Strong Tracking Filter for Nonlinear Systems with Randomly Delayed Measurements and Correlated Noises

This paper proposes a novel strong tracking filter (STF), which is suitable for dealing with the filtering problem of nonlinear systems when the following cases occur: that is, the constructed model does not match the actual system, the measurements have the one-step random delay, and the process and measurement noises are correlated at the same epoch. Firstly, a framework of decoupling filter (DF) based on equivalent model transformation is derived. Further, according to the framework of DF, a new extended Kalman filtering (EKF) algorithm via using first-order linearization approximation is developed. Secondly, the computational process of the suboptimal fading factor is derived on the basis of the extended orthogonality principle (EOP). Thirdly, the ultimate form of the proposed STF is obtained by introducing the suboptimal fading factor into the above EKF algorithm. The proposed STF can automatically tune the suboptimal fading factor on the basis of the residuals between available and predicted measurements and further the gain matrices of the proposed STF tune online to improve the filtering performance. Finally, the effectiveness of the proposed STF has been proved through numerical simulation experiments

Composite Disturbance Filtering: A Novel State Estimation Scheme for Systems With Multi-Source, Heterogeneous, and Isomeric Disturbances

State estimation has long been a fundamental problem in signal processing and control areas. The main challenge is to design filters with ability to reject or attenuate various disturbances. With the arrival of big data era, the disturbances of complicated systems are physically multi-source, mathematically heterogenous, affecting the system dynamics via isomeric (additive, multiplicative and recessive) channels, and deeply coupled with each other. In traditional filtering schemes, the multi-source heterogenous disturbances are usually simplified as a lumped one so that the "single" disturbance can be either rejected or attenuated. Since the pioneering work in 2012, a novel state estimation methodology called {\it composite disturbance filtering} (CDF) has been proposed, which deals with the multi-source, heterogenous, and isomeric disturbances based on their specific characteristics. With the CDF, enhanced anti-disturbance capability can be achieved via refined quantification, effective separation, and simultaneous rejection and attenuation of the disturbances. In this paper, an overview of the CDF scheme is provided, which includes the basic principle, general design procedure, application scenarios (e.g. alignment, localization and navigation), and future research directions. In summary, it is expected that the CDF offers an effective tool for state estimation, especially in the presence of multi-source heterogeneous disturbances

Distributed estimation over a low-cost sensor network: a review of state-of-the-art

Proliferation of low-cost, lightweight, and power efficient sensors and advances in networked systems enable the employment of multiple sensors. Distributed estimation provides a scalable and fault-robust fusion framework with a peer-to-peer communication architecture. For this reason, there seems to be a real need for a critical review of existing and, more importantly, recent advances in the domain of distributed estimation over a low-cost sensor network. This paper presents a comprehensive review of the state-of-the-art solutions in this research area, exploring their characteristics, advantages, and challenging issues. Additionally, several open problems and future avenues of research are highlighted

Strong Tracking Filtering Algorithm of Randomly Delayed Measurements for Nonlinear Systems

This paper focuses on the filtering problems of nonlinear discrete-time stochastic dynamic systems, such as the model simplification, noise characteristics uncertainty, initial conditions uncertainty, or system parametric variation. Under these circumstances, the measurements of system have one sampling time random delay. A new method, that is, strong tracking filtering algorithm of randomly delayed measurements (STF/RDM) for nonlinear systems based on recursive operating by analytical computation and first-order linear approximations, is proposed; a principle of extended orthogonality is presented as a criterion of designing the STF/RDM, and through the residuals between available and predicted measurements, the formula of fading factor is obtained. Under the premise of using the extended orthogonality principle, STF/RDM proposed in this paper can adjust the fading factor online via calculating the covariance of residuals, and then the gain matrices of the STF/RDM adjust in real time to enhance the performance of the proposed method. Lastly, in order to prove that the performance of STF/RDM precedes existing EKF method, the experiment of tracking maneuvering aircraft is carried out

New on-board multipurpose architecture integrating modern estimation techniques for generalized GNSS based autonomous orbit navigation

This dissertation investigates a novel Multipurpose Earth Orbit Navigation System (MEONS) architecture aiming at providing a generalized GNSS based spacecraft orbit estimation kernel matching the modern navigation instance of enhanced flexibility with respect to multiple Space Service Volume (SSV) applications (Precise Orbit Determination for Earth Observation satellite, Low Thrust Low to High Autonomous Orbit Rising, formation flying relative navigation, Small Satellite Autonomous Orbit Acquisition). The possibility to address theoretical and operational solutions within a unified framework is a foundamental step for the implementation of a reusable and configurable high performance navigation capability on next generation platforms

Algorithms for Positioning with Nonlinear Measurement Models and Heavy-tailed and Asymmetric Distributed Additive Noise

Determining the unknown position of a user equipment using measurements obtained from transmitters with known locations generally results in a nonlinear measurement function. The measurement errors can have a heavy-tailed and/ or skewed distribution, and the likelihood function can be multimodal.A positioning problem with a nonlinear measurement function is often solved by a nonlinear least squares (NLS) method or, when filtering is desired, by an extended Kalman filter (EKF). However, these methods are unable to capture multiple peaks of the likelihood function and do not address heavy-tailedness or skewness. Approximating the likelihood by a Gaussian mixture (GM) and using a GM filter (GMF) solves the problem. The drawback is that the approximation requires a large number of components in the GM for a precise approximation, which makes it unsuitable for real-time positioning on small mobile devices.This thesis studies a generalised version of Gaussian mixtures, which is called GGM, to capture multiple peaks. It relaxes the GM’s restriction to non-negative component weights. The analysis shows that the GGM allows a significant reduction of the number of required Gaussian components when applied for approximating the measurement likelihood of a transmitter with an isotropic antenna, compared with the GM. Therefore, the GGM facilitates real-time positioning in small mobile devices. In tests for a cellular telephone network and for an ultra-wideband network the GGM and its filter provide significantly better positioning accuracy than the NLS and the EKF.For positioning with nonlinear measurement models, and heavytailed and skewed distributed measurement errors, an Expectation Maximisation (EM) algorithm is studied. The EM algorithm is compared with a standard NLS algorithm in simulations and tests with realistic emulated data from a long term evolution network. The EM algorithm is more robust to measurement outliers. If the errors in training and positioning data are similar distributed, then the EM algorithm yields significantly better position estimates than the NLS method. The improvement in accuracy and precision comes at the cost of moderately higher computational demand and higher vulnerability to changing patterns in the error distribution (of training and positioning data). This vulnerability is caused by the fact that the skew-t distribution (used in EM) has 4 parameters while the normal distribution (used in NLS) has only 2. Hence the skew-t yields a closer fit than the normal distribution of the pattern in the training data. However, on the downside if patterns in training and positioning data vary than the skew-t fit is not necessarily a better fit than the normal fit, which weakens the EM algorithm’s positioning accuracy and precision. This concept of reduced generalisability due to overfitting is a basic rule of machine learning.This thesis additionally shows how parameters of heavy-tailed and skewed error distributions can be fitted to training data. It furthermore gives an overview on other parametric methods for solving the positioning method, how training data is handled and summarised for them, how positioning is done by them, and how they compare with nonparametric methods. These methods are analysed by extensive tests in a wireless area network, which shows the strength and weaknesses of each method