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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 paper, 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 Cramer-Rao lower bound (CRLB with sufficient ANs under the condition with 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 the 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.

There are many demands for the cooperative localization (CL) of multiple people, such as firefighter rescue. The classical foot-mounted inertial navigation based on zero velocity update (ZUPT) suffers from accumulating error due to the low-cost inertial sensor, and the pre-placed anchors in the ultra-wideband (UWB) system limit the application in an unknown environment. In this study, a group of sensors including the inertial measurement unit (IMU), magnetometer, barometer, and UWB sensor is used. Through the different characteristics of sensors and the position relationship between people, a cooperative localization system using an extended Kalman filter for three-dimensional firefighter tracking is proposed. Ranging information between firefighters from UWB is utilized, and couplings introduced by relative measurement are estimated. Two experiments are designed to verify the proposed algorithm in building and forest environments. Compared with the results of single-person inertial navigation, the average positioning precision of the algorithm in the building and forest is, respectively, improved by 38.93% and 79.01%. This approach successfully suppresses the divergence of positioning errors, and fixed UWB anchors are not needed.

Ionospheric dispersion causes severe distortions and ranging performance degradations of wideband global navigation satellite system (GNSS) signals. To compensate the non-linear and asymmetrical group delay of the dispersive ionosphere, an all-pass filter in the form of cascaded biquad sections was proposed in our previous study. On this basis, this paper develops an optimal delay-equalization all-pass filter by using the trust-region algorithm to construct the desired group delay and improve the fitting accuracy. The simulation results of the AltBOC(15,10) signal performance demonstrate that the proposed design is more accurate for distortion compensation and thus more effective for ranging bias mitigation than the previous approach.

Single-sensor zero-velocity-update (ZUPT)-aided pedestrian inertial navigation system (PINS) is a conventional method. However, the single-sensor systematic error still causes imprecise estimation of step length and high drift of orientation. In this study, three magnetometers and inertial measurement units are mounted on single-leg toe, shank, and thigh, respectively. Gaits are divided into two phases: stance and swing. Based on the biomechanical characteristics of a human lower limb, a velocity-position estimation algorithm is proposed. The positions of the three sensors are fused by dynamic geometric relationships, which are formulated through the natural lower-limb model and attitude estimation. A velocity-difference constraint is proposed to suppress the divergence of velocity, and Coriolis-based velocity correction is designed to observe velocities of the toe, shank, and thigh at the stance phase. A MAHONY-linear-Kalman framework separately estimates attitudes, velocities, and positions to reduce calculations. The proposed method is compared with foot-mounted, shank-mounted, and thigh-mounted ZUPT-aided PINS as well as a dual-sensor foot-to-foot algorithm through experiments. In the flat terrain experiment, compared with the errors of the Shank-mounted INS, the Thigh-mounted INS, the Foot-mounted INS, the Foot-to-Foot Constraint Method, the root mean squared error (RMSE) of the proposed method can be reduced by 40.34%, 71.85%, 29.53%, and 7.08%, respectively. In the slope experiment, compared with the other four methods, the RMSE of the proposed method can be reduced by 80%, 86.74%, 67.54%, and 61.86%, respectively. In the natural terrain experiment, compared with the other four methods, the RMSE of the proposed method can be reduced by 81.63%, 96.27%, 70%, and 60.87% respectively. The results show that the proposed method greatly suppresses the positioning and orientation errors in different scenes.

Global navigation satellite systems (GNSSs) usually adopt constant-envelope multiplexing (CEM) techniques to deal with the nonlinear characteristic of high-power amplifiers (HPAs) on satellites. However, almost all the existing navigation signal CEM techniques assume that the bandwidth of the transmitter is large enough when compared to that of navigation signals, which often contradicts reality, especially for the multiplexing of wideband navigation signals such as the signals in the Galileo E5 and BDS-3 B2 bands. Consequently, the constant-envelope characteristic deteriorates severely when the composite signal passes through the filter, which leads to nonlinear distortion and low amplification efficiency. Even if the nonlinear distortion can be mitigated by using amplifier linearization techniques, the actual transmitted signal power still suffers from a high peak-to-average power ratio (PAPR) of the composite signal. In order to address this problem, we present a new band-limited, dual-frequency multiplexing technique. The main premise of this method is to consider the impact of the filter on the navigation signals at first and then introduce the band-limited auxiliary signals to reduce the peak power of the composite signal as much as possible, thereby increasing the actual transmission power of the navigation signals. Simulation results demonstrate that the proposed method has lower PAPR and higher amplification efficiency than existing methods. In addition, implementation of the proposed multiplexing technique is still based on a look-up table, which has little change compared with previous CEM methods, and the complexity of signal generation is affordable.

Compared with the traditional GPS L1 C/A signal, the existing and emerging new-generation wideband GNSS signals suffer more severe distortions due to the nonlinear characteristics of a high-power amplifier (HPA) in the satellite transmitter. HPA nonlinearity can lead to in-band signal distortion and out-of-band spectral regrowth, which degrade the ranging performance of a GNSS receiver. Researchers have reported power loss, correlation peak asymmetries, lock point bias as well as carrier tracking error caused by the HPA nonlinearity. However, few pre-distortion approaches that compensate for the HPA nonlinear effects have been presented in the GNSS field. We first take BDS-3 B2 asymmetric constant envelope binary offset carrier signal as an example to present the HPA nonlinear effects on wideband GNSS signals. Then, the design principle of a predistorter is investigated, and a Hammerstein predistorter is proposed to eliminate the nonlinear HPA with memory. Finally, we compare the constellation diagram, power spectrum, correlation function, code tracking bias with and without the Hammerstein predistorter. The comparison results demonstrate that a digital predistorter is a potential solution to compensate the HPA nonlinear distortions for wideband GNSS signals. This pre-distortion approach is of great significance that can effectively guarantee the nominal signal quality in space not only during the maintenance of the current GNSSs but also for the future emerging local or global navigation systems.

Compared with the traditional GPS L1 C/A BPSK-R(1) signal, wideband global navigation satellite system (GNSS) signals suffer more severe distortion due to ionospheric dispersion. Ionospheric dispersion inevitably introduces additional errors in pseudorange and carrier phase observations that cannot be readily eliminated by traditional methods. Researchers have reported power losses, waveform ripples, correlation peak asymmetries, and carrier phase shifts caused by ionospheric dispersion. We analyze the code tracking bias induced by ionospheric dispersion and propose an efficient all-pass filter to compensate the corresponding nonlinear group delay over the signal bandwidth. The filter is constructed in a cascaded biquad form based on the estimated total electron content (TEC). The effects of TEC accuracy, filter order, and fraction parameter on the filter fitting error are explored. Taking the AltBOC(15,10) signal as an example, we compare the time domain signal waveforms, correlation peaks, code tracking biases, and carrier phase biases with and without this all-pass filter and demonstrate that the proposed delay-equalization all-pass filter is a potential solution to ionospheric dispersion compensation and mitigation of observation biases for wideband GNSS signals.

Low-cost MEMS-based IMUs, video cameras and portable GNSS devices are commercially available for automotive applications and some manufacturers have already integrated such facilities into their vehicle systems. GNSS provides positioning, navigation and timing solutions to users worldwide. However, signal attenuation, reflections or blockages may give rise to positioning difficulties. As opposed to GNSS, a generic IMU, which is independent of electromagnetic wave reception, can calculate a high-bandwidth navigation solution, however the output from a self-contained IMU accumulates errors over time. In addition, video cameras also possess great potential as alternate sensors in the navigation community, particularly in challenging GNSS environments and are becoming more common as options in vehicles. Aiming at taking advantage of these existing onboard technologies for ground vehicle navigation in challenging environments, this paper develops an integrated camera/IMU/GNSS system based on the extended Kalman filter (EKF). Our proposed integration architecture is examined using a live dataset collected in an operational traffic environment. The experimental results demonstrate that the proposed integrated system provides accurate estimations and potentially outperforms the tightly coupled GNSS/IMU integration in challenging environments with sparse GNSS observations.