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Example: Falling Body The initial mean and covariance are taken to be 105 ft Purdue 2024 mo Ро -6000 ft/sec (140) 2000 lb/ft² 500 ft² 0 = 0 2 x 104 ft²/sec² 0 0 (141) 0 0 2.5 × 105 lb²/ft² Example: Falling Body The system parameters are taken to be 64 Po 3.4 × 10 3 lb sec²/ft4 Kp = 22000 ft g= 32.2 ft/sec² R = 100 ft². (142) (143) The resulting error for each state variable and their associated 10 bounds (from the square root of the corresponding entry in the covariance matrix) can be seen below. ©Purdue 2024 65 Example: Falling Body The equations of motion for the body are given by .x X1 X2 = X3 X2 with d-g = f(x) 0 (135) d px² 2X3 X1 and P = Po exp (136) d is drag acceleration, g is the acceleration of gravity, p is atmospheric density (with Po as the atmospheric density at sea level), and kø is a decay constant. Purdue 2024 Example: Falling Body The differential equation governing X2 (velocity) is nonlinear through the dependence of drag on velocity, air density, and ballistic coefficient. We will assume to take linear measurements of height which are corrupted according to pg(0, R). The initial truth for the simulation is drawn according to XoPg(105 ft, 500 ft²) Purdue 2024 62 (137) = Xo Pg(-6000 ft/sec, 2 × 104 ft²/sec²) (138) B=pg (2000 lb/ft², 2.5 × 105 lb²/ft4) (139) 63

Example: Falling Body The initial mean and covariance are taken to be 105 ft Purdue 2024 mo Ро -6000 ft/sec (140) 2000 lb/ft² 500 ft² 0 = 0 2 x 104 ft²/sec² 0 0 (141) 0 0 2.5 × 105 lb²/ft² Example: Falling Body The system parameters are taken to be 64 Po 3.4 × 10 3 lb sec²/ft4 Kp = 22000 ft g= 32.2 ft/sec² R = 100 ft². (142) (143) The resulting error for each state variable and their associated 10 bounds (from the square root of the corresponding entry in the covariance matrix) can be seen below. ©Purdue 2024 65 Example: Falling Body The equations of motion for the body are given by .x X1 X2 = X3 X2 with d-g = f(x) 0 (135) d px² 2X3 X1 and P = Po exp (136) d is drag acceleration, g is the acceleration of gravity, p is atmospheric density (with Po as the atmospheric density at sea level), and kø is a decay constant. Purdue 2024 Example: Falling Body The differential equation governing X2 (velocity) is nonlinear through the dependence of drag on velocity, air density, and ballistic coefficient. We will assume to take linear measurements of height which are corrupted according to pg(0, R). The initial truth for the simulation is drawn according to XoPg(105 ft, 500 ft²) Purdue 2024 62 (137) = Xo Pg(-6000 ft/sec, 2 × 104 ft²/sec²) (138) B=pg (2000 lb/ft², 2.5 × 105 lb²/ft4) (139) 63

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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I want to code the extended kalman filter in MATLAB of the following falling body problem.

Example: Falling Body The initial mean and covariance are taken to be 105 ft Purdue 2024 mo Ро -6000 ft/sec (140) 2000 lb/ft² 500 ft² 0 = 0 2 x 104 ft²/sec² 0 0 (141) 0 0 2.5 × 105 lb²/ft² Example: Falling Body The system parameters are taken to be 64 Po 3.4 × 10 3 lb sec²/ft4 Kp = 22000 ft g= 32.2 ft/sec² R = 100 ft². (142) (143) The resulting error for each state variable and their associated 10 bounds (from the square root of the corresponding entry in the covariance matrix) can be seen below. ©Purdue 2024 65
Transcribed Image Text:Example: Falling Body The initial mean and covariance are taken to be 105 ft Purdue 2024 mo Ро -6000 ft/sec (140) 2000 lb/ft² 500 ft² 0 = 0 2 x 104 ft²/sec² 0 0 (141) 0 0 2.5 × 105 lb²/ft² Example: Falling Body The system parameters are taken to be 64 Po 3.4 × 10 3 lb sec²/ft4 Kp = 22000 ft g= 32.2 ft/sec² R = 100 ft². (142) (143) The resulting error for each state variable and their associated 10 bounds (from the square root of the corresponding entry in the covariance matrix) can be seen below. ©Purdue 2024 65
Example: Falling Body The equations of motion for the body are given by .x X1 X2 = X3 X2 with d-g = f(x) 0 (135) d px² 2X3 X1 and P = Po exp (136) d is drag acceleration, g is the acceleration of gravity, p is atmospheric density (with Po as the atmospheric density at sea level), and kø is a decay constant. Purdue 2024 Example: Falling Body The differential equation governing X2 (velocity) is nonlinear through the dependence of drag on velocity, air density, and ballistic coefficient. We will assume to take linear measurements of height which are corrupted according to pg(0, R). The initial truth for the simulation is drawn according to XoPg(105 ft, 500 ft²) Purdue 2024 62 (137) = Xo Pg(-6000 ft/sec, 2 × 104 ft²/sec²) (138) B=pg (2000 lb/ft², 2.5 × 105 lb²/ft4) (139) 63
Transcribed Image Text:Example: Falling Body The equations of motion for the body are given by .x X1 X2 = X3 X2 with d-g = f(x) 0 (135) d px² 2X3 X1 and P = Po exp (136) d is drag acceleration, g is the acceleration of gravity, p is atmospheric density (with Po as the atmospheric density at sea level), and kø is a decay constant. Purdue 2024 Example: Falling Body The differential equation governing X2 (velocity) is nonlinear through the dependence of drag on velocity, air density, and ballistic coefficient. We will assume to take linear measurements of height which are corrupted according to pg(0, R). The initial truth for the simulation is drawn according to XoPg(105 ft, 500 ft²) Purdue 2024 62 (137) = Xo Pg(-6000 ft/sec, 2 × 104 ft²/sec²) (138) B=pg (2000 lb/ft², 2.5 × 105 lb²/ft4) (139) 63
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