An apparatus for estimating attitude using an inertia measuring apparatus comprising: a Kalman filter 3 adapted to receive a quantity of state .omega.(t) from the inertia measuring apparatus 1, input the quantity of state into a predetermined system equation and a predetermined observation equation and execute time update processing and observation update processing with regard to the system equation and the observation equation; a processing section 4 adapted to generate an estimated value of a time differentiation of a modified Rodrigues parameter .alpha.(t) based upon an output of the Kalman filter; an integral processing section 5 adapted to generate an estimated value of the modified Rodrigues parameter based upon an output of the processing section; a system propagation matrix generating section 6 adapted to update an observation sensitivity matrix based upon an initial value being given beforehand and an output of the integral processing section and supply the updated output to the Kalman filter; a transformed matrix generating section 7 adapted to generate a coordinate transformation matrix R based upon an output of the integral processing section; and an attitude estimation section 8 adapted to carry out an attitude estimation based upon an output of the transformed matrix generating section, is disclosed.
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