruning

The Gaussian mixture model (GMM) has been extensively investigated in nonlinear/non-Gaussian filtering problems. This paper presents two enhancements for GMM-based nonlinear filtering techniques, namely, the adaptive ordering of the measurement update and normalized innovation square (NIS)-based mixture component management. The first technique selects the order of measurement update by maximizing the marginal measurement likelihood to improve performance. The second approach takes the filtering history of a mixture component into account and prunes those components with NIS larger than a threshold to eliminate their impact on the filtering posterior. The advantage of the proposed enhancements is illustrated via simulations that consider source tracking using the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements received at two unmanned aerial vehicles (UAVs). A GMM-cubature quadrature Kalman filter (CQKF) is implemented and its performances with different measurement update and mixture component management strategies are compared. The superior performance obtained via the use of the two proposed techniques is demonstrated

Bayesian Filtering for Dynamic Systems with Applications to Tracking

This M.Sc. thesis intends to evaluate various algorithms based on Bayesian statistical theory and validates with both synthetic data as well as experimental data. The focus is given in comparing the performance of new kind of sequential Monte Carlo filter, called cost reference particle filter, with other Kalman based filters as well as the standard particle filter. Different filtering algorithms based on Kalman filters and those based on sequential Monte Carlo technique are implemented in Matlab. For all linear Gaussian system models, Kalman filter gives the optimal solution. Hence only the cases which do not have linear-Gaussian probabilistic model are analyzed in this thesis. The results of various simulations show that, for those non-linear system models whose probability model can fairly be assumed Gaussian, either Kalman like filters or the sequential Monte Carlo based particle filters can be used. The choice among these filters depends upon various factors such as degree of nonlinearity, order of system state, required accuracy, etc. There is always a tradeoff between the required accuracy and the computational cost. It is found that whenever the probabilistic model of the system cannot be approximated as Gaussian, which is the case in many real world applications like Econometrics, Genetics, etc., the above discussed statistical reference filters degrade in performance. To tackle with this problem, the recently proposed cost reference particle filter is implemented and tested in scenarios where the system model is not Gaussian. The new filter shows good robustness in such scenarios as it does not make any assumption of probabilistic model. The thesis work also includes implementation of the above discussed prediction algorithms into a real world application, where location of a moving robot is tracked using measurements from wireless sensor networks. The flexibility of the cost reference particle filter to adapt to specific applications is explored and is found to perform better than the other filters in tracking of the robot. The results obtained from various experiments show that cost reference particle filter is the best choice whenever there is high uncertainty of the probabilistic model and when these models are not Gaussian. It can also be concluded that,contrary to the general perception, the estimation techniques based on ad-hoc references can actually be more efficient than those based on the usual statistical reference

Probabilistic models for data efficient reinforcement learning

Trial-and-error based reinforcement learning (RL) has seen rapid advancements in recent times, especially with the advent of deep neural networks. However, the standard deep learning methods often overlook the progress made in control theory by treating systems as black-box. We propose a model-based RL framework based on probabilistic Model Predictive Control (MPC). In particular, we propose to learn a probabilistic transition model using Gaussian Processes (GPs) to incorporate model uncertainty into long-term predictions, thereby, reducing the impact of model errors. We provide theoretical guarantees for first-order optimality in the GP-based transition models with deterministic approximate inference for long-term planning. We demonstrate that our approach not only achieves the state-of-the-art data efficiency, but also is a principled way for RL in constrained environments. When the true state of the dynamical system cannot be fully observed the standard model based methods cannot be directly applied. For these systems an additional step of state estimation is needed. We propose distributed message passing for state estimation in non-linear dynamical systems. In particular, we propose to use expectation propagation (EP) to iteratively refine the state estimate, i.e., the Gaussian posterior distribution on the latent state. We show two things: (a) Classical Rauch-Tung-Striebel (RTS) smoothers, such as the extended Kalman smoother (EKS) or the unscented Kalman smoother (UKS), are special cases of our message passing scheme; (b) running the message passing scheme more than once can lead to significant improvements over the classical RTS smoothers. We show the explicit connection between message passing with EP and well-known RTS smoothers and provide a practical implementation of the suggested algorithm. Furthermore, we address convergence issues of EP by generalising this framework to damped updates and the consideration of general -divergences. Probabilistic models can also be used to generate synthetic data. In model based RL we use ’synthetic’ data as a proxy to real environments and in order to achieve high data efficiency. The ability to generate high-fidelity synthetic data is crucial when available (real) data is limited as in RL or where privacy and data protection standards allow only for limited use of the given data, e.g., in medical and financial data-sets. Current state-of-the-art methods for synthetic data generation are based on generative models, such as Generative Adversarial Networks (GANs). Even though GANs have achieved remarkable results in synthetic data generation, they are often challenging to interpret. Furthermore, GAN-based methods can suffer when used with mixed real and categorical variables. Moreover, the loss function (discriminator loss) design itself is problem specific, i.e., the generative model may not be useful for tasks it was not explicitly trained for. In this paper, we propose to use a probabilistic model as a synthetic data generator. Learning the probabilistic model for the data is equivalent to estimating the density of the data. Based on the copula theory, we divide the density estimation task into two parts, i.e., estimating univariate marginals and estimating the multivariate copula density over the univariate marginals. We use normalising flows to learn both the copula density and univariate marginals. We benchmark our method on both simulated and real data-sets in terms of density estimation as well as the ability to generate high-fidelity synthetic data.Open Acces