The study is concerned with the filtering problem of discrete time positive switched delay systems under an improved delay-dependent persistent dwell time (PDT) switching, which includes delay-independent PDT switching as a special case. Under delay-dependent PDT switching, a pair of state bounding positive filters is designed such that the output of positive switched delay systems can be estimated at all times, and the effect of delay on PDT switching and the performance is also discussed. Finally, a numerical example is presented to demonstrate the effectiveness of the developed results.