A fast and precise positioning method implemented by a user receiver, comprising: a step 1 of acquiring observation data of navigation satellites and Low Earth Orbit augmentation satellites at a current epoch and preprocessing the observation data; characterized in that the method further comprises: a step 2 of respectively acquiring navigation telegrams of the navigation satellites and the LEO augmentation satellites, and obtaining a precise orbit and a clock bias of the navigation satellites and a precise orbit and a clock bias of the LEO augmentation satellites according to the acquired navigation telegrams of the LEO augmentation satellites; a step 3 of correcting errors received in the positioning process according to the acquired navigation telegrams; a step 4 of normalizing by taking a type of satellite navigation system as reference to obtain unified linear observation equations, and calculating observation values of positioning and velocity measurement parameters; a step 5 of obtaining estimated values of positioning and velocity measurement parameters at the current epoch through a state equation according to the calculated observation values of positioning and velocity measurement parameters and estimated values of positioning and velocity measurement parameters at the previous epoch; and a step 6 of generating and saving positioning and velocity measurement results at the current epoch according to the estimated values of positioning and velocity measurement parameters at the current epoch and returning to the step 1. a step 1 of acquiring observation data of navigation satellites and Low Earth Orbit augmentation satellites at a current epoch and preprocessing the observation data; characterized in that the method further comprises: a step 2 of respectively acquiring navigation telegrams of the navigation satellites and the LEO augmentation satellites, and obtaining a precise orbit and a clock bias of the navigation satellites and a precise orbit and a clock bias of the LEO augmentation satellites according to the acquired navigation telegrams of the LEO augmentation satellites; a step 3 of correcting errors received in the positioning process according to the acquired navigation telegrams; a step 4 of normalizing by taking a type of satellite navigation system as reference to obtain unified linear observation equations, and calculating observation values of positioning and velocity measurement parameters; a step 5 of obtaining estimated values of positioning and velocity measurement parameters at the current epoch through a state equation according to the calculated observation values of positioning and velocity measurement parameters and estimated values of positioning and velocity measurement parameters at the previous epoch; and a step 6 of generating and saving positioning and velocity measurement results at the current epoch according to the estimated values of positioning and velocity measurement parameters at the current epoch and returning to the step 1. a step 2 of respectively acquiring navigation telegrams of the navigation satellites and the LEO augmentation satellites, and obtaining a precise orbit and a clock bias of the navigation satellites and a precise orbit and a clock bias of the LEO augmentation satellites according to the acquired navigation telegrams of the LEO augmentation satellites; a step 3 of correcting errors received in the positioning process according to the acquired navigation telegrams; a step 4 of normalizing by taking a type of satellite navigation system as reference to obtain unified linear observation equations, and calculating observation values of positioning and velocity measurement parameters; a step 5 of obtaining estimated values of positioning and velocity measurement parameters at the current epoch through a state equation according to the calculated observation values of positioning and velocity measurement parameters and estimated values of positioning and velocity measurement parameters at the previous epoch; and a step 6 of generating and saving positioning and velocity measurement results at the current epoch according to the estimated values of positioning and velocity measurement parameters at the current epoch and returning to the step 1.