  This paper demonstrates the impact of state-of-the-art instrumental
calibration techniques on the precision of arrival times obtained from 9.6
years of observations of millisecond pulsars using the Murriyang 64-m CSIRO
Parkes Radio Telescope. Our study focuses on 21-cm observations of 25
high-priority pulsars that are regularly observed as part of the Parkes Pulsar
Timing Array (PPTA) project, including those predicted to be the most
susceptible to calibration errors. We employ Measurement Equation Template
Matching (METM) for instrumental calibration and Matrix Template Matching (MTM)
for arrival time estimation, resulting in significantly improved timing
residuals with up to a sixfold reduction in white noise compared to arrival
times estimated using Scalar Template Matching and conventional calibration
based on the Ideal Feed Assumption. The median relative reduction in white
noise is 33 percent, and the maximum absolute reduction is 4.5 microseconds.
For PSR J0437-4715, METM and MTM reduce the best-fit power-law amplitude (2.7
sigma) and spectral index (1.7 sigma) of the red noise in the arrival time
residuals, which can can be tentatively interpreted as mitigation of 1/f noise
due to otherwise unmodeled steps in polarimetric response. These findings
demonstrate the potential to directly enhance the sensitivity of pulsar timing
array experiments through more accurate methods of instrumental calibration and
arrival time estimation.
