Kalman filtering (KF)-based tracking has been commonly employed in global navigation satellite system (GNSS) receivers to achieve robust tracking. However, under more serious conditions, such as severe strength attenuation and abrupt dynamic coexisting environments, it is difficult for KF-based tracking to keep tracking well due to the fixed noise statistics. To further enhance the carrier tracking performance, this paper proposes an adaptive KF carrier tracking method for resisting signal strength fading and high dynamic environments. The proposed method introduces the adaptive factor to adjust the process noise covariance to accommodate the noise statistics in actual variable situations. Moreover, we apply the chi-square hypothesis test to detect system stability. The adaptive factor is only applied when the system is not stable, which can enhance computational efficiency. The proposed method is conducted in the GPS L1 software receivers. According to the results, the proposed algorithm can improve the robustness in tracking performance compared with other tracking methods under signal serious fading and high dynamic conditions. Using the proposed method, GNSS receivers’ navigation performance can be improved under complex conditions.

Many practical systems, such as target tracking, navigation systems, autonomous vehicles, and other applications, are usually applied in dynamic conditions. Thus, the actual noise statistics characteristics of these systems are generally time varying and unknown, which will deteriorate the state estimation accuracy of the Kalman filter (KF) and even cause filter diverging. To address this issue, this paper proposes an adaptive process noise covariance (Q_k)-based variational Bayesian adaptive Kalman filter (AQ-VBAKF) algorithm. Firstly, the adaptive factor is introduced to self-tune the process noise covariance; the adaptive factor is obtained based on the innovation sequences, which can adapt to the input measurement values. Then, the VB solution is applied to approximate the time variant and unknown measurement noise covariance. Therefore, this proposed algorithm can adjust the process noise covariance and the measurement noise covariance simultaneously based on the variable input signals, which can improve the self-adaptive ability of the state estimation filter in dynamic conditions. According to the dynamic target tracking test results, the proposed AQ-VBAKF outperforms several other existing filtering methods in estimation accuracy, robustness, and computational efficiency.

This paper investigates a unified theory to derive vector network analyzer calibration algorithms based on the T-matrix representation, by which means the line-reflect-match (LRM), line-reflect-match-match (LRMM), and the line-reflect-reflect-match (LRRM) calibrations are formulated. The proposed calibration theory is more general than other versions of LRM, LRMM, and LRRM in that an arbitrary known two-port device can be used as the line standard L, rather than a perfect thru or transmission line. Experimental verifications of the proposed theory using on-wafer calibrations from 0.5 GHz to 110 GHz are given.

A 3-cm-long optical reference cavity for transportable miniaturized ultra-stable laser is designed and analyzed using finite element analysis (FEA). Although the tiny cavity is formed in a conventional way, in which a cylinder spacer made of ultra-low expansion (ULE) glass is optically contacted with fused-silica mirror substrates and compensation rings, the compensation rings are specially designed in order to broaden the zero-thermal-expansion temperature tuning range. In addition, the cavity is capable of being rigidly fixed by clamping both end sections of the cylinder spacer along the axis. The thermodynamic analysis shows that a larger tuning span of the zero-thermal-expansion temperature varying from −10 K to + 23 K compared to all-ULE cavity is benefited, resulting in the whole optical reference cavity could work around room temperature. Meanwhile, the statics analysis indicates the design is insensitive to extrusion force and vibration so that it owns a potential of solid performance after transportation.

Quantum frequency standards are crucial for time measurement, satellite navigation, telecommunication, and other essential applications. Beijing Institute of Radio Metrology and Measurement (BIRMM) has been working on quantum frequency standards and their applications for tens of years. This paper introduces the latest progress on quantum frequency standards at BIRMM, including a calcium optical clock, an active hydrogen maser, and a mercury ion microwave clock. Based on the ¹S₀-³P₁ transition of calcium atoms, a transportable optical clock prototype is built with a stability of 8 × 10^–15 at 1 s. A compact active hydrogen maser has been developed for the Chinese space station. It will be used for scientific research such as examining Einstein’s theory of general relativity and has just been lunched. The preliminary frequency stability of the maser is 1.27 × 10^–15 at 10000 s. Additionally, a prototype mercury ion microwave clock is developed using the hyperfine transition between 6²S_1/2, F = 0 and 6²S_1/2, F = 1. The trapped Hg⁺ ions are pumped by mercury discharge lamps and cooled by Helium gas. The measured clock transition linewidth is about 1 Hz, and frequency stability of 4 × 10^–13 at 1 s and 4 × 10^–14 at 1000 s is achieved.

In response to the demand for operation in non-laboratory environments, there has been a trend toward the development of compact, transportable ultra-stable lasers. This paper reports on this sort of laser system assembled in a cabinet. The whole optical part utilizes fiber-coupled devices to simplify the integration. In addition, spatial beam collimation and alignment into the high-finesse cavity are realized by a five-axis positioner and a focus-adjustable fiber collimator, which significantly relax the alignment and adjustment. A theoretical analysis is performed on how the collimator adjusts the beam profile and coupling efficiency. The support structure of the system is specially designed as well so that it features robustness and transportation without performance degradation. The observed linewidth is 1.4 Hz within a duration of 1 s. After subtracting the linear drift of 70 mHz/s, the fractional frequency instability is better than 4 × 10⁻¹⁵, for the averaging time ranging from 1 to 100 s, which is close to the thermal noise limit of the high-finesse cavity.