The motion of sensors during the measurement period, if not accounted for, can degrade significantly the localization accuracy. This paper investigates the sensor motion effect for the positioning of an object, using angles of arrival only or together with time of arrival measurements. The biases from the AOA and TOA data models when ignoring the motion effect are examined. Positioning algorithms for AOA localization and mixed AOA-TOA localization that account for the motion effect are developed by the pseudo-linear formulation. The algorithms derived include the computationally attractive closed-form estimators and the noise resilient semidefinite programming solutions. The bias coming from the pseudo-linear formulation is analyzed in detail, and it can be subtracted from the closed-form solution to obtain a bias-suppressed estimate. Simulation validates the effectiveness of the proposed solutions in achieving the CRLB performance under Gaussian noise before the thresholding effect occurs.

Mitigating Sensor Motion Effect for AOA and AOA-TOA Localizations in Underwater Environments

The accuracy and robustness of tightly coupled GNSS/SINS integrated navigation parameter estimation are hindered by outliers caused by GNSS measurements under multipath interference and non-line-of-sight (NLOS) conditions. To address the limitations of robust estimation and the mismatch of state posterior PDF approximation, a novel M-estimation-based robust iterated cubature kalman filter (ICKF) is developed to minimize the impact of GNSS outliers while improving the correction effect of high-quality LOS GNSS measurement in this paper. The nonlinear weighted least squares regression model and objective function are established for outlier mitigation, including a sigma-point iterative filtering framework and an M-estimation method of down-weighting GNSS measurements. Specifically, the maximum a posteriori (MAP) estimation idea is used to design the sigma-point iterated filtering framework, which makes the posteriori probability density function (PDF) constantly close to the high likelihood confidence interval to obtain excellent nonlinear approximation effects. Furthermore, to avoid the inherent non-convexity of the traditional M-estimation method, the relaxation compensation scheme based on the adaptive control factor is introduced into the robust loss function to accelerate the convergence of the penalty weight of GNSS outliers. The availability of the proposed method for GNSS outlier mitigation is proved by vehicle field tests under multipath interference and NLOS conditions. 

Robust M-Estimation-Based ICKF for GNSS Outlier Mitigation in GNSS/SINS Navigation Applications

Accurately obtaining the navigation information of the device is crucial for realizing various emerging Internet of Things (IoT) applications, and a multisource fusion navigation system is the key to achieving this goal. A distributed integrated inertial navigation system (INS), polarization compass (PC), and geomagnetic compass (MAG) enhanced direction approach is presented to improve the accuracy and robustness of the multisource fusion navigation system in complex environments. To estimate the time-varying measurement noise covariance in a nonlinear multisource fusion navigation system, the traditional federated Kalman filter (FKF) is improved. In the FKF framework, the third-order spherical radial cubature rule and variational Bayesian (VB) theory are introduced, and a VB federated cubature Kalman filter (VBFCKF) is proposed. Furthermore, a distributed information monitoring and compensation algorithm based on residuals is developed to address issues like anomalous measured values and asynchronous multirate problems. Finally, an experimental platform for unmanned vehicle navigation is designed, and the tests are conducted to confirm the efficacy of the suggested approach. The experimental results show that the system can precisely estimate values based on the measurement quality of subfilters during navigation. It effectively adjusts measurement noise covariance during updates, thereby mitigating the negative impact of interferences like occlusions and electromagnetic noise on the multisource fusion navigation system in complex environments. This can strengthen the accuracy and robustness of the navigation system.

Information Monitoring and Adaptive Information Fusion of Multi-Source Fusion Navigation Systems in Complex Environments

Dynamic short-delay multipath in increasing dense urban canyons is a challenge to the global navigation satellite system (GNSS)-based positioning systems. However, the performance of existing multipath methods for a stand-alone receiver is limited on dealing with short-delay multipath. Vector tracking-based deep coupling with an inertial navigation system (INS) has the potential to suppress multipath errors by tracking direct signals using more accurate and robust positions. However, in the typical deep couplings reported, the unmodeled multipath error is generally regarded as noise with other errors, and consequently, their capacity for multipath suppression is not satisfying. To solve these problems, an improved deep coupling structure with a multipath error estimator (MPEE) is proposed and implemented in two schemes. Different from other methods, this modification creates nearly no extra complexity and computation cost. In this way, the inner correlation caused by multipath interference between channels can be decoupled, and the underlying requirements for modeling the errors accurately to construct vector feedback are fulfilled. Besides, for comparison analysis, a software-defined platform, including different tracking and integration approaches, is designed. Finally, the proposed methods are evaluated in a weak signal, short-delay multipath, dynamic multipath, and the real-life multipath scenarios, and their superiority in positioning, measurement improvement, and tracking robustness are validated.

Design and Performance Evaluation of the Improved INS-Assisted Vector Tracking for the Multipath in Urban Canyons


 In ship navigation, the most widely used technology is Global Navigation Satellite Systems (GNSS), which provide the ship’s position and velocity continuously over a period of time. However, when ships are blocked by port buildings or bridges, the quality of signals received from shipborne GNSS receivers may be reduced, resulting in inaccurate ship positioning that poses a risk to navigational safety. In an occluded environment, the measurement process during the signal processing of shipborne GNSS receivers is nonstationary and prone to measurement anomalies, which can contaminate measurement noise with outliers. To address this problem, a cascaded non-coherent vector tracking loop (VTL) is designed, with the Maximum correntropy Kalman filter (MCKF) serving as a cascaded carrier/code pre-filter for shipborne GNSS receivers. The measurement noise covariance matrix of the pre-filter is adaptively calculated and corrected using the carrier-to-noise ratio (CNR) and the maximum correntropy criterion, respectively. The algorithm proposed is more sensitive to outliers than the traditional tracking methods and can effectively solve the state estimation problem under the condition of measurement anomalies. Specifically, the algorithm offers ships with more precise position and velocity estimations and lower signal tracking errors than traditional tracking methods under both static and dynamic conditions, as demonstrated by shipboard experiments. The horizontal positioning is increased by 88.4% and the horizontal velocity error is reduced by 62.1% in the occluded environment under dynamic conditions.

A MCKF-based Cascade Vector Tracking Method Designed for Ship Navigation

A well-designed carrier tracking loop in a receiver of the Global Navigation Satellite System (GNSS) is the premise of accurate positioning and navigation in an aircraft-based surveying and mapping system. To deal with the problems of Doppler estimation in high-dynamic maneuvers, the interest on maximum-likelihood estimation (MLE) is increasing among the academic community. Levenberg-Marquardt (LM) method is usually regarded as an effective and promising approach to obtain the solution of MLE, but the computation of Hessian matrix loads a great burden on the algorithm. Besides, a poor performance on convergency in final iterations is the common failing of LM implementations. To solve these problems, an LM method based on Gauss-Newton and a Quasi-Newton (QN) method based on Hessian approximation are derived, making the computation cost of Hessian decline from O(N) to O(1). Then, on the basis of these two methods, a closed carrier loop with adaptive LM-QN algorithm is further proposed which can switch between LM and QN adaptively according to a damping parameter. Besides, an ideal LM with super-linear convergence (SLM) is constructed and proved as a reference of the convergence analysis. Finally, through the analyses and experiments using aircraft data, the improvements on computation cost and convergence are verified. Compared with scalar tracking and vector tracking, results indicate a magnitude increase in the precision of LM-QN loop, even though more computation counts are needed by LM-QN.

A Novel Carrier Loop Based on Adaptive LM-QN Method in GNSS Receivers

For improving the navigation ability of the INS/CNS/GNSS system in the non-Gaussian noise environment, a novel navigation algorithm based on maximum correntropy generalized high-degree CKF (MCHCKF) is proposed. First, the INS/GNSS and INS/CNS systems obtain the sub-states by the MCHCKF algorithm, respectively. Then, according to the minimum variance criterion and cubature rule, the sub-state estimations are fused to get the global state. Finally, the superior performance of the proposed method is proved in the missile-borne navigation simulation system.

A Novel INS/CNS/GNSS Integrated Navigation Algorithm

The traditional receiver employs scalar tracking loops, resulting in degraded navigation performance in weak signal and high dynamic scenarios. An innovative design of a vector tracking receiver based on nonlinear Kalman filter (KF) tracking loops is proposed in this paper, which combines the strengths of both vector tracking and KF-based tracking loops. First, a comprehensive description of the vector tracking receiver model is presented, and unscented Kalman filter (UKF) is applied to nonlinear tracking loop. Second, to enhance the stability and robustness of the KF tracking loop, we introduce square root filtering and an adaptive mechanism. The tracking loop based on square root UKF (SRUKF) can dynamically adjust its filtering parameters based on signal noise and feedback Doppler error. Finally, the proposed method is implemented on a software-defined receiver (SDR), and the field vehicle experiment demonstrates the superiority of this method over other tracking methods in complex dynamic environments.

Performance Enhancement and Evaluation of a Vector Tracking Receiver Using Adaptive Tracking Loops

An INS-assisted vector tracking receiver with multipath error estimation for dense urban canyons

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