  We developed a beam telescope system comprising five layers of
300-$\mu$m-thick INTPIX4NA monolithic pixel sensors with each pixel size of 17
$\mu$m square. The sensors were fabricated using silicon-on-insulator (SOI)
technology. The signal-to-noise ratio of 140--230 is realized at a bias voltage
of 20~V. The tracker system was tested using a positron beam of 200--822 MeV/c,
and various tracking methods are examined to optimize spatial precision
achievable at these energies. The best tracking precision including the
precision of the sensor under test itself is 11.04 $\pm$ 0.10 $\mu$m for
822-MeV/c positrons for an equidistant sensor spacing of 32 mm. The achieved
precision results combined with the intrinsic spatial resolution value obtained
for a similar system using 120 GeV protons are used to estimate the tracking
performance of electrons in the GeV energy range; a tracking precision of 2.22
$\mu$m is evaluated for 5-GeV electrons. The method to estimate the tracking
performance is verified using a Geant4-based simulation. The developed high
precision tracker system enables to map the detailed performance of the sensors
with pixel sizes of $\mathcal{O}$(10 $\mu$m), therefore will be a powerful
system for development of devices targeting precision position resolutions.
