In practical applications, the topology of a sensor network is commonly time-varying and even unknown, but almost all existing networked filtering methods rely on this unavailable topology information. In view of this, we investigate a topology ignorant communication scheme that does not need to know the topology of the network, where nodes use only neighboring information to trigger their activations. The triggering condition considers the estimation accuracy which benefits the purpose of networked filtering (i.e., distributed filtering in sensor network). With this communication mode, we propose a filter: self triggered activation based distributed filter (STA-DF). Its convergence to the centralized estimation along with iteration length and stability are analyzed. Simulation results are provided to verify its superiority to existing methods.

Received signal strength (RSS) measurements can be converted to the distance estimates between the emission source and the sensors to construct a system of linear equations, thereby allowing for the use of the weighted linear least squares (WLLS) estimators for location estimation. However, estimating the squared distances from the RSS measurements governed by the log-normal shadowing effect presents a major challenge in such approaches. In this paper, we propose a linear minimum mean square error (LMMSE) estimator of the squared distance between the emission source and the sensor first. Then a LMMSE-aided WLLS (LMMSE-WLLS) location estimator and its unbiased counterpart are presented for source localization. Furthermore, their estimation performance are analyzed in terms of mean square error (MSE) and covariance. It is found that the proposed LMMSE-aided WLLS location estimators have better estimation performance than existing WLLS estimators. Numerical examples also demonstrate the performance superiority of the proposed location estimators for source localization.

The problem of association of measurements acquired by passive bearings-only sensors in two dimensional (2D) plane is addressed in this paper. This problem can be formulated mathematically as a multidimensional assignment (MDA) problem with two steps of cost calculation and optimization. Compared with the optimization step, the cost calculation consumes more time (at least 80%; of the total time for solving the MDA problem). In order to reduce the computational requirements of the assignment costs of infeasible associations, a practical coarse gating strategy is proposed. First, two bearing measurements from different sensors are used to predict the bearing measurements of other sensors. Then, infeasible associations can be identified using gates centered on the predicted bearing measurements. This strategy is also extended to the measurement data association of heterogeneous sensors. Numerical examples verify the effectiveness of the proposed strategy.

Abstract Joint Cramér‐Rao lower bound (JCRLB) is very useful for the performance evaluation of joint state and parameter estimation (JSPE) of non‐linear systems, in which the current measurement only depends on the current state. However, in reality, the non‐linear systems with two‐adjacent‐states dependent (TASD) measurements, that is, the current measurement is dependent on the current state as well as the most recent previous state, are also common. First, the recursive JCRLB for the general form of such non‐linear systems with unknown deterministic parameters is developed. Its relationships with the posterior CRLB for systems with TASD measurements and the hybrid CRLB for regular parametric systems are also provided. Then, the recursive JCRLBs for two special forms of parametric systems with TASD measurements, in which the measurement noises are autocorrelated or cross‐correlated with the process noises at one time step apart, are presented, respectively. Illustrative examples in radar target tracking show the effectiveness of the JCRLB for the performance evaluation of parametric TASD systems.

Joint state and parameter estimation (JSPE) has a surge of interest due to its dual purposes in many fields, such as sensor registration and signal processing. In this letter, a recursive joint Cramér-Rao lower bound (JCRLB) is developed for JSPE of nonlinear parametric systems with cross-correlated process and measurement noises at the same time. The JCRLBs for two special cases of such systems with additive Gaussian noises are also studied. Illustrative examples show the effectiveness of the JCRLB for the performance evaluation of JSPE of nonlinear parametric systems with cross-correlated noises at the same time.

The Kalman filter has successful applications in many fields. The applicability of the standard Kalman filter critically hinges on the accurate prior knowledge of all the system model parameters. However, in practical applications, it can be difficult or unrealistic to obtain these parameters, in which case it is a common practice to employ some pre-determined alternatives for the unknown model parameters. This letter investigates the case of unknown initial state priors by assessing how their pre-determined alternatives affect the performance of the Kalman filter. The ranking of three types of mean squared errors is established. It is found that the definiteness of the initial state prior deviation is critical, which determine the ranking of the three types of mean squared errors. Such results provide guideline on the choice of the pre-determined initial state prior. Numerical examples are provided to validate the results.

Angle of arrival (AOA) and received signal strength (RSS) measurements have been commonly used in wireless localization due to easy access and simple implementation. In this paper, we investigate source localization using the AOA-only and hybrid RSS/AOA measurements, respectively. In AOA localization, we approximate the angle error using a range-related quantity. Then the optimization problem based on maximum likelihood (ML) is converted to a convex semidefinite programming (SDP) problem. In hybrid AOA/RSS localization, the ML estimator is decomposed into an RSS part and an AOA part. The AOA part follows a similar procedure as in the AOA localization. Taylor series expansion and relaxation are applied in optimizing the RSS part. These two parts are closely related through the range. The proposed methods avoid the nonconvexity in the original ML estimators for both AOA-only and hybrid AOA/RSS localization problems. Numerical examples show good performance of the proposed methods in both AOA and hybrid AOA/RSS localizations. They are close to or better than the LS methods in the literature.

In transportation networks, the majority of moving vehicles are route-based or trajectory-scheduled. Taking advantage of such predictive information generally produces more accurate dynamic models and better surveillance performance. This paper is concerned with the route-based dynamic modeling along with the route-aided tracking. First, the evolution of the positions across the route is formulated as a stationary Markov process from the characteristics of the route-based dynamics, which follows that the second- and third-order models of the straight-line route-based motions are constructed. This novel modeling strategy is in reverse to the conventional ones starting from the acceleration and its resultant dynamic models are easy to implement due to the linearity with respect to the system states. Second, an optimal initialization technique for route-aided tracking is proposed by utilizing the stationary process information sufficiently. Furthermore, an extension to the circular route-based dynamic modeling and a combinational modeling structure are also presented. Finally, in the context of aerial surveillance, numerical simulations are provided to show the effectiveness of the proposed dynamic modeling and to verify the theoretical results given in the paper.

Source localization is of great importance for wireless sensor network applications. Locating emission sources using received signal strength (RSS) measurements is investigated in this paper. As RSS localization is a non-convex optimization problem, it is difficult to achieve global optima. Many optimization methods have been proposed to relax it to a convex optimization problem. Unlike these methods, we propose a convex combination scheme. By introducing a highly accurate linear approximation of a logarithmic function, the source location is represented by a convex combination of a set of virtual anchors. Then the original problem is relaxed to be a convex optimization problem of finding the optimal combination coefficients, which can be solved efficiently using constrained least squares. To obtain the virtual nodes, we construct parallel lines and use their intersections to form a convex polygon, which covers the source location with certain probability. The vertices of the polygon are taken as the virtual nodes. Numerical examples verify the performance of the proposed method in both localization accuracy and computational efficiency.

A lot of performance evaluation metrics exist for nonlinear filters. At present, the most commonly used one is a single and incomprehensive metric of performance. This metric can continuously and quantitatively describe the performance of the nonlinear filters. But in many cases, we need to rank the performance of the filters. It is in general very hard to rank the filters just using a single metric. First, the rankings using a single metric at different times may be different. Then how to get a unique rank for all times? A typical existing solution is to average the single metric over all times. But it is easy to be dominated just by very large values at just some times. Second, a single metric is usually incomprehensive in measuring performance. To make the ranking more comprehensive, multiple metrics are usually needed. But how to get a comprehensive unique rank from the ranks, possibly conflicting with each other? In this paper, we propose a framework to rank multiple nonlinear filters using ranking vectors and voting fusion based on a single metric or multiple metrics. Illustrative examples show that this framework is very effective.

Emission source localization and sensor registration using received signal strength (RSS) measurements is investigated. Previous studies for RSS localization assume that the sensors receiving signals are bias free, which is not the case in practice. This issue is taken into consideration in this paper for the localization problem. To avoid non-convexity of the global optimization problem for the traditional maximum likelihood (ML) or least squares (LS) estimation, we present novel semidefinite programming methods, linear least squares (LLS) and constrained LS (CLS) methods by approximating and linearizing the original model. The methods are divided into two types: URSS and DRSS. The former estimates the source location and sensor bias simultaneously while the latter estimates the sensor bias after localizing the source. Numerical examples show that our proposed methods have good performance. Some of them are close to the Cramer-Rao Lower Bound (CRLB).

We present a drift-free pose estimation scheme for rigid body and its supporting platform by fusing only two gyroscopes and the relative complementary measurements. The fusion design not only provides robust relative attitude estimation between the rigid body and the platform, but also is capable of identifying partial global absolute attitudes without capturing any absolute attitude information. The pose estimation is built on a special design of the coupled kinematic model with the relative measurements between the rigid body and its supporting platform. We compare the fusion design with an alternative kinematic model and the posterior Cramer-Rao bound analyses are presented to show the completely different estimation performances. An extended Kalman filter (EKF) implementation of the fusion design is presented for the bicycle riding application.

The transformation of belief function into probability is one of the most important and common ways for decision making under the framework of evidence theory. In this paper, we focus on the evaluation of such probability transformations (PTs), which are crucial for their proper applications and the design of new ones. Shannon entropy or probabilistic information content (PIC) measure is traditionally used in evaluating PTs. The transformation having the lowest entropy or highest PIC is considered as the best one. This standpoint is questioned in this paper by comparing a PT based on uncertainty minimization with other available PTs. It shows experimentally that entropy or PIC is not comprehensive to evaluate a PT. To make a comprehensive evaluation, some new approaches are proposed by the joint use of PIC and the distance of evidence according to the value- and rank-based fusion. A pattern classification application oriented evaluation approach for PTs is also proposed. Some desired properties for PTs are also discussed. Experimental results and related analysis are provided to show the rationality of the new evaluation approaches.

The commonly used root‐mean‐square error for estimation performance evaluation is easily dominated by large error terms. So many new alternative absolute metrics have been provided in X. R. Li's work. However, each of these metrics only reflects one narrow aspect of estimation performance, respectively. A comprehensive measure, error spectrum, was presented aggregating all these incomprehensive measures. However, when being applied to dynamic systems, this measure will have three dimensions over the total time span, which is not intuitive and difficult to be analysed. To overcome its drawbacks, a new metric, dynamic error spectrum (DES), is proposed in this study to extend the error spectrum measure to dynamic systems. Three forms under different application backgrounds are given, one of which is balanced taking into account both good and bad behaviour of an estimator and so can provide more impartial evaluation results. It can be applied to a variety of dynamic systems directly. Then the challenge in performance evaluation of the interacting multiple model (IMM) algorithm is considered, and the IMM algorithm is chosen as the testing case to illustrate the superiority of the DES metric. The simulation results validate its utility and effectiveness.

Reconstruction of signaling pathway structures is essential to decipher complex regulatory relationships in living cells. Existing approaches often rely on unrealistic biological assumptions and do not explicitly consider signal transduction mechanisms. Signal transduction events refer to linear cascades of reactions from cell surface to nucleus and characterize a signaling pathway. We propose a novel approach, Gene Set Gibbs Sampling, to reverse engineer signaling pathway structures from gene sets related to pathways. We hypothesize that signaling pathways are structurally an ensemble of overlapping linear signal transduction events which we encode as Information Flows (IFs). We infer signaling pathway structures from gene sets, referred to as Information Flow Gene Sets (IFGSs), corresponding to these events. Thus, an IFGS only reflects which genes appear in the underlying IF but not their ordering. GSGS offers a Gibbs sampling procedure to reconstruct the underlying signaling pathway structure by sequentially inferring IFs from the overlapping IFGSs related to the pathway. In the proof-of-concept studies, our approach is shown to outperform existing network inference approaches using data generated from benchmark networks in DREAM. We perform a sensitivity analysis to assess the robustness of our approach. Finally, we implement GSGS to reconstruct signaling mechanisms in breast cancer cells.