Xiangwei Zhu

A Novel Definition and Measurement Method of Group Delay and Its Application

The time synchronization accuracy demanded in satellite navigation systems, deep space exploration, and spread spectrum radar has reached the subnanosecond range. The phase distortion induced by RF cables, amplifiers, and mixers affects the spread spectrum signal delay and causes dominant error in time synchronization. To measure and calibrate the influence of phase distortion, it is necessary to devise a high-accuracy group delay measurement method and study its relationship with signal delay. The traditional definition and measurement formula of group delay is based on the derivative, which has some inherent faults such as inconsistency of resolution and accuracy, incapacity to describe the global phase character of signal bandwidth, and difficulty in establishing a relationship with spread spectrum signal delay. To overcome such shortcomings, a novel group delay definition and measurement formula has been put forward based on Taylor series expansion, which has been used in Global Positioning System timing receiver RF cable group delay measurement. The experiment showed that the accuracy of the new group delay measurement was better than 0.01 ns and was very consistent with the signal delay. The maximum bias between the signal delay and the zeroth-order group delay was less than 0.3 ns.

Comparison of Short-Term Stability Estimation Methods of GNSS On-Board Clock

The short-term frequency stability of satellite on-board clock is of great significance for GNSS applications, such as satellite clock modeling, simulation and clock offset prediction. In this paper, four short-term frequency stability estimation methods are analyzed, which need observation data from only one station in contrast with ODTS needing continuous observation of large ground monitoring networks. Performance and accuracy of all these four methods is analyzed and compared using GPS and COMPASS observation data, and their advantage and disadvantage are discussed correspondingly. For COMPASS and Galileo systems which are currently in the early stage of construction, this paper proposes some meaningful suggestions of on-board clock short-term frequency stability estimation.

A High-Precision Time Interval Measurement Method Using Phase-Estimation Algorithm

High-precision time interval measurement is widely used in time synchronization, satellite navigation, laser ranging, and nuclear electronics. The resolution and accuracy of the currently used time counter are about 25 and 100 ps, respectively. A new time interval measurement method, in which the signal under test is used to trigger a sampler and the phase of the reference sinusoid signal is sampled to record the time stamp of the test signal, was put forward. Then, the sampled reference sine signals phase is estimated by the interpolated fast Fourier transform (FFT), and 1-ps resolution and accuracy can theoretically be achieved. The test experiment of the prototype instrument shows that a 10-ps accuracy has been reached. If the hardware prototype is improved to reduce trigger jitter and sampling clock jitter, the measurement instrument may reach 1-ps accuracy. The measurement system is used not only for time interval measurement but also for period measurement and even modulation domain analysis.

Uncertainty Derivation and Performance Analyses of Clock Prediction Based on Mathematical Model Method

The prediction of the clock offset plays an important role in the generation of a time scale, clock steering, and time offset prediction of the onboard clocks. The mathematical model method based on the stochastic differential equations has been dealt with the clock prediction problem. In this paper, we examine the method from a theoretical point of view. We derive the analytic expressions of the theoretical prediction uncertainties when the clocks are modeled by the sum of a white frequency modulation noise, a random walk frequency modulation noise in both the linear model case and the quadratic polynomial model case. Simulations and an experiment for predicting the time deviations of International Atomic Time-TA(National Time Service Center) are used to validate the theoretical analyses. The simulations and the experiment show that the prediction performances agree with the theoretical evaluations; therefore, we consider that the research is useful in applications. Furthermore, we illustrate that the prediction uncertainty can be minimized only by choosing an optimal observation interval. From simulations, for a typical cesium clock, the method is effective for short-term prediction, whereas for a typical hydrogen maser, for all prediction times the uncertainties of the deterministic part are predominant, and we thus consider that the method in the quadratic polynomial model case deserves further investigation.

Detection of weak frequency anomalies for atomic clocks with a Kalman filter

An algorithm presented in a previous paper by the authors detects frequency anomalies. The algorithm was shown to be effective for early detection of weak frequency jumps, and also valid for frequency drift jumps that belong to the class of errors that are most difficult to detect. A modification to the original frequency jump detector algorithm is suggested by the addition of a noise-removal filter. The performance is then compared with the original algorithm and improvement is shown. An analysis of real data from a real satellite is also adopted.

An Integrity Monitoring Algorithm for Satellite Clock Based on Test Statistics

As a core part of satellite payload, satellite clock has a direct influence on GNSS service performance. Therefore, it is necessary to monitor its integrity. In this paper, real-time test statistics for satellite clock phase and frequency anomaly are built, and an integrity monitoring algorithm for satellite clock based on these statistics is proposed. It is composed of two parts, including phase anomaly monitoring and frequency anomaly monitoring, which mainly aims at three anomalies comprising occasional bad or outlier points, anomaly jumps that later return to stable values and phase or frequency steps. The new algorithm can not only detect phase and frequency anomalies, but also identify and deal with clock anomaly instantly, including eliminating and replacing the anomaly data. Satellite clock anomalies are simulated using the IGS observation clock data and performance of the new algorithm is verified. The results show that the new algorithm has a perfect performance of detecting the satellite clock anomaly including both phase anomaly and frequency anomaly. At the same time, it can also eliminate and replace the anomaly data, and the replaced error is negligible. The integrity monitoring algorithm for satellite clock proposed in this paper is helpful to GNSS satellite clock autonomous integrity monitoring.

Multipath detection based on single orthogonal dual linear polarized GNSS antenna

Based on the polarization difference between the multipath and the line-of-sight (LOS) signal, a method for multipath detection using a single antenna is proposed. The antenna has two channels to receive two orthogonal linear polarized components of the multipath and LOS signal, respectively. A hypothetical model of the antenna is employed such that the antenna patterns of the channels are assumed identical regarding amplitude and phase and are independent of azimuth. The antenna gain in the direction below the local horizon is assumed to be larger than in the direction toward LOS signals. Parallel cross-cancellation is used to remove the LOS signal from the received signals based on the magnitude and phase difference between the two orthogonal components. Then the residual signals are processed by a conventional digital processor of global navigation satellite system. The multipath can be detected by parallel cross-cancellation in the receiver in real time. The proposed method makes use of the polarization and spatial information of the multipath and LOS signal, and can detect short-delay multipath.

Impact of reference element selection on performance of power inversion adaptive arrays

Antenna arrays with adaptive algorithms are widely used to provide anti-jamming abilities for Global Navigation Satellite System (GNSS) receivers, among which Power-Inversion (PI) algorithm is attractive for suppression of jammers before de-spreading of signals and simplicity for implementation. Most of previous works either selected the reference element arbitrarily or naturally selected the center element of the array geometry as reference. In this paper, we studied the effect of reference element selection on the performance of the adaptive array receivers. The results show that although the selection of reference element has negligible effects on interference cancellation, it does affect the array gain in the direction of desired signal as well as the array output signal-to-interference-plus-noise ratio (SINR). When the optimal reference element is selected, it will give more than 30% improvement in terms of available angular region under no SNR loss condition over arbitrary reference element selection.

Non-Reciprocity Correction Using Broadcast Ephemeris in Two-Way Satellite Time and Frequency Transfer (TWSTFT)

Two-way satellite time and frequency transfer (TWSTFT) is applied in BeiDou Navigation Satellite System for time synchronization of the ground stations. In fact, the geostationary (GEO) satellites have periodic motions around their planned orbits instead of being stationary to the ground stations, which results in periodic fluctuations of Sagnac correction and signal path geometry correction in TWSTFT. Precise TWSTFT is relaying on the non-reciprocity corrections. An analysis method with broadcast ephemeris of GEO satellite for Sagnac correction and signal path geometry correction is introduced in this paper. With this method, TWSTFT experiment result using BeiDou GEO satellite at 140°E of three links between Beijing and three different sites is analyzed and the periodic fluctuation of Sagnac correction and signal path geometry correction are presented in detail. The fluctuation range of Sagnac correction is from 0.04 to 0.16 ns and that of signal path geometry correction is from 0.01 to 0.53 ns for the three links, which shows that Sagnac correction and signal path geometry correction can not be ignored in time transfer requiring sub-nanosecond precision generally for the three links.

A Novel Method with Ps Accuracy for Time Interval Measurement

High precise time interval measurement is widely used in time synchronization, satellite navigation, aerospace tracking telemetering, laser metering and nuclear electronics. The resolution and accuracy of the current used time counter is 25 ps and nearly 100 ps, respectively. A new time interval measurement method was put forward, in which, the signal under test is used to trigger a sampler and the phase of the reference sine signal sampled record the time stamp of the test signal. The sampled reference sine signals phase is estimated by interpolated FFT and 1 ps resolution and accuracy can be achieved theoretically. The test experiment of prototype instrument show 10 ps accuracy has been achieved. If the hardware prototype is improved to reduce trigger jitter and sampling clock jitter, the measurement instrument may reach 1ps accuracy. The measurement system is used not only time interval measurement, but also for period measurement and modulation domain analysis.