Influence of GPS code tracking on multipath performance

It is well known that code and carrier-phase multipath, which has been under study for over two decades, is the limiting error sources in high-precision differential GPS applications. In virtually every study, however, the effects of autocorrelation function are considered little. This article focuses on the bounds of code and carrier-phase multipath error in terms of GNSS (Global Navigation Satellite Systems) signals autocorrelation functions, which result from a fundamental theoretical description and mathematical modeling of GNSS receiver. Firstly, an overview of the characteristics of the BOC (Binary Offset Carrier) signal ACF (autocorrelation function) is given in the paper. The impact on the DLL (delay-lock loop) and PLL (phase lock loop) discriminator functions are derived in the followed section and consequently a general description of multipath errors are obtained for the BOC signals. This quantifies the influence of limited bandwidth on receiver tracking error due to multipath. Finally, the simulation results show a distinct change in the error envelope for BOC signals from which has been got using current GPS C/A code signal.

Multipath, where GPS signals arrive by more than one path and thereby create a range error, has remained the long-lasting major error source in GPS solutions although having been a target of the GPS research community since the day the system started operating. Seeking to understand the GPS multipath errors, this report aims to ef?ciently mitigate multipath effects at observable levels to improve the accuracy and precision of GPS solutions.Based on an analysis of the geometry of a multipath signal's reflections, and the principle of GPS receiver's tracking loop, geometrical models of multipath errors are developed at observable levels (both code and carrier-phase multipath). More specifically, multipath errors corresponding to a satellite are mathematically proven to be functions of the satellite's geometry with respect to a receiver which is parameterized by azimuth and elevation angles. Hence, the problem of multipath error estimation amounts to a regression problem where the multipath functions are approximated using training data. Whereas the theory behind regression problem is robust, the regression problem solution would be feasible as long as a priori data (e.g. training data) is available. As code multipath errors can be easily isolated using a combination of GPS measurements and satellites' geometrical information can be computed using orbital information broadcast from the satellites, training data for the problem code multipath error estimation can be extracted. An experiment was conducted to demonstrate the performance of the proposed method. A real data set was recorded at 0.1 Hz during 5 days to use for the experiment. After training the multipath estimators with data from 31 visible satellites over four days using the epsilon-SVR algorithm, multipath estimation and correction have been performed on the data from the successive day. Results show approximately 80% reduction in term of code multipath error standard deviation, the proposed method shows great promise for understanding and removing multipath errors. Advantageously, while being scalable with data rate, the proposed method is shown to be not harmful to other signals (simulation). An analogous experiment was also conducted to address carrier-phase multipath error. Unfortunately, for a standalone receiver, carrier-phase multipath error cannot be isolated by a combination of measurements as has been done with code multipath error, a carrier-phase double difference between two short-basedlined receivers needs to be made. It results in combinatorial carrier-phase multipath error of 4 satellite-receiver pairs involved in double-difference. Mitigation of this error is beneficial for relative positioning applications. With the same rationale, the multipath error is modeled as a function of the geometries of 4 satellite-receiver pairs. Training the multipath estimation using 1-Hz data from two short-baselined stations of IGS network, preliminary experimental result showed 57% reduction in multipath error for a pair of satellites. My next target is to unify an evaluation framework for multipath mitigation problems with well-defined tests, and evaluation criteria, as this is missing in the literature. Whereas further experiments on carrier-phase multipath mitigation as well as on data recorded from the field need to be done, there is also still room for improvement in multipath estimation algorithms with the focus on computational complexity reduction and incremental learning ability. Integration of the new signals in GPS modernization plans is also worth exploring.

Carrier phase multipath caused by reflections in the vicinity of GNSS stations is a major error source of precise differential positioning. Detection and mitigation of carrier phase multipath errors can be based on signal quality measurements, i.e. signal-to-noise ratio (S/N) or carrier-to-noise ratio (C/N), as provided by GNSS receivers. Variations of the signal quality oscillation frequency are caused by changes of the reflected signal's additional path length. Calculating carrier phase multipath corrections from signal quality time series is not simple. Most published algorithms need various interim results, e.g. phase shift or attenuation factors, to calculate the final correction value. Our algorithm, however, directly estimates carrier phase multipath corrections from signal quality measurements. In order to validate the potential of this multipath mitigation method in practice, GPS/GLONASS observation data sets of six continuously operating reference stations (CORS) of the German SAPOS network were corrected. All these stations are equipped with receivers for which the signal quality based multipath mitigation performs similarly well for both frequencies. Thus multipath mitigation may even improve coordinate results based on the ionosphere-free linear combination. We present a detailed analysis of the effects of carrier phase multipath corrections on positioning results in this CORS subnetwork.

The effect of signal multipath is one of the main reasons which lead to positioning error in Global Positioning System (GPS). Although the differential technology can improve the positioning accuracy of the navigation system, but the reference stations and users being in different geographical environment, the differential GPS system still can’t eliminate the positioning error caused by multipath signal. In the light of the characters of GPS multipath signal model, a GPS multipath mitigation algorithm based on C/A code correlation character is proposed in this paper. Firstly, Doppler frequency is estimated when the signal delay is unknown. Then, we use the estimated Doppler frequency to get signal delay information with C/A code correlation character which is realized by correlating the reconstructed zero delay signal with the original signal. In addition, we consider the previous estimated results as the initial value and a two-dimension search method is implemented in a small range so as to further improve the estimation accuracy. It can be shown from the simulation results that the proposed method has a better time delay and Doppler frequency estimation performance compared with the conventional method and narrow correlator spacing algorithm.KeywordsGlobal positioning systemMultipath mitigationC/A code correlation characterImprove the estimation accuracy

Continuous and precise code delay tracking is essential in challenging environments such as urban canyons where multipath and frequent signal blockage may lead to performance degradation and loss of lock of signals. The strobe correlator (SC) is an effective technique for baseband multipath mitigation and is commonly used for GNSS signal tracking enhancement. An SC has two pairs of early and late correlators, one with a wide and another with a narrow correlator spacing. This paper extends the conventional SC design by applying its correlator pairs on dual-band GNSS signals to realize an extended strobe correlator (ESC). An ESC takes advantage of the natural distinct bandwidth of narrow-band and wide-band signals, e.g., L1 C/A and L5Q signals, to form a dual-band combination at the correlator level in a deeply-coupled manner. Narrow-band L1 signal tracking ensures robustness, while the wide-band L5 signal improves the tracking precision. A moving average window filters the L1 measurement to prevent the noise impact on L5 tracking, providing necessary inter-band assistance to resolve challenges such as code delay misalignment and precision mismatch. Through both Monte Carlo simulation and real data collected in urban environments, this work demonstrates that an ESC can achieve improved overall robustness against loss-of-lock and multipath mitigation performance over standalone tracking. Compared with KF-based combined (KFC-based) tracking, ESC has higher tracking precision under weak signal environment and robustness during signal blockage, but larger residual multipath error.

In this paper, the performance of aerostatic thrust bearings compensated by different methods is investigated using computational fluid dynamics (CFD) method. By analyzing the relationships between the bearings’ parameters and load carrying capacity (LCC), mass flow rate (MFR) and the maximum gas velocity (MGV), the effects of restrict area on the bearing’s performance are discussed in the first time. Under the same restrict area, the bearing with multi-pocketed orifices has the largest LCC, the bearing with single inherently orifice has the least MFR and the minimum gas velocity. Moreover, the pressure fluctuation inside the bearing with single inherently orifice is minimal and the possibility of the bearing to generate self-active vibration is the smallest. So the bearing with multi-pocketed orifices is more suitable for the application of high load and relative low precision. And the bearing with single inherently orifice is more suitable for the application of low load and relative high precision.

Delta robots have been widely used in industrial contexts for pick-and-place applications because of their high precision and speed. These qualities are also desirable at the millimeter scale for applications such as vibration cancellation in microsurgery and microassembly or micromanipulation. Developing a millimeter-scale Delta robot that maintains the characteristic input-output behavior and operates with high speed and precision requires overcoming manufacturing and actuation challenges. We present the design, fabrication, and characterization of an adapted Delta robot at the millimeter scale (the "milliDelta") that leverages printed circuit microelectromechanical system manufacturing techniques and is driven by three independently controlled piezoelectric bending actuators. We validated the design of the milliDelta, where two nonintersecting perpendicular revolute joints were used to replace an ideal universal joint. In addition, a transmission linkage system for actuation was introduced to the laminate structure of the milliDelta. This 15 millimeter-by-15 millimeter-by-20 millimeter robot has a total mass of 430 milligrams and a payload capacity of 1.31 grams and operates with precision down to ~5 micrometers in a 7.01-cubic-millimeter workspace. In addition, the milliDelta can follow periodic trajectories at frequencies up to 75 hertz, experiencing velocities of ~0.45 meters per second and accelerations of ~215 meters per squared second. We demonstrate its potential utility for high-bandwidth, high-precision applications that require a compact design.

The design and evaluation of an optically triggered, fully integrated sample and hold circuit (OS/H) is described. Measured results are presented that demonstrate operation of this circuit at 250 Ms/s and with effective resolution approaching 8 bits. The integrated circuit, which measures 2.1 mm/spl times/1.4 mm, is realized in -1.0-V threshold, 20-GHz ft GaAs MESFET technology, consumes approximately 200 mW of power, and requires one optical address. The OS/H will find applications in high precision, hybrid, and integrated signal processing systems where high speed, high levels of parallelism, and low timing jitter are important. Measured results of a series photoconducting (Auston switch) OS/H realized in the same technology are presented for comparison purposes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The introduction of computer vision and machine learning into agricultural systems has produced significant new opportunities for high precision application of liquid products in both grain and livestock agriculture. These technologies, which enable liquid application in site-specific, non-broadcast applications, are driving new evaluations of nozzle technologies which apply a consistent dose of liquid product in a non-conventional manner compared to historic perceptions. This field of innovation is driving the need for improved high-capacity systems for evaluating nozzle performance in high-precision applications. Historically, patternator tables with volumetric measurements of total applied liquid have served as the standard for fluid nozzle evaluation. These volumetric measurements are based on measuring the displaced distance of liquid over a defined time to determine flow rate. However, current distance sensors present challenges for achieving small-volume measurements and enabling automation at a scale necessary to meet innovation demands of high-precision nozzle systems. A novel concept for high speed and automated measurement of a high precision patternator table was developed using an ultrasonic sensor and a carefully designed liquid retainment system to maximize measurement precision. The performance of this system was quantified by comparing calibrations and performance across different vessels for volume measurement (tubes and pipes) used in the application of a nozzle patternator. A total of three square tubes (15.9, 22.3, 31.0 mm widths) and three pipes (25.2, 27.0, 35.1 mm diameters) were evaluated, with the 27 mm pipe matching the ultrasonic sensor’s rating. All calibrations were successful, depicting linear characteristics with R2 &gt; 0.99. The smallest pipe presented issues for the sensor to measure in post-calibration and was thus not evaluated further. The residual values from operational performance highlight that the 25.2 mm tube and the 27.0 mm pipe are highly accurate with no indication of bias or non-normality. The relative uncertainty ranges from 2.9 to 42% (350 mL to 25 mL) depending on the tube and pipe cross-sectional diameter or width with the sensor accuracy and uncertainty in the tube and pipe area being the largest factors. The results of this study indicate that the 25.2 mm tube and the 27.0 mm pipe could be excellent options for autonomous liquid volume measurement with the ultrasonic sensor. A key challenge identified in this study is that the assumptions in the sensor’s intrinsic calibration are violated with the tubes and pipes evaluated.

Aiming at the complexity of the new system B1C signal system and the characteristics of many components, the ranging performance research on B1C signal is carried out. The theoretical analysis is carried out from two aspects: code tracking accuracy and multipath error analysis, and BOC(1,1) non-matching is adopted. The received RMS bandwidth and associated output signal-to-noise ratio and code tracking errors at different intervals are analyzed and compared. The simulation results show that the theoretical code tracking accuracy of B1C signal pilot component is the lowest, and the multipath performance is better than BOC(1,1) signal. In the study of non-matching method, better output can be obtained with wide interval. The error indicates that the performance of non-matching reception under certain conditions is better than the matching algorithm.

Relative Navigation for Satellite Formation Flying based on Radio Frequency Metrology

In this work an adaptive approach for friction compensation based on the Generalized Maxwell Slip (GMS) Model is presented. The model is utilized in a feed-forward controller in combination with a standard feedback controller to improve the dynamical performance of a two dimensional high precision positioning stage with a working range of 200 mm. The GMS model is extended to be used as an inverse system model. The parameter identification shows, that the identified model does not represent the system behavior at every position. On this account the linear model parameters are adapted online to ensure precise friction compensation. Experiments show that this approach can improve the dynamical behavior of the system significantly. In combination with a feedback controller the adaptive GMS model based friction compensation is robust against disturbances and reduces the tracking error while moving over the whole operating range.

The significant drawback of the permanent magnet linear synchronous motor (PMLSM) is force ripples, which are generated by the distortion of the stator flux linkage distributions, cogging forces caused by the interaction of the permanent magnet and the iron core and the end effects. This will deteriorate the performance of the drive system in high precision applications. The PMLSM and its parasitic effects are analyzed and modeled using the complex state-variable approach. To minimize the force ripple and realize the high precision control, the components of force ripples are extracted first and then compensated by injecting the instantaneous current to counteract the force ripples. And this method of the PMLSM system is realized by the field oriented control method. In order to verify the validity of this proposed method, the system simulations are carried out and the results are analyzed. The effectiveness of the proposed force ripples reduction method can be seen according to the comparison between the compensation and non-compensation cases.

One of the most important functions for the safety of autonomous driving is the self-localisation of a moving platform. The GNSS (Global Navigation Satellite System) sensor is - compared to other sensors as, e.g., video, radar or camera - the only sensor that provides absolute positioning. Under clear sky conditions, GNSS positioning methods yield high level of accuracy and integrity. Poor signal propagation conditions make precise GNSS positioning challenging under urban conditions where multipath degrades the attainable accuracy and integrity. In the last decades, various correction or mitigation approaches for multipath errors have been developed and tested, but for carrier phase observations it is still the most critical error with magnitudes of up to a quarter of the wavelength. Since the carrier phase multipath error is location dependent, this property can be used to construct a correction map. In this paper, we report on the necessary steps to construct such a multipath correction map. The carrier phase error is a function of the multipath characteristics and the extra path delay. Hence, it is dependent on the distance to the reflection surface. Using a 3D building model, the geometry between the building and potentially multipath affected satellite signals is established to obtain one periodic cycle of the carrier phase error. A pseudo-kinematic experiment in an urban environment is planned and designed based on simulation studies of a ray-tracing algorithm to ensure ideal receiving properties for multipath signals in a realistic scenario. Two different approaches of carrier phase residuals will be compared to derive the multipath error from the observations. Firstly, double difference residuals are computed. Secondly, carrier phase residuals extracted from a positioning engine will be analysed. Finally, the developed functions are evaluated in the context of generating GNSS multipath correction maps for moving platforms.

The conventional asymmetric inertial impact motors are driven by using the difference in inertial impact forces in the forward and reverse directions, implemented by using asymmetric drive signals, clamping blocks of different sizes or different materials, etc. An adjustable magnetic force type resonant inertia impact motor has been designed, assembled, and tested. The novel motor features a simple and compact structure, allowing for the attainment of different output performance by adjusting the magnetic force to meet various working requirements, and the reverse motion can be easily achieved by simply altering the orientation of the magnet located at the end of the piezoelectric vibrator, without requiring any additional structure The part of the motor’s structure was simulated and optimized using the finite element analysis software COMSOL6.0, with the first and second order vibration modes selected as the working mode. The experimental platform has been established to verify the working performance of the motor. Experimental results demonstrate that, under excitation voltage of 120 VP–P and frequency of 163 Hz, the maximum speed achieved by the motor prototype is 36.55 mm s−1, with maximum load capacity of 320 g, and under excitation voltage of 40 VP–P and frequency of 928 Hz, the minimum step of the prototype reaching up to 134 nm. The motor proposed in this paper features an innovative asymmetric strong magnetic design, enabling high speed and load through the large amplitude of the piezoelectric vibrator in first-order vibration mode. As the amplitude gradually decreases in second and higher order modes, this motor achieves higher displacement resolution, making it has potential applications in high precision positioning and medical fields.