Calculating ripple voltage across sense resistor (SEPIC DC-DC Converter)
It appears that \$\chi\$ is simply a design parameter that is related to the voltage ripple (or current ripple) across the sense resistor. As per page 22 of the data sheet, 'A good starting point for \$\chi\$ is 0.2 and careful evaluation of system stability should be made to ensure adequate design margin'. So, the only way to know if the value chosen for \$\chi\$ is acceptable is by designing and analyzing the circuit.