The ability of navigation receiver to track signals is affected by phase locked loop tracking accuracy. Phase discriminator plays an important role in the design of phase locked loop. Base on the influence on the finite word length effect to the dot product and the arctangent discriminator’s performance, a word length error model was proposed. The theoretical analysis of the finite word-length affected to the discriminator’s converge range and gain was presented by deducing the input signal’s statistical characteristic. Analysis and simulation show that the deviation of input signals of the phase discriminator with up to 3 bits has no influence on the carrier tracking accuracy.