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

Quadratic estimation for stochastic systems in the presence of random parameter matrices, time-correlated additive noise and deception attacks

This research was suported by the ``Ministerio de Ciencia e Innovación, Agencia Estatal de Investigación'' of Spain and the European Regional Development Fund [grant number PID2021-124486NB-I00].Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of suboptimal estimators. Among them, the LS quadratic estimation approach has attracted considerable interest in the scientific community for its balance between computational complexity and estimation accuracy. When it comes to stochastic systems subject to different random uncertainties and deception attacks, the quadratic estimator design has not been deeply studied. In this paper, using covariance information, the LS quadratic filtering and fixed-point smoothing problems are addressed under the assumption that the measurements are perturbed by a time-correlated additive noise, as well as affected by random parameter matrices and exposed to random deception attacks. The use of random parameter matrices covers a wide range of common uncertainties and random failures, thus better reflecting the engineering reality. The signal and observation vectors are augmented by stacking the original vectors with their second-order Kronecker powers; then, the linear estimator of the original signal based on the augmented observations provides the required quadratic estimator. A simulation example illustrates the superiority of the proposed quadratic estimators over the conventional linear ones and the effect of the deception attacks on the estimation performance.Ministerio de Ciencia e Innovación MICINNEuropean Regional Development Fund PID2021-124486NB-I00 ERDFAgencia Estatal de Investigación AE

Variance-Constrained H∞H_{\infty } finite-horizon filtering for multi-rate time-varying networked systems based on stochastic protocols

summary:In this paper, the variance-constrained $H_\infty$ finite-horizon filtering problem is investigated for a class of time-varying nonlinear system under muti-rate communication network and stochastic protocol (SP). The stochastic protocol is employed to determine which sensor obtains access to the muti-rate communication network in order to relieve communication burden. A novel mapping technology is applied to characterize the randomly switching behavior of the data transmission resulting from the utilization of the SP in muti-rate communication network. By using relaxation method, sufficient conditions are derived for the existence of the finite-horizon filter satisfying both the prescribed $H_\infty$ performance and the covariance requirement of filtering errors, and the solutions of filters satisfying the above indexes are obtained by using linear matrix inequalities. Finally, the validity and effectiveness of the proposed filter scheme are verified by numerical simulation

Localization Algorithms for GNSS-denied and Challenging Environments

In this dissertation, the problem about localization in GNSS-denied and challenging environments is addressed. Specifically, the challenging environments discussed in this dissertation include two different types, environments including only low-resolution features and environments containing moving objects. To achieve accurate pose estimates, the errors are always bounded through matching observations from sensors with surrounding environments. These challenging environments, unfortunately, would bring troubles into matching related methods, such as fingerprint matching, and ICP. For instance, in environments with low-resolution features, the on-board sensor measurements could match to multiple positions on a map, which creates ambiguity; in environments with moving objects included, the accuracy of the estimated localization is affected by the moving objects when performing matching. In this dissertation, two sensor fusion based strategies are proposed to solve localization problems with respect to these two types of challenging environments, respectively. For environments with only low-resolution features, such as flying over sea or desert, a multi-agent localization algorithm using pairwise communication with ranging and magnetic anomaly measurements is proposed in this dissertation. A scalable framework is then presented to extend the multi-agent localization algorithm to be suitable for a large group of agents (e.g., 128 agents) through applying CI algorithm. The simulation results show that the proposed algorithm is able to deal with large group sizes, achieve 10 meters level localization performance with 180 km traveling distance, while under restrictive communication constraints. For environments including moving objects, lidar-inertial-based solutions are proposed and tested in this dissertation. Inspired by the CI algorithm presented above, a potential solution using multiple features motions estimate and tracking is analyzed. In order to improve the performance and effectiveness of the potential solution, a lidar-inertial based SLAM algorithm is then proposed. In this method, an efficient tightly-coupled iterated Kalman filter with a build-in dynamic object filter is designed as the front-end of the SLAM algorithm, and the factor graph strategy using a scan context technology as the loop closure detection is utilized as the back-end. The performance of the proposed lidar-inertial based SLAM algorithm is evaluated with several data sets collected in environments including moving objects, and compared with the state-of-the-art lidar-inertial based SLAM algorithms