In kinematic Global Navigation Satellite Systems (GNSS) navigation, the Kalman Filter (KF) solution relies, to a great extent, on the quality of the dynamic model that describes the moving object's motion behaviour. However, it is rather difficult to establish a precise dynamic model that only connects the previous state and the current state, since these high-order quantities are usually unavailable in GNSS navigation receivers. To overcome such limitations, the Window-Recursive Approach (WRA) that employs the previous multiple states to predict the current one was developed in Zhou et al., (2010). Its essence is to adaptively fit the moving object's motion behaviour using the multiple historical states in a short time span. Up to now, the WRA method has been performed only using GNSS pseudorange measurements. However, in GNSS navigation fields, the strength of pseudorange observation model is usually weak due to various reasons, e.g., multi-path delay, outliers, insufficient visible satellites. As an important complementary measurement, Doppler can be used to aid Position and Velocity (PV) estimation. In this contribution, implementation of WRA will be developed using the pseudorange and Doppler measurements. Its corresponding state transition matrix is constructed based on the Newton's Forward Difference Extrapolation (NFDE) and Definite Integral (DI) methods for the efficient computation. The new implementation of WRA is evaluated using the real kinematic vehicular GNSS data with two sampling rates. The results show that:
(i) aided by GNSS Doppler measurement, the new implementation of WRA significantly improves the accuracy compared with the pseudorange-only WRA.
(ii) In high sampling rate, the WRA works best in the case of 2 epochs in time window, while in the low sampling rate, it obtains better solutions if more epochs involved in time window.
(iii) Compared with KF with constant velocity dynamic model, the WRA demonstrates better in the self-adaptation and validity.
(iv) As a benefit of WRA itself, the NFDE/DI-based state transition matrix for WRA can be previously computed offline without increasing the computation burdens.
