Tham khảo tài liệu 'crc press mechatronics handbook 2002 by laxxuss episode 3 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | FIGURE LKF tracking of a two-dimensional trajectory. Reference Trajectory The true dynamic system is described by a general first-order ordinary differential equation X t f X t a t w t where f is the nonlinear dynamics function that incorporates all significant deterministic effects of the environment a is a vector of parameters used in the model and w t is a random process that accounts for the noise present from mismodeling in f or from the quantum uncertainty of the universe depending on the accuracy of the deterministic model in use. With these general models available a linear Kalman filter LKF may be derived in a discrete-time formulation. The dynamics and measurement functions are linearized about a known reference state XL t which is related to the true environment state X t via X t x t X t The LKF state estimate is related to the true difference by Xk Xk Sxk where the denotes the state estimate or filter state Sx is the estimation error and indicates whether the estimate and error are evaluated instantaneously before - or after measurement update at discrete time tk. It is important to emphasize that the LKF filter state is the estimate of the difference between the environment and the reference state. The LKF mode of operation will therefore carry along a reference state and the filter state between measurement updates. Only the filter state is at the time of measurement update. Figure illustrates the generalized relationship between the true reference and filter states in an LKF estimating a two-dimensional trajectory. Linearization of Dynamic and Measurement System Models The dynamics and measurement functions may be linearized about the known reference state X t according to f X a t f X t a t F X t a t x t w t h X a t h X t p t H X t p t x t v t 2002 CRC Press LLC FIGURE LKF tracking of a two-dimensional trajectory. Reference Trajectory The true dynamic system is described by a general first-order ordinary .
