GB1118663A - Inertial navigation system error correcting methods - Google Patents

Abstract

1,118,663. Navigation computing. NORTH AMERICAN AVIATION Inc. 3 June, 1966 [3 June, 1965], No. 24934/66. Heading G4G. [Also in Division G1] A gyroscope stabilized inertial navigation system comprises a computer from which output navigation signals are obtained, the computer also being arranged to formulate in differential equation form an augmented navigation system which incorporates the effects of applied correction signals, the computer being further arranged to estimate the correction signals to be applied from the output signals and from position or azimuth reference data obtained intermittently or continuously, the gyroscope drift rates obtained in this way being split into two components, a constant drift rate and a random drift, the applied correction signals thus being related to both these components and not merely to an estimated linear gyro drift. In analysing the system three co-ordinate systems are defined, the true, platform and computer systems. The true and platform systems have the same centre but are displaced by a vector angle #. The computer system has its origin at the computed vehicle system giving a position error 80 relative to the true co-ordinate system. Platform drift is defined by a vector # relating the platform and computer co-ordinate systems. Thus # = # + ##. The # vector has three components representative of the misalignments between the computer and platform co-ordinate systems. In vector rotation this can be given by the differential equation # = V# + # g (1) where # is the time derivative of #, and V is a matrix representative of the velocity of the system relative to inertial space. # represents the drift rate of the platform. If the reference data is obtained from a star tracker having an azimuth a and elevation # then the output equation of the system assuming error angles #α and ## takes the form or more simply y = M 2 (α, #)# where M 2 is the above 2 x 3 matrix. It is desired to estimate the drift rate vector # assuming this to be variable. The random drift rate vector # r can be represented by the differential equation # r = H# r + w (2) where H is a diagonal matrix and w represents a white noise vector. The constant drift rate vector # o is simply # o = 0 (3). Combining equations (1), (2) and (3). the augmented system is now obtained as or more simply X = Fx + #w. The output of the augmented system is of the form y = Mx + v. Adding the effect of control to the augmented system equation we get X = Fx + #w + Ju where J is a control distribution matrix and u is the control vector. The optimum control vector is determined by relating the performance index L of the system i.e. positional error with time, to the control vector u by integrating L with respect to u. The optimum control vector is then used to apply corrections to the inertial system and generate the augmented system.