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In received signal strength (RSS) based radio source localisation, RSS measurements can be converted to the squared distance estimates between the emission source and the sensors to construct a system of pseudolinear equations, allowing for the use of the weighted linear least squares (WLLS) estimators for location estimation. The WLLS estimators are widely applied in practice because of their simplicity and computational efficiency. Nevertheless, the major challenge of this approach lies in estimating the squared distance from RSS measurements governed by the log‐normal shadowing effect. A pseudo conditional distribution (PCD) of the squared distance between the emission source and the sensor is introduced first, given the RSS measurement at each sensor. Then, the authors propose a series of new WLLS location estimators, using three typical statistical characteristics, that is, mean, median, and mode, of the PCD. Analysis of their estimation performance are also provided through performance rankings in terms of their mean square errors and covariances. It is found that estimation performance of the PCD‐induced WLLS estimators heavily depends on the choice of the statistical characteristic of the PCD and different choices lead to estimators with better, worse, or equal performance. Numerical examples show that the proposed mode‐WLLS estimator always performs better than the existing WLLS estimators, and also better than the existing convex optimisation based algorithms in most cases but with much less computations. [ABSTRACT FROM AUTHOR]

The performance evaluation of state estimators for nonlinear regular systems, in which the current measurement only depends on the current state directly, has been widely studied using the Bayesian Cramér-Rao lower bound (BCRLB). However, in practice, the measurements of many nonlinear systems are two-adjacent-states dependent (TASD) directly, i.e., the current measurement depends on the current state as well as the most recent previous state directly. In this paper, we first develop the recursive BCRLBs for the prediction and smoothing of nonlinear systems with TASD measurements. A comparison between the recursive BCRLBs for TASD systems and nonlinear regular systems is provided. Then, the recursive BCRLBs for the prediction and smoothing of two special types of TASD systems, in which the original 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 proposed recursive BCRLBs for the prediction and smoothing of TASD systems. [ABSTRACT FROM AUTHOR]

Goal-guided behavior and destination-directed motion appear in a wide range of human activities and physical processes. Taking advantage of such predictive information can produce better system models and state estimates. This paper focuses on modeling and filtering issues of linear dynamic systems with linear destination constraints. We examine deficiencies of the existing destination constrained (DC) estimation methods. Basically, they resort to post-treatment by imposing destination constraints on updated states only. Viewing destination constraints as an attribute implicit of the state evolution, we propose to incorporate the destination constraints accordingly, particularly on the predictive distribution of the whole state sequence. We construct a congruous DC dynamic model by sufficiently refining the relaxed dynamics with the destination constraint using the state augmentation technique, and analyze its characterization and properties. Next, for the proposed DC model, we develop an optimal DC state estimator and describe its properties. Finally, in the context of aerial surveillance, the superiority of the proposed estimator to existing DC estimators is verified by simulation results, and the effectiveness of the proposed DC dynamic model is demonstrated using real data. [ABSTRACT FROM AUTHOR]

Cooperative localization in wireless sensor network (WSN) using biased received signal strength (RSS) measurements is investigated in this letter. In the existing work on cooperative RSS localization, measurements of sensor nodes (including both target-anchor and target-target measurements) are generally assumed bias-free. However, in practice, they may be subject to biases, which directly affect localization accuracy. As a result, the existing localization methods are not applicable any more. In this letter, RSS observation biases are considered as the extra parameters to be estimated as well as locations of target nodes. To overcome the nonconvexity of the maximum likelihood (ML) estimator, semidefinite programming (SDP) is applied with $l_{1}$ and $l_{2}$ norms, respectively. Then, the locations of multiple target nodes and observation biases are simultaneously estimated through convex optimization. Numerical examples demonstrate the performance superiority of the proposed methods compared to the existing bias-free SDP methods for wireless cooperative localization. [ABSTRACT FROM AUTHOR]

The coordinated turn (CT) model is often used to track maneuvering target which performs CT motion. The key point to the successful use of this model is to determine the turn rate parameter. A new method to estimate the turn rate by using radar range-rate measurements is presented. First, four possible turn rates can be achieved with the range-rate measurements. Second, the minimum turn rate and its opposite value are chosen to be the possible turn rates. Finally, an interacting multiple model (IMM) algorithm with one constant velocity (CV) model and two CT models is designed to track the maneuvering target which performs uniform and ct motions. Monte-Carlo simulation results show that this algorithm is not only better than equivalent noise approach in tracking performance, but also better than the conventional IMM algorithm with the adaptive turn rate model. Further simulations show that the algorithm is robust with the accuracy of the range-rate measurements.

In this note, we show that there exists a compatibility problem in the derivation of the mean and covariance of the converted measurement errors in [1], and then present a modification to the computation of them, in which both the mean and the covariance are computed strictly conditioned on the measurements.

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. [ABSTRACT FROM AUTHOR]

Received signal strength (RSS)-based techniques are promising for location estimation because of low cost and easy implementation. RSS measurements can be used to determine the location of a receiver, given the positions of multiple emitters. In addition, RSS measurements at receivers with known positions can be used to determine the location of an emitter. This article investigates both 3-D receiver navigation and source localization using RSS measurements. In practice, sensor measurements are often biased owing to design problems or other effects. However, almost all existing methods deal with bias-free cases. In contrast, we focus on biased cases. For both receiver navigation and source localization, we propose united-RSS (URSS) and differential-RSS (DRSS) approaches, where URSS estimates the location and sensor bias together, while DRSS estimates the location by eliminating the effect of bias. They are based on semidefinite programming and constrained least squares, respectively. The proposed methods avoid the nonconvexity in the maximum likelihood method. Numerical examples verify the necessity for sensor registration in RSS-based location estimation and show better performance of the proposed methods. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The Kalman filter is a powerful recursive state estimator and has been widely used in many applications. To guarantee its optimality, the noise covariances should to be exactly known. In reality, however, for most practical applications, it is difficult or unrealistic to obtain the noise covariances. A typical practice is to use some pre‐determined alternatives for unknown noise covariances. The main issue concerning this is how the pre‐determined alternatives will affect the performance of the Kalman filter. In this study, the authors study recursive performance ranking of Kalman filter with mismatched noise covariances. For this purpose, three types of mean squared errors (MSEs) have been used, i.e., the ideal MSE (IMSE), the filter calculated MSE (FMSE), and the true MSE (TMSE). This study considers the recursive ranking of these three types of MSEs at each time step. It is found that for the case with positive semi‐definite deviation from the truth, they have FMSE ⪰ TMSE ⪰ IMSE at each time step recursively. On the contrary, for the case with negative semi‐definite deviation, they have TMSE ⪰ IMSE ⪰ FMSE at each time step recursively. Target tracking examples further verify these results. [ABSTRACT FROM AUTHOR]

Many outdoor activities, such as bicycling, driving, and riding segways can be modeled as rigid bodies on a moving platform. In this study, an attitude estimation scheme is established for the rigid body-moving platform system by using two gyroscopes and relative measurements between the rigid body and the platform. The proposed scheme estimates the drift-free attitudes of the rigid body and the partial drift-free absolute attitudes of the platform without using any global information or reference. The kinematic model plays an important role to obtain the drift-free estimation of the absolute attitude angles. To illustrate this, the estimation scheme is compared to another design with an alternative kinematic model. The estimation result differences between the two designs are analyzed through observability and posterior Cramer–Rao bound calculations. Extensive experiments are also conducted to demonstrate the performance of the proposed attitude estimation scheme with application to bicycle riding examples. [ABSTRACT FROM AUTHOR]

Due to the complexity of practical systems, the used models generally mismatch the practical ones. For the Kalman filtering with a single mismatched measurement noise covariance, the ranking of the ideal MSE (IMSE), the filter calculated MSE (FMSE), and the true MSE (TMSE) has been established. This study considers the ranking of the relative closenesses from the FMSE and TMSE to the IMSE when multiple mismatched measurement noise covariances are used. It is found that for the case with two deviations of the same signs, the larger the absolute deviation is, the farther away the FMSE or TMSE is from the IMSE. It is also found that for the case with two deviations of different signs, if the positive deviations are less than the absolute value of the negative deviation, then the FMSE or TMSE with positive deviation is relatively closer to the IMSE. Otherwise the ranking of the two corresponding relative closenesses depends on the parallel sum of two deviations with a non‐zero threshold. Then the pair‐wised ranking of the relative closenesses corresponding to two arbitrary deviations is further extended to the case with more than two deviations. Numerical examples are provided to validate the results. [ABSTRACT FROM AUTHOR]

Due to physical laws or mathematical properties the states of some dynamic systems satisfy certain constraints, and taking advantage of such constraints generally will produce more accurate system models. This paper is concerned with dynamic modeling and state estimation of equality constrained systems. First, an effective framework for constrained dynamic modeling is proposed by which equality constraints and an original dynamics are optimally fused. In particular, modeling of linear and quadratic equality constrained dynamic systems is systematically investigated. Meanwhile, the effects of the original dynamics on the constructed dynamic model are analyzed. Next, properties of the constrained state estimation are presented, and in particular, the constrained minimum mean square error (CMMSE) estimator is proposed and its differences from the conventional constrained estimators are illustrated. Finally, the proposed modeling is assessed on benchmark scenarios of road-confined vehicle tracking. Simulation results demonstrate that the proposed CMMSE estimator outperforms the conventional constrained ones. [ABSTRACT FROM AUTHOR]

The generalized Hermitian eigenvalue problem (GHEP) is of great use in modern signal processing. Compared with other methods, neural network model based algorithms provide an efficient way to solve such problems online. Up to now, a class of neural network model based generalized feature extraction algorithms have been reported in the literature. However, most existing noncoupled algorithms suffer from the so-called speed-stability problem. In contrast, coupled learning algorithms estimate the generalized eigenvector and generalized eigenvalue simultaneously in coupled manners. Therefore they can solve the speed-stability problem and perform better than noncoupled algorithms. In this paper, we first propose a coupled generalized system, which is obtained by using the Newton’s method and a novel generalized information criterion. Then, based on this coupled generalized system, we successfully obtain two coupled algorithms with normalization steps for minor/principal generalized eigen-pairs extraction. And the technique of multiple generalized eigen-pairs extraction is also introduced in this paper. The convergence of the proposed algorithms is justified by deterministic discrete-time (DDT) approach, with the efficiency and feasibility validated by experimental results as well. Compared with similar work, the proposed algorithms have lower computational complexity, better numerical stability and higher estimation accuracy. [ABSTRACT FROM AUTHOR]

Straight line motion is a fundamental target motion. Its modeling has been well studied for unconstrained targets (e.g., air targets). However, existing straight line motion models cannot be directly used for tracks constrained on a straight line, which has wide application, e.g., in ground target tracking. In this paper, modeling of the target motion constrained on a straight line is considered. First, linear equality constraints imposed by the straight line are set up explicitly. Then both direct elimination and along-track motion projection are applied to obtain two forms of constrained motion models. Connections between the two forms are studied. For the first form, conditions that guarantee the traditional linear Gaussian assumption are obtained. For the second form, conditions under which the motion along each axis is similar to the along-track motion are obtained. Supporting numerical examples are also provided. [ABSTRACT FROM PUBLISHER]

Estimation for discrete-time stochastic systems with parameters varying in a continuous space is considered in this paper. Justified by an analysis of model approximation, a novel approach, called hybrid grid multiple model (HGMM), is proposed for state estimation. The model set used by HGMM is a combination of a fixed coarse grid and an adaptive fine grid to cover the mode space with a relatively small number of models. Next, two fundamental problems of the HGMM approach?model-set sequence-conditioned estimation and design of adaptive fine models?are addressed. Then, based on two model-set designs by moment matching, HGMM estimation algorithms are presented. Finally, performance of the developed HGMM estimation algorithms is evaluated on benchmark tracking scenarios, and simulation results demonstrate their superiority to the state-of-the-art MM estimation algorithms in terms of accuracy and computational complexity. [ABSTRACT FROM AUTHOR]

The state of many dynamic systems evolves subject to some equality constraints. Most existing work focuses on developing state estimation algorithms for an equality-constrained dynamic system assuming the system is given. How to design and analyze such a system is rarely addressed, even though it is critically important for application and performance evaluation. In this paper, we first analyze the underlying structural information of linear equality-constrained (LEC) dynamic systems through direct elimination. It is found that the process noise of such a system is state dependent in general. This means that existing formulations of such a system are quite limited. Based on the analysis, we then propose a new systematic way to design LEC systems. The key idea is to design only the unconstrained part of the system. Unlike existing system conversion-based design techniques, in our work the desired model class is given and only the distributions of the initial state and process noise need to be determined, which is comparatively easier. To handle state dependency of the process noise, a new constrained state estimation algorithm based on direct elimination is also proposed. Three examples are provided to illustrate the effectiveness of the proposed methods of analysis, design, and estimation, respectively. [ABSTRACT FROM PUBLISHER]