To improve smartphone GNSS positioning performance using extra inequality information, an inequality constraint method was introduced and verified in this study. Firstly, the positioning model was reviewed and three constraint applications were derived from it, namely, vertical velocity, direction, and distance constraints. Secondly, we introduced an estimator based on the density function truncation method to solve the inequality constraint problem. Finally, the performance of the method was investigated using datasets from three smartphones, including a Huawei P30, a Huawei P40, and a Xiaomi MI8. The results indicate that the position and velocity accuracy can be improved in the up component using a vertical velocity constraint. The horizontal positioning accuracy was increased using a heading direction constraint with dynamic datasets. Numerically, the root mean square error (RMSE) improvement percentages were 16.77%, 14.57%, and 31.09% for HP40, HP30, and XMI8, respectively. Using an inter-smartphone distance constraint could enhance the horizontal positioning of all participating smartphones, with improvement percentages of 34.27%, 75.58%, and 23.66% for HP40, HP30, and XMI8, respectively, in the static dataset. Additionally, the improvement percentages were 15.90%, 5.55%, and 0.17% in dynamic datasets. In summary, this study demonstrates that utilizing inequality constraints can significantly improve smartphone GNSS positioning.

An inter-system model for multi-GNSSs (global navigation satellite systems) makes the interoperability among different GNSS constellations possible. In recent years, inter-system models for geodetic receivers have been extensively studied. However, the precise positioning of smartphones suffers from various problems, and the current research mostly focuses on how to achieve the GNSS ambiguity resolution. Based on the research of receiver channel-dependent bias, in this study, we will research the temporal behaviors of differential inter-system bias (DISB) and implement an inter-system model for smartphones. A representative Huawei P40 (HP40) smartphone was used in the experiments, and the results show the following: (1) For the HP40, the frequencies of Code Division Multiple Access (CDMA) systems are free of receiver channel-dependent phase bias, which provides the chances for further interoperability among these systems. However, the code observations of the HP40 are influenced by receiver channel-dependent code bias; it is therefore suggested to set a large initial standard deviation (STD) value for code observations in the positioning. (2) GPS L1/QZSS L1 and BDS-2 B1I /BDS-3 B1I are free of phase DISB, and there is obvious phase DISB between GPS L1 and Galileo E1; even so, the valuations are sufficiently stable and the STD is close to 0.005 cycles. However, the phase DISB of GPS L1/BDS B1I is unstable. (3) For kinematic positioning, when the stable phase DISB is introduced, a 3–38.9% improvement in the N/E/U directions of the positioning accuracies in the inter-system differencing is achieved compared with the intra-system differencing.

By calibrating the inter-system bias (ISB), an inter-system model can be achieved to improve the performance of multi-global navigation satellite system (GNSS) positioning. A number of studies were carried out to compose inter-system models among code division multiple access (CDMA) systems. However, due to the frequency division multiple access (FDMA) technique, GLONASS phase and code observations suffer from inter-frequency phase bias (IFPB) and inter-frequency code bias (IFCB) respectively, which make it difficult to obtain the ISB among GLONASS and CDMA systems. In addition, most of the current inter-system models are unable to handle mixed frequencies. A new single difference-based uniform inter-system model suitable for all of the CDMA and FDMA frequency combinations is proposed in this study. We first utilize a particle filter approach to extract the IFPB rate. Afterwards, the multi-ISB parameters can be estimated by the proposed model simultaneously. Four short baselines containing the signals of GLONASS, GPS, BDS3, BDS2, Galileo, and QZSS are selected to validate the model. The quantitative results indicate that the IFPB rate can be extracted precisely by a particle filter within ten epochs. The inter-system phase bias valuations are sufficiently stable on a daily scale and have standard deviation near 0.01 cycles. After de-weighting the GLONASS code observations to reduce the influence of IFCB, the inter-system code bias is also stable. Furthermore, imposing the stable ISB on the multi-GNSS inter-system model can effectively improve the single-frequency real-time kinematic positioning accuracy and reliability for severely obstructed situations with only a small number of satellites observed.

Positioning methods that rely solely on global satellite navigation system (GNSS) measurements have significantly decreased reliability in urban environments and cannot meet the needs of industries, such as autonomous driving. This article introduces a novel fifth-generation (5G) joint time of arrival (TOA) and unit vector observation model that takes rotation into account, and evaluates its performance through multiple sets of simulated data. The results show that compared with the traditional joint TOA and angle of arrival (AOA) observation model, the proposed model can notably improve the positioning accuracy, and the effect is better after iteration. Furthermore, we conduct a new stochastic model for 5G measurements and investigate the impact of model coefficients on performance. The results reveal that inappropriate coefficients will lead to loss of observational information, highlighting the importance of stochastic models. In urban environments, the proposed 5G joint observation model can effectively assist GNSS and provide more accurate navigation services and rotation estimation, providing valuable insights for the future development of smart transportation.

The need for high-precision and dependable navigation and positioning services is rising in the mass market as a result of the BDS-3’s completion and the performance development of smartphone chips. However, compared with the geodesic receiver, the positioning accuracy of smartphones is severely degraded due to the low antenna gain and poor anti-interference ability. In March 2022, Redmi released K50 smartphones that support BDS tri-frequency, providing conditions for further improvement of smartphone positioning. First, we collected the multi-constellation and multi-frequency data of the K50 to evaluate the availability of tri-frequency observations. Then, we compared the observations between different frequencies and found that the pseudorange data quality of the L5/E5a is better than that of L1/E1. For the BDS, the pseudorange data quality of the B2a is obviously better than that of the other two frequencies. For carrier observations, expect for the initial phase biases of B1C, there is no significant difference in data quality between different frequencies. It means that the traditional random model cannot accurately reflect the pseudorange quality of smartphone observation. We used the zero-baseline double difference residual method to calculate the smartphone observation accuracy and refined the random model. Finally, we verified the performance of the refined model through location tests. The results show that the model refinement can significantly improve positioning accuracy and reliability in the single point positioning test and shorten the convergence time in relative positioning. In kinematic positioning, the improved model can obtain the positioning accuracy of a single epoch centimeter-level even when the signal is slightly blocked, which is of great significance for high-precision navigation of smartphones in urban environments.

In the process of composing a double-differenced positioning model, it is difficult to separate different frequency signals between code division multiple access (CDMA) systems, the single-difference ambiguity of the pivot satellite and phase differential inter-system biases (PDISBs). Hence it is difficult to calibrate in advance the bias between systems in order to build an inter-system model which only needs one pivot satellite. Based on analysis of the stability of PDISB parameters for non-overlapping frequency CDMA systems, this study adopts a particle filter to estimate the fractional part of the PDISBs (F-PDISBs) between the systems and proposes a particle filter-based inter-system positioning model. Results show that the F-PDISBs and code DISBs for the baselines with the same receiver types and some with different receiver types are rather stable over time and for these baselines it is feasible to use a particle filter to estimate the F-PDISB parameters in the initial stage. Having attained the F-PDISBs, the inter-system model can be constructed to improve positioning accuracy in complex operational environments.