Apparatus and method for estimating system state

An apparatus for estimating a system state, the apparatus comprising:

• at least one processor configured to:
• generate a plurality of partial state estimation values ({circumflex over (z)}1,{circumflex over (z)}2, . . . {circumflex over (z)}p;
• {circumflex over (z)}i) for a current state of a target system, based on a control input for the target system and output values (y1, y2, . . . , yp;
• yi) of a plurality of sensors disposed in the target system corresponding to state observation values of the target system according to the control input;
• determine a set (Γ({circumflex over (z)}(t)) of a plurality of candidate estimation values (X(t)) for a total state estimation value of the target system, based on the plurality of partial state estimation values;
• and
• determine a final state estimation value ({circumflex over (x)}(t) for the current state of the target system among the plurality of candidate estimation values (X(t)),
• wherein, in order to generate the observer state (gi) and the plurality of partial state estimation values ({circumflex over (z)}1,{circumflex over (z)}2, . . . {circumflex over (z)}p;
• {circumflex over (z)}i), the at least one processor is configured to perform:
• a first calculation of generating a first observability matrix (Ai1) and a second observability matrix (G), based on a property matrix (A) of the dynamic state equation and an output matrix (C) for the plurality of sensors,
• a second calculation of generating a first linear transformation matrix (Mi), based on a range space (P) of a transpose matrix (GT) of the second observability matrix (G) and orthogonal bases (Q) of a null space of the second observability matrix (G),
• a third calculation of generating a second linear transformation matrix (MiAi1MiT) by performing a coordinate change for the first observability matrix (Ai1) through the first linear transformation matrix (Mi),
• a fourth calculation of generating a fourth linear transformation matrix (Ni′AiōNi′−1) by performing a coordinate change for a matrix block Aiō through a third linear transformation matrix Ni′ making the matrix block Aiō of the second linear transformation matrix (MiAi1MiT) to be block diagonal,
• a fifth calculation of generating a sixth linear transformation matrix (Ti), based on a fifth linear transformation matrix (Ni) defined based on the third linear transformation matrix and, the first linear transformation matrix (Mi),
• a sixth calculation of generating a seventh linear transformation matrix (Ui) and an eighth linear transformation matrix (Vi), based on the sixth linear transformation matrix (Ti) and an inverse matrix (Ti−1) of the sixth linear transformation matrix (Ti), and
• a seventh calculation of transforming the dynamic state equation, based on the seventh linear transformation matrix (Ui) and the eighth linear transformation matrix (Vi).