A Two-stage Kalman Filter for Sensorless Direct Torque Controlled PM Synchronous Motor Drive

Table 2

OTSEKF arithmetic operation requirements.

	Number of multiplications; (𝑛=4, 𝑚=2, 𝑞=2, 𝑝=2)	Number of additions; (𝑛=4, 𝑚=2, 𝑞=2, 𝑝=2)
𝐴𝑘, 𝐶𝑘, 𝐸𝑘, 𝐻^1𝑘, 𝐻^2𝑘, 𝐵^𝑢𝑘, 𝐵^Θ𝑘	Function of system (20)	Function of system (3)
𝑃^Θ𝑘|𝑘−1	2𝑝^3 (16)	2𝑝^3−𝑝^2 (12)
𝑀𝑘−1	𝑛^2𝑝+𝑛𝑝^2 (16)	𝑛^2𝑝+𝑛𝑝^2−𝑛𝑝 (12)
𝑀𝑘−1	2𝑛𝑝^2 (16)	2𝑛𝑝^2 (16)
𝑄^𝑥𝑘−1	2𝑛^2𝑝+𝑛𝑝^2 (24)	2𝑛^2𝑝+𝑛𝑝^2 (24)
𝑃^𝑥𝑘|𝑘−1	2𝑛^3 (16)	2𝑛^3−𝑛^2 (12)
Θ𝑘|𝑘−1	𝑝^2 (4)	𝑝^2−𝑝 (2)
𝑢𝑘−1	𝑛^2𝑝+𝑛𝑝^2+𝑛𝑝 (20)	𝑛^2𝑝+𝑛𝑝^2+𝑛𝑝−𝑛 (18)
𝑋𝑘|𝑘−1	𝑛^2+𝑛𝑞 (8)	𝑛^2+𝑛𝑞 (8)
𝑆𝑘	𝑚𝑛𝑝 (8)	𝑛𝑚𝑝 (8)
𝑆𝑘	𝑚𝑛𝑝 (8)	𝑚𝑛𝑝−𝑚𝑝 (4)
𝐵𝑘	2𝑚𝑛^2 (16)	2𝑚𝑛^2−𝑚^2 (12)
𝐾^Θ𝑘|𝑘	3𝑝^2𝑚+𝑝𝑚^2 (32)	3𝑝^2𝑚+𝑝𝑚^2+𝑚^2−4𝑝𝑚 (20)
𝑃^Θ𝑘|𝑘	𝑝^3+𝑝^2𝑚 (16)	𝑝^3+𝑝^2𝑚−𝑝^2 (12)
Θ𝑘|𝑘	2𝑚𝑝+𝑛𝑚 (12)	2𝑚𝑝+𝑛𝑚 (12)
𝐾^𝑥𝑘|𝑘	𝑛^2𝑚+𝑛𝑚^2 (16)	𝑛^2𝑚+𝑛𝑚^2−2𝑛𝑚 (8)
𝑃^𝑥𝑘|𝑘	𝑛^2𝑚+𝑛^3 (16)	𝑛^2𝑚+𝑛^3−𝑛^2 (12)
𝑋𝑘|𝑘	2𝑛𝑚+𝑚𝑝 (12)	2𝑛𝑚+2𝑚𝑝 (16)
𝑁𝑘	𝑛𝑝𝑚 (8)	𝑛𝑝 (4)
Total	284	215