MatlabHelp：Kalman.docVIP

Open kalmdemo.m in the Editor Run in the Command Window Kalman Filter Design This demo demonstrates MATLAB® ability to perform Kalman filtering. Both a steady state filter and a time varying filter are designed and simulated below. Problem Description Steady-State Kalman Filter Design Time-Varying Kalman Filter Design Problem Description Given the following discrete plant where A = [1.1269 -0.4940 0.1129, 1.0000 0 0, 0 1.0000 0]; B = [-0.3832 0.5919 0.5191]; C = [1 0 0]; D = 0; design a Kalman filter to estimate the output y based on the noisy measurements yv[n] = C x[n] + v[n] Steady-State Kalman Filter Design You can use the function KALMAN to design a steady-state Kalman filter. This function determines the optimal steady-state filter gain M based on the process noise covariance Q and the sensor noise covariance R. First specify the plant + noise model. CAUTION: set the sample time to -1 to mark the plant as discrete. Plant = ss(A,[B B],C,0,-1,inputname,{u w},outputname,y); Specify the process noise covariance (Q): Q = 2.3; % A number greater than zero Specify the sensor noise covariance (R): R = 1; % A number greater than zero Now design the steady-state Kalman filter with the equations Time update: x[n+1|n] = Ax[n|n-1] + Bu[n] Measurement update: x[n|n] = x[n|n-1] + M (yv[n] - Cx[n|n-1]) where M = optimal innovation gain using the KALMAN command: [kalmf,L,P,M,Z] = kalman(Plant,Q,R); The first output of the Kalman filter KALMF is the plant output estimate y_e = Cx[n|n], and the remaining outputs are the state estimates. Keep only the first output y_e: kalmf = kalmf(1,:); M, % innovation gain M = 0.5345 0.0101 -0.4776 To see how this filter works, generate some data and compare the filtered response with the true plant response: To simulate the system above, you can generate the response of each part separately or generate both together.