State of charge (SOC) estimation of lithium batteries is one of the most important unresolved problems in the field of electric vehicles. Due to the changeable working environment and numerous interference sources on vehicles, it is more difficult to estimate the SOC of batteries. Particle filter is not restricted by the Gaussian distribution of process noise and observation noise, so it is more suitable for the application of SOC estimation. Three main works are completed in this paper by taken LFP (lithium iron phosphate) battery as the research object. Firstly, the first-order equivalent circuit model is adapted in order to reduce the computational complexity of the algorithm. The accuracy of the model is improved by identifying the parameters of the models under different SOC and minimum quadratic fitting of the identification results. The simulation on MATLAB/Simulink shows that the average voltage error between the model simulation and test data was less than 24.3 mV. Secondly, the standard particle filter algorithm based on SIR (sequential importance resampling) is combined with the battery model on the MATLAB platform, and the estimating formula in recursive form is deduced. The test data show that the error of the standard particle filter algorithm is less than 4% and RMSE (root mean square error) is 0.0254. Thirdly, in order to improve estimation accuracy, the auxiliary particle filter algorithm is developed by redesigning the importance density function. The comparative experimental results of the same condition show that the maximum error can be reduced to less than 3.5% and RMSE is decreased to 0.0163, which shows that the auxiliary particle filter algorithm has higher estimation accuracy.The intrinsic parameter measurement method is to select suitable battery parameters that can directly characterize the SOC for direct measurement, and then estimate the battery SOC through these parameters. The commonly used intrinsic parameters include open circuit voltage (OCV), impedance spectrum [7], electromotive force (EMF), and internal resistance (IR). The advantage of this method is that the battery SOC can be directly obtained through the mapping relationship between the SOC and the battery intrinsic parameter, and the disadvantage is that the estimation accuracy relies excessively on the accuracy of the mapping relationship between SOC and intrinsic parameters of battery. Holger [8] summarized the SOC estimation method based on the impedance spectrum. Waag [9] confirmed that the impedance parameter of a Li-ion battery changes negatively as the battery ages.Computer intelligence methods found in literature mainly include the neural network model, genetic algorithm and particles swarm optimization. The advantage of these methods is that they do not require a thorough understanding of battery internal mechanism, but they do require large amounts of data for the machine learning process. Sheikhan et al. [10] used an artificial neural network to realize feedback correction of the traditional time-integration m...