Range-based Target Localization Research Articles

Denoising, Outlier/Dropout Correction, and Sensor Selection in Range-Based Positioning

Range-based target localization combines the range measurements and appropriate algorithms [such as time of arrival (TOA)] to determine the real-time position of a moving target not only in a satellite-denied environment but also for high-precision applications in an open (i.e., satellite-available) environment. However, the measurements from sensors always suffer from uncertainties, such as noises, outliers, dropouts, and biases, which make measurements not reliable enough to directly utilize in positioning. This article is, therefore, concerned with two kinds of sensor correction problems: 1) attenuating the noises, removing the outliers, and completing the dropouts and 2) identifying the discredited sensors and forbidding them from use. Specifically, we model a range measurement time series from a ranging sensor as a nonstationary stochastic process and then use a local polynomial to regress the mean function in an online manner. The derivatives of the mean function are identified as the state variables in the state space, and the Kalman filter is used to estimate the states. We will show that: 1) the proposed method is simple yet effective in denoising the measurements and correcting the outliers/dropouts with very high accuracy and precision and 2) the defined and estimated states can clearly reflect the pattern of one type of nonspecific anomaly contained in the range time series, which enables the recognition of the dysfunctional sensors.

Range-based target localization and pursuit with autonomous vehicles: An approach using posterior CRLB and model predictive control

We address the general problem of multiple target localization and pursuit using measurements of the ranges from the targets to a set of autonomous pursuing vehicles, referred to as trackers. We develop a general framework for targets with models exhibiting uncertainty in the initial state, process, and measurement noise. The main objective is to compute optimal motions for the trackers that maximize the range-based information available for target localization and at the same time yield good target pursuit performance. The solution proposed is rooted in an estimation-theoretical setting that involves the computation of an appropriately defined Bayesian Fisher Information Matrix (FIM). The inverse of the latter yields a posterior Cramér–Rao Lower Bound (CRLB) on the covariance of the targets’ state estimation errors that can be possibly achieved with any estimator. Using the FIM, sufficient conditions on the trackers’ motions are derived for the ideal relative geometry between the trackers and the targets for which the range information acquired is maximal. This allows for an intuitive understanding of the types of ideal tracker trajectories. To deal with realistic constraints on the trackers’ motions and the requirement that the trackers pursue the targets, we then propose a model predictive control (MPC) framework for optimal tracker motion generation with a view to maximizing the predicted range information for target localization while taking explicitly into account the trackers’ dynamics, strict constraints on the trackers’ states and inputs, and prior knowledge about the targets’ states. The efficacy of the MPC is assessed in simulation through the help of representative examples motivated by operational scenarios involving single and multiple targets and trackers.

Adaptive Range-Based Target Localization Using Diffusion Gauss–Newton Method in Industrial Environments

In a noisy manufacturing environment, range-based target localization for wireless sensor networks (WSNs) experiences various variations in range measurements, thus causing the unsatisfactory results. Starting from an empirical observation on the existing various industrial noise distribution, in this paper, a diffusion Gauss–Newton (GN) algorithm with cooperation strategy is proposed for solving target localization non linear-least-squares problem in a WSN. The proposed algorithm has an equalization effect on the unbalance noise distribution over the network by aggregating the global estimates into local GN update via diffusion strategy. When facing a hostile industrial environment where the ambient noise is heterogeneous or has the sudden changes across partial nodes, the significant performance degradation is produced by diffusion GN. To solve the problem, we propose further an improved version of diffusion GN, which is adaptive to sudden changes on noisy range measurements. Instead of using a static combiner, the new algorithm leverages the evolutionary game theory to assign a time-varying weight for the estimate from each neighboring node based on the individual range error. Consequently, the good estimates from the neighbors with high SNR have a larger weight in the combiner than the bad estimates caused by the low SNR or high noise. We also propose a simple but effective energy-accuracy tradeoff scheme by using a sigmoidal utility function. Some simulation examples show that the standard diffusion GN is effective in stationary noise and its improved version provides the adaptation to changing noisy environment. The effectiveness of energy–accuracy tradeoff is also validated.

A bisection-based approach for exact target localization in NLOS environments

This work addresses the range-based target localization problem in adverse non-line-of-sight (NLOS) environments. We start by deriving the maximum likelihood (ML) estimator from the measurement model, since it is asymptotically efficient. However, this estimator is highly non-convex and difficult to solve directly. Hence, we convert the localization problem into a generalized trust region sub-problem (GTRS) framework. Although still non-convex in general, the derived estimator is strictly decreasing over a readily obtained interval, and thus, can be solved exactly by a bisection procedure. In huge contrast to existing algorithms, which either require the knowledge about the magnitude of the NLOS bias or to a priori distinguish between line-of-sight (LOS) and NLOS links, the new one does not require such prerequisites. Also, the computational complexity of the proposed algorithm is linear in the number of reference nodes, unlike the majority of existing ones. Our simulation results show that the new algorithm possesses a steady NLOS bias mitigation capacity and that it represents an excellent alternative in the sense of the trade off between accuracy and complexity. To be more specific, it not only matches the performance of existing methods (majority of which significantly more computationally complex) but outperforms them in general. Moreover, the performance of the proposed algorithm is validated through real-indoor experimental data.