The signal quality of a global navigation satellite system can easily be affected in a complex urban environment. Signals from inertial navigation systems (INSs) may also be affected by hardware and structures. To solve the problems of excessive robustness and mishandling of INS errors in the conventional robust and adaptive Kalman filter (CRAKF), an improved non-holonomic robust and adaptive Kalman filter (NRAKF) is proposed in this paper. The NRAKF algorithm first judges whether the INS contains gross errors according to non-holonomic constraint, then selects the order of calculation of the covariance of robust measurement noise and adaptation to state noise covariance, and finally uses an extended Kalman filter (EKF) to obtain the position, velocity, and attitude of the real time kinematic (RTK)/INS integrated navigation system. To demonstrate the performance of the NRAKF, two land vehicle tests were conducted; the results indicate that the tightly integrated model is more robust than the loosely integrated model. Compared with the EKF, both the CRAKF and the NRAKF have stronger robustness. Compared to the CRAKF, the NRAKF improves the position and velocity accuracy in the east and north directions by more than 36.85%, 33.13%, 36.46%, and 22.65% under the loosely coupled RTK/INS integration, and by 61.5%, 57.42%, 73.94%, and 33.53% under the tightly coupled RTK/INS integration. Therefore, the NRAKF performs better than the CRAKF for both loosely and tightly integrated models, and can effectively avoid the phenomena of excessive robustness and mishandling of INS errors.

Time-differenced carrier phase (TDCP) is a commonly used method of precise velocimetry, but when the receiver is in a dynamic or complex observation environment, the estimation accuracy is reduced. Doppler velocimetry aims at estimating instantaneous velocity, and the accuracy is restricted by the accuracy of measurement. However, in such unfavourable cases, the Doppler measurement is more reliable than the carrier phase measurement. This paper derives the relationship between Doppler observation and TDCP observation, then proposes a Doppler enhanced TDCP algorithm, for the purpose of improving the velocity estimation accuracy in dynamic and complex observation environments. In addition, considering the error caused by the constant speed state update model in the robust Kalman filter (RKF), this paper designs a terrain adaptive and robust Kalman filter (TARKF). After three experimental tests, the improved TDCP algorithm can significantly increase the speed measurement accuracy to sub-metre per second, and the accuracy can be further improved after using TARKF.

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Ultra-wideband (UWB) is essential in precise point positioning (PPP)/inertial navigation systems (INS)/UWB integrated navigation with the advantage of highly accurate observations. However, its accuracy could be affected by its sparse distribution, limited operating distance and low space height. In a dynamic environment, it is not easy to determine its variance precisely for an integrated system. Sometimes, the system performs poorly due to improper variance. In this paper, a map-matching variance optimization of UWB observation was firstly developed for tightly coupled positioning. Instead of the characteristic analysis of the UWB signal directly, the optimization can be realized based on the accuracy of PPP/INS solutions. The proposed map-matching algorithm can be adopted to access the accuracy of PPP/INS and determine the optimization factor so that the variance of UWB can be dynamically obtained. Then, the variance was adopted in the stochastic model of the PPP/INS/UWB system. The actual experiments were conducted to validate the proposed method under two different scenarios, and the effectiveness of this method was analysed. The results indicated that the proposed method could obtain suitable variance and improve the performance in both these two scenarios.

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