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

Approximate Bayesian inference methods for stochastic state space models

This thesis collects together research results obtained during my doctoral studies related to approximate Bayesian inference in stochastic state-space models. The published research spans a variety of topics including 1) application of Gaussian filtering in satellite orbit prediction, 2) outlier robust linear regression using variational Bayes (VB) approximation, 3) filtering and smoothing in continuous-discrete Gaussian models using VB approximation and 4) parameter estimation using twisted particle filters. The main goal of the introductory part of the thesis is to connect the results to the general framework of estimation of state and model parameters and present them in a unified manner.Bayesian inference for non-linear state space models generally requires use of approximations, since the exact posterior distribution is readily available only for a few special cases. The approximation methods can be roughly classified into to groups: deterministic methods, where the intractable posterior distribution is approximated from a family of more tractable distributions (e.g. Gaussian and VB approximations), and stochastic sampling based methods (e.g. particle filters). Gaussian approximation refers to directly approximating the posterior with a Gaussian distribution, and can be readily applied for models with Gaussian process and measurement noise. Well known examples are the extended Kalman filter and sigma-point based unscented Kalman filter. The VB method is based on minimizing the Kullback-Leibler divergence of the true posterior with respect to the approximate distribution, chosen from a family of more tractable simpler distributions.The first main contribution of the thesis is the development of a VB approximation for linear regression problems with outlier robust measurement distributions. A broad family of outlier robust distributions can be presented as an infinite mixture of Gaussians, called Gaussian scale mixture models, and include e.g. the t-distribution, the Laplace distribution and the contaminated normal distribution. The VB approximation for the regression problem can be readily extended to the estimation of state space models and is presented in the introductory part.VB approximations can be also used for approximate inference in continuous-discrete Gaussian models, where the dynamics are modeled with stochastic differential equations and measurements are obtained at discrete time instants. The second main contribution is the presentation of a VB approximation for these models and the explanation of how the resulting algorithm connects to the Gaussian filtering and smoothing framework.The third contribution of the thesis is the development of parameter estimation using particle Markov Chain Monte Carlo (PMCMC) method and twisted particle filters. Twisted particle filters are obtained from standard particle filters by applying a special weighting to the sampling law of the filter. The weighting is chosen to minimize the variance of the marginal likelihood estimate, and the resulting particle filter is more efficient than conventional PMCMC algorithms. The exact optimal weighting is generally not available, but can be approximated using the Gaussian filtering and smoothing framework

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

Distributed joint probabilistic data association filter with hybrid fusion strategy

This paper investigates the problem of distributed multitarget tracking (MTT) over a large-scale sensor network, consisting of low-cost sensors. Each local sensor runs a joint probabilistic data association filter to obtain local estimates and communicates with its neighbors for information fusion. The conventional fusion strategies, i.e., consensus on measurement (CM) and consensus on information (CI), are extended to MTT scenarios. This means that data association uncertainty and sensor fusion problems are solved simultaneously. Motivated by the complementary characteristics of these two different fusion approaches, a novel distributed MTT algorithm using a hybrid fusion strategy, e.g., a mix of CM and CI, is proposed. A distributed counting algorithm is incorporated into the tracker to provide the knowledge of the total number of sensor nodes. The new algorithm developed shows advantages in preserving boundedness of local estimates, guaranteeing global convergence to the optimal centralized version and being implemented without requiring no global information, compared with other fusion approaches. Simulations clearly demonstrate the characteristics and tracking performance of the proposed algorithm

5G mmWave Cooperative Positioning and Mapping using Multi-Model PHD Filter and Map Fusion

5G millimeter wave (mmWave) signals can enable accurate positioning in vehicular networks when the base station and vehicles are equipped with large antenna arrays. However, radio-based positioning suffers from multipath signals generated by different types of objects in the physical environment. Multipath can be turned into a benefit, by building up a radio map (comprising the number of objects, object type, and object state) and using this map to exploit all available signal paths for positioning. We propose a new method for cooperative vehicle positioning and mapping of the radio environment, comprising a multiple-model probability hypothesis density filter and a map fusion routine, which is able to consider different types of objects and different fields of views. Simulation results demonstrate the performance of the proposed method.Comment: This work has been accepted in the IEEE Transactions on Wireless Communication

5G mmWave Cooperative Positioning and Mapping Using Multi-Model PHD Filter and Map Fusion

5G millimeter wave (mmWave) signals can enable accurate positioning in vehicular networks when the base station and vehicles are equipped with large antenna arrays. However, radio-based positioning suffers from multipath signals generated by different types of objects in the physical environment. Multipath can be turned into a benefit, by building up a radio map (comprising the number of objects, object type, and object state) and using this map to exploit all available signal paths for positioning. We propose a new method for cooperative vehicle positioning and mapping of the radio environment, comprising a multiple-model probability hypothesis density filter and a map fusion routine, which is able to consider different types of objects and different fields of views. Simulation results demonstrate the performance of the proposed method

Poisson Multi-Bernoulli Mixtures for Multiple Object Tracking

Multi-object tracking (MOT) refers to the process of estimating object trajectories of interest based on sequences of noisy sensor measurements obtained from multiple sources. Nowadays, MOT has found applications in numerous areas, including, e.g., air traffic control, maritime navigation, remote sensing, intelligent video surveillance, and more recently environmental perception, which is a key enabling technology in automated vehicles. This thesis studies Poisson multi-Bernoulli mixture (PMBM) conjugate priors for MOT. Finite Set Statistics provides an elegant Bayesian formulation of MOT based on random finite sets (RFSs), and a significant trend in RFSs-based MOT is the development of conjugate distributions in Bayesian probability theory, such as the PMBM distributions. Multi-object conjugate priors are of great interest as they provide families of distributions that are suitable to work with when seeking accurate approximations to the true posterior distributions. Many RFS-based MOT approaches are only concerned with multi-object filtering without attempting to estimate object trajectories. An appealing approach to building trajectories is by computing the multi-object densities on sets of trajectories. This leads to the development of many multi-object filters based on sets of trajectories, e.g., the trajectory PMBM filters. In this thesis, [Paper A] and [Paper B] consider the problem of point object tracking where an object generates at most one measurement per time scan. In [Paper A], a multi-scan implementation of trajectory PMBM filters via dual decomposition is presented. In [Paper B], a multi-trajectory particle smoother using backward simulation is presented for computing the multi-object posterior for sets of trajectories using a sequence of multi-object filtering densities and a multi-object dynamic model. [Paper C] and [Paper D] consider the problem of extended object tracking where an object may generate multiple measurements per time scan. In [Paper C], an extended object Poisson multi-Bernoulli (PMB) filter is presented, where the PMBM posterior density after the update step is approximated as a PMB. In [Paper D], a trajectory PMB filter for extended object tracking using belief propagation is presented, where the efficient PMB approximation is enabled by leveraging the PMBM conjugacy and the factor graph formulation

Distributed target tracking in wireless camera networks

PhDDistributed target tracking (DTT) is desirable in wireless camera networks to achieve scalability and robustness to node or link failures. DTT estimates the target state via information exchange and fusion among cameras. This thesis proposes new DTT algorithms to handle five major challenges of DTT in wireless camera networks, namely non-linearity in the camera measurement model, temporary lack of measurements (benightedness) due to limited field of view, redundant information in the network, limited connectivity of the network due to limited communication ranges and asynchronous information caused by varying and unknown frame processing delays. The algorithms consist of two phases, namely estimation and fusion. In the estimation phase, the cameras process their captured frames, detect the target, and estimate the target state (location and velocity) and its uncertainty using the Extended Information Filter (EIF) that handles non-linearity. In the fusion phase, the cameras exchange their local target information with their communicative neighbours and fuse the information. The contributions of this thesis are as follows. The target states estimated by the EIFs undergo weighted fusion. The weights are chosen based on the estimated uncertainty (error covariance) and the number of nodes with redundant information such that the information of benighted nodes and the redundant information get lower weights. At each time step, only the cameras having the view of the target and the cameras that might have the view of the target in the next time step participate in the fusion (tracking). This reduces the energy consumption of the network. The algorithm selects the cameras dynamically by using a threshold on their shortest distances (in the communication graph) from the cameras having the view of the target. Before fusion, each camera predicts the target information of other cameras to temporally align its information with the (asynchronous) information received from other cameras. The algorithm predicts the target state using the latest estimated velocity of the target. The experimental results show that the proposed algorithms achieve higher tracking accuracy than the state of the art under the five DTT challenges

Approximate Gaussian Conjugacy: Parametric Recursive Filtering Under Nonlinearity, Multimodal, Uncertainty, and Constraint, and Beyond

This is a post-peer-review, pre-copyedit version of an article published in Frontiers of Information Technology & Electronic Engineering. The final authenticated version is available online at: https://doi.org/10.1631/FITEE.1700379Since 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

Cooperative Perception for Social Driving in Connected Vehicle Traffic

The development of autonomous vehicle technology has moved to the center of automotive research in recent decades. In the foreseeable future, road vehicles at all levels of automation and connectivity will be required to operate safely in a hybrid traffic where human operated vehicles (HOVs) and fully and semi-autonomous vehicles (AVs) coexist. Having an accurate and reliable perception of the road is an important requirement for achieving this objective. This dissertation addresses some of the associated challenges via developing a human-like social driver model and devising a decentralized cooperative perception framework. A human-like driver model can aid the development of AVs by building an understanding of interactions among human drivers and AVs in a hybrid traffic, therefore facilitating an efficient and safe integration. The presented social driver model categorizes and defines the driver\u27s psychological decision factors in mathematical representations (target force, object force, and lane force). A model predictive control (MPC) is then employed for the motion planning by evaluating the prevailing social forces and considering the kinematics of the controlled vehicle as well as other operating constraints to ensure a safe maneuver in a way that mimics the predictive nature of the human driver\u27s decision making process. A hierarchical model predictive control structure is also proposed, where an additional upper level controller aggregates the social forces over a longer prediction horizon upon the availability of an extended perception of the upcoming traffic via vehicular networking. Based on the prediction of the upper level controller, a sequence of reference lanes is passed to a lower level controller to track while avoiding local obstacles. This hierarchical scheme helps reduce unnecessary lane changes resulting in smoother maneuvers. The dynamic vehicular communication environment requires a robust framework that must consistently evaluate and exploit the set of communicated information for the purpose of improving the perception of a participating vehicle beyond the limitations. This dissertation presents a decentralized cooperative perception framework that considers uncertainties in traffic measurements and allows scalability (for various settings of traffic density, participation rate, etc.). The framework utilizes a Bhattacharyya distance filter (BDF) for data association and a fast covariance intersection fusion scheme (FCI) for the data fusion processes. The conservatism of the covariance intersection fusion scheme is investigated in comparison to the traditional Kalman filter (KF), and two different fusion architectures: sensor-to-sensor and sensor-to-system track fusion are evaluated. The performance of the overall proposed framework is demonstrated via Monte Carlo simulations with a set of empirical communications models and traffic microsimulations where each connected vehicle asynchronously broadcasts its local perception consisting of estimates of the motion states of self and neighboring vehicles along with the corresponding uncertainty measures of the estimates. The evaluated framework includes a vehicle-to-vehicle (V2V) communication model that considers intermittent communications as well as a model that takes into account dynamic changes in an individual vehicle’s sensors’ FoV in accordance with the prevailing traffic conditions. The results show the presence of optimality in participation rate, where increasing participation rate beyond a certain level adversely affects the delay in packet delivery and the computational complexity in data association and fusion processes increase without a significant improvement in the achieved accuracy via the cooperative perception. In a highly dense traffic environment, the vehicular network can often be congested leading to limited bandwidth availability at high participation rates of the connected vehicles in the cooperative perception scheme. To alleviate the bandwidth utilization issues, an information-value discriminating networking scheme is proposed, where each sender broadcasts selectively chosen perception data based on the novelty-value of information. The potential benefits of these approaches include, but are not limited to, the reduction of bandwidth bottle-necking and the minimization of the computational cost of data association and fusion post processing of the shared perception data at receiving nodes. It is argued that the proposed information-value discriminating communication scheme can alleviate these adverse effects without sacrificing the fidelity of the perception