In challenging environments, conventional positioning algorithms often exhibit performance degradation due to outlier-contaminated sensor measurements. To address this issue, this paper proposes a robust localization method based on regularization with adaptive scaling (RAS). The proposed method introduces the scaling factor to characterize the amplification of noise variance caused by outliers and integrates them within a probabilistic model. RAS factor graph optimization (FGO) is developed as a robust localization method based on the prior probability distribution of the scaling factor, and is derived from the maximum a posteriori (MAP) estimation to suppress the influence of abnormal measurements. A data-driven parameter calibration approach is also proposed to avoid manual tuning. Theoretical analysis is further conducted to examine the robustness of RAS FGO. The influence of the prior distribution parameters of the scaling factor on the suppression of abnormal measurements loss is investigated. It is also shown that the Weighted Least Squares and the Switchable Constraints methods are special cases of RAS FGO. Experimental results on the Google Smartphone Decimeter Challenge datasets demonstrate that the proposed method significantly outperforms traditional FGO in terms of both accuracy and robustness, particularly in scenarios with frequent measurement anomalies. In representative scenarios, the 3D RMSE decreases from 18.87 m to 4.77 m, which corresponds to a reduction of 74.72%. In addition, the 95% cumulative 3D error decreases from 18.13 m to 8.16 m, representing a reduction of 54.99%.

We present a two-dimensional relative pose estimation framework for cooperative unmanned ground vehicles that fuses two-way ranging with phase-difference-of-arrival (PDoA) measurements from multi-antenna UWB modules. The fusion significantly improves observability by exploiting mutual orientation information. To resolve PDoA phase ambiguities, we introduce a wavevector-norm-consistency-based unwrapping algorithm that outputs per-pair quality metrics. These metrics are integrated into a robust adaptive optimization combining quality-weighted Huber loss with a shortest-path initialization, effectively mitigating outliers and initialization sensitivity. Simulations and real-world experiments demonstrate superior robustness and accuracy over conventional approaches, especially under phase ambiguity and outlier conditions.

With the growing reliance on Global Navigation Satellite System (GNSS) for navigation and positioning in autonomous systems, the vulnerability to spoofing attacks has emerged as a critical concern. The increasing deployment of dual-frequency GNSS receivers in vehicular applications has drawn attention to their potential for efficient spoofing detection. Dual-Frequency Doppler Consistency Checking (DFDCC) offers an intuitive approach by assessing the Doppler consistency between two frequency signals. This method not only enables the identification of spoofed signals but also exhibits robustness and flexibility in vehicular scenarios. Despite its practical advantages, DFDCC currently lacks a comprehensive theoretical framework and detailed performance analysis, particularly in the context of vehicular applications. To bridge these gaps, this study aims to develop a theoretical foundation and evaluate the real-world applicability and effectiveness of DFDCC in vehicular scenarios. The paper begins by deriving a Doppler observation model for both authentic and spoofing signals, deriving key sources of Doppler bias. These include the deviation between false and real user states, the spoofer clock bias, and the relative velocity between the spoofer and the user. Besides, extensive simulation experiments are conducted to analyze the influence of these factors on DFDCC performance, revealing an offset phenomenon when multiple factors coexist. This method is further validated through field tests under three typical vehicular motion patterns, demonstrating its feasibility across diverse vehicular scenarios. The results confirm that DFDCC is a viable solution for spoofing detection for autonomous vehicles, offering valuable insights for its practical implementation and serving as a reference for future research.

Autonomous in-pipe inspection robots can automatically navigate through complex pipeline networks and detect potential risks from corrosion and defects, demonstrating great potential for replacing costly manual inspections. However, there is no publicly available simulation environment where researchers can validate their in-pipe navigation algorithms as far as we know, and the navigation algorithms on constrained 3D pipe surface which is the critical software component are less discussed. Firstly, this paper proposes an open-source In-Pipe Navigation Development Environment. It contains various pipeline models, a magnetic wheel climbing robot model realized by the adhesion plugin, and baseline algorithms for navigation tasks. Secondly, a novel effective path planning method is introduced. Instead of planning based on surface structures, the proposed method plans based on pipeline axis and maps it into local path using the Frenet-Serret formula, thereby generating smooth, feasible, and efficient paths. Finally, we conduct both qualitative and quantitative experiments in the proposed simulation and real-world environments. The results show the usability of the development environment, also robustness and efficiency of the proposed planning method.

In a time-division broadcast positioning system (TDBPS), localizing mobile targets using classical time difference of arrival (TDOA) methods poses significant challenges. Concurrent TDOA measurements are infeasible because targets receive signals from different anchors and extract their transmission times at different reception times, as well as at varying positions. Traditional TDOA estimation schemes implicitly assume that the target remains stationary during the measurement period, which is impractical for mobile targets exhibiting high dynamics. Existing methods for mobile target localization are mostly specialized and rely on motion modeling and do not rely on the concurrent TDOA measurements. This issue limits their direct use of the well-established classical TDOA-based localization methods and complicating the entire localization process. In this article, to obtain concurrent TDOA estimates at any instant out of the sequential measurements for direct use of existing TDOA-based localization methods, we propose a novel TDOA estimation method, termed parameterized TDOA (P-TDOA). By approximating the time-varying TDOA as a polynomial function over a short period, we transform the TDOA estimation problem into a model parameter estimation problem and derive the desired TDOA estimates thereafter. Theoretical analysis shows that, under certain conditions, the proposed P-TDOA method closely approaches the Cramér–Rao Lower Bound (CRLB) for TDOA estimation in concurrent measurement scenarios, despite measurements being obtained sequentially. Extensive numerical simulations validate our theoretical analysis and demonstrate the effectiveness of the proposed method, highlighting substantial improvements over existing approaches across various scenarios.

In indoor environments, conventional Global Navigation Satellite System (GNSS) is difficult to provide accurate localization due to signal interference. In this paper, we propose a robust single-point localization technique using downlink TDOAAOA fusion for self-localization systems, which can be applied to hierarchical self-organized wireless sensor network (WSN) to provide tags with localization that does not consume communication bandwidth. The positioning algorithm proposed in this paper utilizes a planar antenna array to receive the broadcast signal from base stations (BS), and constructs a nonlinear least-squares optimization problem to achieve single-point localization by fusing the time difference of arrival (TDOA) and angle of arrival (AOA) measurements. Aiming at the non-line-of-sight (NLOS) problem in real indoor scenarios, we establish an outlier isolation strategy (OIS) based on the geometrical constraints between the tag and BS, which is combined with M-estimation to realize the robust localization algorithm. Real-world experiments conducted in an underground parking lot verify the feasibility and localization accuracy of the proposed technique.

Carrier phase positioning with indoor pseudolite can achieve high-precision positioning and has received extensive attention. Correct ambiguity resolution (AR) is the key to carrier phase positioning. However, the complex indoor environment has serious blocking, which can lead to signal interference and cycle slips. Existing methods, like the OTF method and the KPI method, are unable to deal with these problems. This paper proposes a single epoch carrier phase positioning algorithm for indoor pseudolite systems, which is more resistant to interference and cycle slips. The algorithm consists of a positioning algorithm and a validation algorithm. The positioning algorithm searches in the ambiguity domain for the smallest carrier phase residuals to achieve AR, and then realizes high-precision positioning. The validation algorithm evaluates positioning results through the residual ratio and eliminates the positioning results that may have errors. Numerical simulation proves the effectiveness of this algorithm.

The accuracy of ionospheric delay modeling for user stations is intimately tied to the precise characterization of the ionospheric information in the domain of Global Navigation Satellite Systems (GNSSs). Current methods for model identification often face difficulties due to the scarcity of data from limited and sparsely located ground reference stations, and the irregular ionospheric characteristics during active periods. This is particularly true in active low latitudes, where disturbances, including GNSS signal scintillation and influence outcomes. This article introduces a universal framework, termed the global and local consistency methodology (GLCM), dedicated to extracting ionospheric spatial information by aligning estimated characteristics across global and subset spatial information. The proposed model adheres to a specifically designed objective to generate the appropriate form of functions and, based on them, to derive the ionospheric information for given areas. We carried out the simulation test to intuitively demonstrate the capabilities to improve the accuracy of the model in a direct and noninterference way. In addition, the model has been verified based on real-world data at low latitudes from a network of ground GNSS stations from all visible Global Position System (GPS) and GALILEO (GAL) satellites. The model achieves a reduction in the root-mean-square error (RMSE) of differential slant total electron content (dSTEC) by approximately 18% and 15% compared with the multiquadratic model and the Kriging model, respectively, during periods of high ionospheric activity. The proposed model has demonstrated effectiveness in ionospheric modeling and is actively being adapted for a wide range of GNSS applications and beyond.

In this paper, we propose a simple method, termed TWO, of directly closing the loop for LiDAR odometry. TWO suggests assigning high weights to the LIDAR observations corresponding to the old parts of the map; since these parts are built with the low-drift poses from the early odometry and can help drag the drifted odometry back to the correct global position when the LiDAR scans the points of these parts again. Also, we present the method of checking the consistency of the plane normal to address the two-side problem that may cause damage when using TWO. Moreover, we show that the proposed method is lightweight and needs little extra computation and storage space compared to the original odometry. The proposed TWO is integrated into the state-of-the-art LiDAR odometry A-LOAM and LiDAR-inertial odometry FAST-LIO2, and it is tested thoroughly on five public datasets and our private handheld dataset. The experiments show that the TWO can effectively help these two methods directly close most loops and produce localization results with apparently lower drifts.

The self-localization of wireless sensor networks (WSNs) is facing the problem of insufficient positioning accuracy in indoor environment due to multipath and interference issues. At the same time, without external references, through mutual measurement nodes can calculate only a set of relative coordinates. Therefore, it is difficult to achieve the mapping of coordinate values to the physical world. The development of simultaneous localization and mapping (SLAM) technologies has provided new opportunities to solve the above problems by making it easier to obtain real-time indoor maps. This article proposes a Lidar-assisted self-localization (LASL) technique to further improve the localization accuracy of WSNs in indoor scenes by combining spatial constraint information obtained from real-time maps, and to place the relative node coordinate network in the visualized maps. Based on the general assumption that the nodes are deployed on the surface of the object, the proposed technique combines the spatial constraints obtained by plane fitting of a local point cloud map (PCM) and finite-area approximation of object surfaces with the distance constraints provided by radio ranging. Subsequently, the self-localization results under the joint constraints are solved by the alternating coordinate descent (ACD) method. Simulations and experiments demonstrate that the proposed technique can effectively combine the spatial constraints provided by the Lidar PCM to further improve the self-localization accuracy of the sensor nodes, and further optimize the relative position relationship between each node and the map environment to achieve better matching and integration of the WSN and the real-time map.

Based on carrier phase positioning, narrow band systems such as pseudolites and cellular networks can achieve decimeter-level to centimeter-level positioning accuracy. In this paper, we propose a new carrier phase positioning method based on dual-antenna transmitters (TXs). All TXs maintain frequency synchronization, while each TX broadcasts distinguishable signals through two antennas respectively. The two signals from the same TX maintain time synchronization, and single difference makes the partial fixed solutions available. In this way, the proposed method can realize single point positioning (SPP) and avoid data transmission brought by double difference. It is shown by the simulation results that our method has better accuracy than traditional SPP methods with floating-point solutions.

Simultaneous Localization and Mapping (SLAM) is essential for robots, especially in unfamiliar indoor environments where other localization methods such as GNSS, UWB are unavailable. LOAM, as a state-of-the-art LiDAR SLAM method, works by extracting corner and surf points from raw point clouds and matching them with accumulated maps. However, the bisquare weight it uses for each observation is derived from the observation residual, which cannot reflect the actual observation quality and is of little help in improving the system accuracy. In this paper, we propose a novel method termed OW-LOAM, which takes the difference in the observation qualities into account by replacing the bisquare weight in LOAM with the inverse of the estimated variance of the observation noise based on Bayesian estimation theory. We conduct a series of experiments in various indoor environments of different scales, and the results show that the proposed OW-LOAM outperforms the original LOAM in both accuracy and robustness.

With the widespread application of wireless sensor networks, localization issue has attracted much attention. It is a major challenge for many sensor network tasks to locate a large number of asynchronous nodes in an unknown environment without external references. In this article, we present an asynchronous collaborative localization system (ACLS) to address the localization challenge for large-capacity sensor networks (LCSNs). ACLS exploits a hierarchical architecture, under which the wireless sensor nodes in the network are divided into parent nodes that can communicate with each other through wireless signals and child nodes that can only passively receive signals. Specific protocols and nonlinear distance estimators for this broadcast communication ranging technique are proposed. These characteristics are verified through theoretical analyses to have a strong suppression effect on local clock errors and are not sensitive to measurement noise. The simulation experiments further illustrate that the proposed ACLS can achieve high-rate and high-precision ranging and localization for asynchronous LCSN without preinstalled infrastructures.

Local positioning systems (LPSs) serve as a feasible alternative to provide positioning service in global navigation satellite system (GNSS)-denied environments. When the area of interest is unknown and potentially dangerous, e.g., urban search and rescue (USAR), or unreachable, e.g., extraterrestrial exploration, the autonomous establishment of LPSs by a robot is an attractive approach to coping with the demand for positioning service. In this article, we investigate the autonomous establishment problem in indoor scenarios, where a robot carrying several positioning beacons intends to place them sequentially to establish high-quality positioning services for the area of interest. To solve the complicated sequential decision problem, we first model the optimal positioning beacon configuration problem and then model the autonomous establishment process as a partially observable Markov decision process (POMDP). We apply deep reinforcement learning (DRL) to solve the POMDP. Extensive simulations, including comparisons with other baselines and generalization experiments, demonstrate the advantages of the proposed DRL-based autonomous establishment of LPSs.

Doppler shift is an important measurement for localization and synchronization (LAS), and is available in various practical systems. Existing studies on LAS techniques in a time-division broadcast LAS system (TDBS) only use sequential time-of-arrival (TOA) measurements from the broadcast signals. In this article, we develop a new optimal LAS method in the TDBS, namely, LAS-SDT, by taking advantage of the sequential Doppler shift and TOA measurements. It achieves higher accuracy compared with the conventional TOA-only method for user devices (UDs) with motion and clock drift. Another two variant methods, LAS-SDT-v for the case with UD velocity aiding and LAS-SDT-k for the case with UD clock drift aiding, are developed. We derive the Cramér–Rao lower bound (CRLB) for these different cases. We show analytically that the accuracies of the estimated UD position, clock offset, velocity, and clock drift are all significantly higher than those of the conventional LAS method using TOAs only. Numerical results corroborate the theoretical analysis and show the optimal estimation performance of the LAS-SDT.

A two-way time-of-arrival (TOA) system is composed of anchor nodes (ANs) and user devices (UDs). Two-way TOA measurements between AN-UD pairs are obtained via round-trip communications to achieve localization and synchronization (LAS) for a UD. Existing LAS method for a moving UD with clock drift adopts an iterative algorithm, which requires accurate initialization and has high computational complexity. In this letter, we propose a new closed-form two-way TOA LAS approach, namely CFTWLAS, which does not require initialization, has low complexity and empirically achieves optimal LAS accuracy. We first linearize the LAS problem by squaring and differencing the two-way TOA equations. We employ two auxiliary variables to simplify the problem to finding the analytical solution of quadratic equations. Due to the measurement noise, we can only obtain a raw LAS estimation from the solution of the auxiliary variables. Then, a weighted least squares step is applied to further refine the raw estimation. We analyze the theoretical error of the new CFTWLAS and show that it empirically reaches the Cramér-Rao lower bound (CRLB) with sufficient ANs under the condition of proper geometry and small noise. Numerical results in a 3D scenario verify the theoretical analysis that the estimation accuracy of the new CFTWLAS method reaches CRLB in the presented experiments when the number of ANs is large, the geometry is appropriate, and the noise is small. Unlike the iterative method whose complexity increases with the iteration count, the new CFTWLAS has constant low complexity.

For radio-based time-of-arrival (TOA) positioning systems applied in harsh environments, obstacles in the surroundings and on the vehicle itself will block the signals from the anchors, reduce the number of available TOA measurements and thus degrade the localization performance. Conventional multi-antenna positioning technique requires a good initialization to avoid local minima, and suffers from location ambiguity due to insufficient number of TOA measurements and/or poor geometry of anchors at a single epoch. In this paper, taking advantage of the multi-epoch and multi-antenna (MEMA) TOA measurements bridged by inter-epoch constraints to utilize more information and improve the geometry of visible anchors, we propose a new positioning method, namely MEMA-TOA method. A new initialization method based on semidefinite programming (SDP), namely MEMA-SDP, is first designed to address the initialization problem of the MEMA-TOA method. Then, an iterative refinement step is developed to obtain the optimal positioning result based on the MEMA-SDP initialization. We derive the Cramér-Rao lower bound (CRLB) to analyze the accuracy of the new MEMA-TOA method theoretically, and show its superior positioning performance over the conventional single-epoch and multi-antenna (SEMA) localization method. Simulation results in harsh environments demonstrate that i) the new MEMA-SDP provides an initial estimation that is close to the real location, and empirically guarantees the global optimality of the final refined positioning solution, and ii) compared with the conventional SEMA method, the new MEMA-TOA method has higher positioning accuracy without location ambiguity, consistent with the theoretical analysis.

Ground-based positioning systems (GBPSs), such as cellular networks and pseudolites, can provide high-precision positioning services through carrier phase positioning (CPP). Most existing methods are based on having accurate coordinates of all transmitters (TXs). In some applications, however, it could be too expensive and time-consuming to measure the coordinates of all TXs accurately, and requiring precise manual measurements severely degrades the flexibility of GBPSs. In this paper, we propose a carrier phase based autonomous coordinate evolution (CPACE) method for GBPSs, which uses the observations of multiple users to continuously improve the accuracy of TX coordinates. We first propose a Batch CPACE (B-CPACE) method and analyze its theoretical advantages over traditional single-point positioning (SPP). In the case of a large number of users, to avoid heavy burden on data transmission and calculation, we propose two distributed CPACE (D-CPACE) methods which have the same asymptotic performance with B-CPACE. Our numerical simulations prove that both B-CPACE and D-CPACE have better accuracy than SPP and reach the Cramer-Rao lower bounds. A real-world experiment shows that the proposed method can achieve centimeter-level accuracy.

In a localization system based-on asymmetric network, only one of the anchor nodes (ANs) transmits signal. A sensor node (SN) receives it and then transmits signal that is received by all ANs to form time-of-arrival (TOA) measurements. SN localization is achieved based-on these TOA measurements along with the known AN positions. Existing work all assumes the SN is stationary. This will cause extra localization error for a moving SN. We develop an optimal localization method based-on maximum likelihood (ML) estimator, namely ML-LOC, utilizing information on the SN velocity and clock drift, to determine the position of a moving SN. We analyze its localization error and derive the Cramér-Rao lower bound (CRLB). Results from numerical simulations verify its optimal performance. We implement a prototype hardware localization system based-on consumer level ultra-wide band (UWB) chips. Experiments using the real system are carried out. Results validate the performance of the proposed method and show its feasibility in real-world applications.

In a time of arrival (TOA) or pseudorange-based positioning system, user location is obtained by observing multiple anchor nodes (ANs) at known positions. Utilizing more than one positioning systems, e.g., combining global positioning system (GPS) and BeiDou navigation satellite system (BDS), brings better positioning accuracy. However, ANs from two systems are usually synchronized to two different clock sources. Different from single-system localization, an extra user-to-system clock offset needs to be handled. Existing dual-system methods either have high computational complexity or suboptimal positioning accuracy. In this article, we propose a new closed-form dual-system localization (CDL) approach that has low complexity and optimal localization accuracy. We first convert the nonlinear problem into a linear one by squaring the distance equations and employing intermediate variables. Then, a weighted least-squares (WLSs) method is used to optimize the positioning accuracy. We prove that the positioning error of the new method reaches Cramér-Rao lower bound (CRLB) in far-field conditions with small measurement noise. Simulations on 2-D and 3-D positioning scenes are conducted. Results show that, compared with the iterative approach, which has high complexity and requires a good initialization, the new CDL method does not require initialization and has lower computational complexity with comparable positioning accuracy. The numerical results verify the theoretical analysis on positioning accuracy, and show that the new CDL method has superior performance over the state-of-the-art closed-form method. Experiments using real GPS and BDS data verify the applicability of the new CDL method and the superiority of its performance in the real world.

In a time-division broadcast positioning system, a user device (UD) determines its position by obtaining sequential time of arrival or pseudorange measurements from signals broadcast by multiple synchronized base stations. The existing localization method using sequential pseudorange measurements and a linear clock drift model for the TDPBS, namely, LSPM-D, does not compensate the position displacement caused by the UD movement and will result in position error. In this article, depending on the knowledge of the UD velocity, we develop a set of optimal localization methods for different cases. First, for known UD velocity, we develop the optimal localization method, namely, LSPM-KVD, to compensate the movement-caused position error. We show that the LSPM-D is a special case of the LSPM-KVD when the UD is stationary with zero velocity. Second, for the case with unknown UD velocity, we develop a maximum-likelihood (ML) method to jointly estimate the UD position and velocity, namely, LSPM-UVD. Third, in the case that we have prior distribution information of the UD velocity, we present a maximum a posteriori estimator for localization, namely, LSPM-PVD. We derive the Cramér-Rao lower bound for all three estimators and analyze their localization error performance. We show that the position error of the LSPM-KVD increases as the assumed known velocity deviates from the true value. As expected, the LSPM-KVD has the smallest position error while the LSPM-PVD and the LSPM-UVD are more robust when the prior knowledge of the UD velocity is limited. Numerical results verify the theoretical analysis on the optimality and the positioning accuracy of the proposed methods.

In this article, we design a new time-of-arrival (TOA) system for simultaneous user device (UD) localization and synchronization with a periodic asymmetric ranging network, namely, PARN. The PARN includes one primary anchor node (PAN) transmitting and receiving signals, and many secondary ANs (SANs) only receiving signals. All the UDs can transmit and receive signals. The PAN periodically transmits sync signal and the UD transmits response signal after reception of the sync signal. Using TOA measurements from the periodic sync signal at SANs, we develop a Kalman filtering method to virtually synchronize anchor nodes (ANs) with high accuracy estimation of clock parameters. Employing the virtual synchronization, and TOA measurements from the response signal and sync signal, we then develop a maximum-likelihood (ML) approach, namely, ML-LAS, to simultaneously localize and synchronize a moving UD. We analyze the UD localization and synchronization error, and derive the Cramér-Rao lower bound (CRLB). Different from existing asymmetric ranging network-based TOA systems, the new PARN 1) uses the periodic sync signals at the SAN to exploit the temporal correlated clock information for high accuracy virtual synchronization and 2) compensates the UD movement and clock drift using various TOA measurements to achieve consistent and simultaneous localization and synchronization performance. Numerical results verify the theoretical analysis that the new system has high accuracy in AN clock offset estimation and simultaneous localization and synchronization for a moving UD. We implement a prototype hardware system and demonstrate the feasibility and superiority of the PARN in real-world applications by experiments.

In two-way time-of-arrival (TOA) systems, a user device (UD) obtains its position by round-trip communications to a number of anchor nodes (ANs) at known locations. The objective function of the maximum likelihood (ML) method for two-way TOA localization is nonconvex. Thus, the widely-adopted Gauss-Newton iterative method to solve the ML estimator usually suffers from the local minima problem. In this letter, we convert the original estimator into a convex problem by relaxation, and develop a new semidefinite programming (SDP) based localization method for moving UDs, namely SDP-M. Numerical result demonstrates that compared with the iterative method, which often fall into local minima, the SDP-M always converge to the global optimal solution and significantly reduces the localization error by more than 40%. It also has stable localization accuracy regardless of the UD movement, and outperforms the conventional method for stationary UDs, which has larger error with growing UD velocity.

Critical government and industry sectors (such as law enforcement, transportation, communication, and finance) are growing increasingly dependent on Global Navigation Satellite Systems (GNSS) for positioning, navigation, and timing. At the same time, the availability of low-cost GNSS jamming devices are presenting a serious threat to GNSS and increasing the likelihood of outages to infrastructures relying on GNSS. The attacks range from malicious parties intentionally jamming GNSS signals within a targeted geographical region to uninformed users causing accidental interference. This paper is an overview of different approaches adopted to date to mitigate GNSS disruption caused by intentional and unintentional jamming. The first approach outlined in this paper is the use of inertial systems to aid GNSS. The second and third approaches are the filtering of jamming/interference in the spatial and time-frequency domains, respectively. The fourth approach is vector tracking of GNSS signals in the receiver.

In global positioning system modernisation, to further enhance the anti‐jamming capability of authorised signals, the new designed M‐code signal utilises a few revolutionary techniques. While enduing the signal with excellent performance, the techniques make the acquisition methods for conventional pseudo‐noise codes, such as C/A‐code and P(Y)‐code, inapplicable. Furthermore, compared with time‐domain correlation, frequency‐domain correlation is favourable for saving computation requirements and suppressing interferences. Thus, it is quite desirable to develop frequency‐domain‐based ones. To this end, a frequency‐domain‐based acquisition method is developed, and based on the method the acquisition performance of M‐code signal is evaluated and the factors associated with the performance are investigated. It is shown that M‐code provides flexible tradeoffs between performance and implementation complexity through the sidebands and chips of the signal. Numerical and simulation results demonstrate the results.

In the last decade, 2q -MUSIC, an extension of MUSIC algorithm to an arbitrary even order 2q, has been proposed to process direction-finding problems. Despite of its better performance compared with MUSIC, it suffers from the high computational complexity, thus limiting its practical application. This letter proposes a method called Non-Redundant-2q-MUSIC using 2qth order statistics for uniform linear arrays and uniform rectangular arrays. The proposed method lowers the computational complexity effectively by removing the redundancy of the virtual array and the 2q th-order cumulant matrix. And root-MUSIC can be applied to avoid calculating the pseudo-spectrum. It is illustrated in both theoretical proof and computer simulations that the proposed method performs properly and effectively.

In this letter, a side-peak cancellation unambiguous acquisition technique is proposed for sine-phased binary offset carrier (BOC) modulated signals. The test criterion used in this technique is based on a synthesized correlation function which has no major positive side peak. This synthesized correlation function is obtained by subtracting the cross-correlation between the received sin-BOC signal and an auxiliary signal from the autocorrelation of sin-BOC signal. For different types of BOC signal, the proposed technique employs corresponding modulated symbols of the auxiliary signal. The common solution of the symbol shape vector is derived, and the theoretical false alarm and detection performance formulas are given. Theoretical and simulation results show that at the expense of some performance degradation this technique completely removes the ambiguity threat in acquisition process.

In this letter, we propose an unambiguous tracking technique for the new multiplexed binary offset carrier (MBOC) modulated signals, which will most likely be employed in both European Galileo system and modernized global positioning system (GPS). The discriminator used in this technique is based on a pseudo correlation function. It uses two kinds of gating correlators and a novel combination function, which completely removes side peaks from the correlation function while keeping the sharp main peak. Results demonstrate that this technique is totally unambiguous while maintaining the same level of tracking performance with respect to thermal noise as the traditional MBOC tracking method.

Because of the long period and high chip rate of GPS P-code, direct acquisition is challenging. In the letter, the widely used zero-padding scheme (ZPS) for direct GPS P-code acquisition is generalized to investigate the effects of the ZPS on detection performance, parallel searching capability, and mean acquisition time. It is shown that, by adjusting the zeros padded to received signal according to signal to noise ratio, the generalized zero-padding scheme (GZPS) makes a better tradeoff between detection performance and parallel searching capability and further reduces mean acquisition time. The generalized zero-padding scheme can be easily applied to the previously proposed zero-padding method (ZPM) and the direct average method (DAM) to improve their mean acquisition time performance and it does not increase the implementation complexity of a receiver.

For long PN-code, rapid acquisition is difficult due to large search space. To speed up the search process, extended replica folding acquisition search technique (XFAST), which directly reduces the code phases to be searched by folding local signal, provides an efficient approach to rapid acquisition. Nevertheless, after folding the correlation properties of PNcode are degraded; hence, the detection performance of XFAST to weak signal is worse than that of nonfolding methods. To improve the detection performance, a dual-folding acquisition method (DF) is proposed. By folding both incoming signal and local signal, DF extends coherent integration time to enhance detection performance and indirectly reduce mean acquisition time. Numerical results demonstrate the enhancement of the proposed method with respect to other methods such as serial search (SS), zero-padding method (ZP), and XFAST.