EBook - Mathematical Methods for Robotics and Vision Part 1 pdf

... own right. 1. 1 Who Should Take This Class The main goal of this class is to present a collection of mathematical tools for both understandingand solving problems in robotics and computer vision. ... and D. Hilbert, Methods of Mathematical Physics, Volume I and II, John Wiley and Sons, 19 89. D. A. Danielson, Vectors and Tensors in Engineering and Physics, Addison-Wes...

Ngày tải lên: 10/08/2014, 02:20

... equation (6 .1) . In summary, we have the following result. The solution to x x b (6.7) with initial value x x (6.8) is x x x (6.9) where x x (6 .10 ) and x b (6 .11 ) Since we now have a formula for the ... is the -th column of , and e is the -th column of , which is the conjugate of the -th row of . Since conjugationdoes not change the norm of a vector, the equality (5 .13 ) implies t...

Ngày tải lên: 10/08/2014, 02:20

... the equalityof left- and right-hand side. When this process is finished, is in echelon form. In particular, if the matrix is square and if all columns have a pivot, then is upper-triangular. “Stop” ... once for the nonhomogeneous system, and times for the homogeneous system, with suitable values of the free variables. This yields the solution in the form (2 .11 ). Notice that the vec...

Ngày tải lên: 10/08/2014, 02:20

... DECOMPOSITION equation (3 .17 ) yields d n 1 n 1 n n 1 1 n 1 n 1 from which we obtain n 1 that is, p n By replacing this expression into equation (3 .16 ), we obtain n d n n 1p n n n where 1p collects the ... DECOMPOSITION 29 2 x 1 x v 2 v 1 22 2 v’ 1 v’ 2 y y 1 u 3 y 3 u σ 22 u σ 11 σ 22 u’ σ 11 u’ x ξ ξ 1 ξ η η 1 y η Figure 3.2: Decomposition of the mapping in fig...

Ngày tải lên: 10/08/2014, 02:20

... x where and are, respectively, the largest and smallest singular value of . Proof. From the definitions y x x and y y y (4 .10 ) we immediately obtain the expression for steepest descent in terms of and ... equations (4.3) and (4.6) and the Kantorovich inequality we obtain x x y g g g g g g y y (4 .11 ) x x (4 .12 ) Since the ratio in the last term is smaller than one, it follows...

Ngày tải lên: 10/08/2014, 02:20

... STATE ESTIMATION 89 k | k -1 ^ y H k x k | k -1 ^ x ^ k | k k | k P x ^ P k +1 | k k +1 | k propagatepropagate x ^ P k -1 | k -1 k -1 | k -1 y k y k -1 y k +1 k update k | k -1 P k -1 k +1 time Figure 7.2: The ... Re Im Re where Re, Im denote the real and imaginary part and where the two-argument function is defined as follows for if if if and if and and is undefi...

Ngày tải lên: 10/08/2014, 02:20

... Kalman filter computes up-to-date information about the current state. 7.7. LINEAR SYSTEMS AND THE KALMAN FILTER 97 5 10 15 20 25 30 35 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1. 4 true (dashed) and estimated (solid) ... 7.3: The true and estimated trajectories get closer to one another. Trajectories start on the right. 0 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1 1.2 1. 4 1. 6 1. 8 2 distanc...

Ngày tải lên: 10/08/2014, 02:20

... and D. Hilbert, Methods of Mathematical Physics, Volume I and II, John Wiley and Sons, 19 89. D. A. Danielson, Vectors and Tensors in Engineering and Physics, Addison-Wesley, 19 92. J. W. Demmel, ... own right. 1. 1 Who Should Take This Class The main goal of this class is to present a collection of mathematical tools for both understandingand solving problems in robotic...

Ngày tải lên: 14/08/2014, 11:20

... subtracts row 1 multipliedby 2 /1 from row 2, and subtracts row 1 multiplied by -1 /1 from row 3. When applied to both and c this yields , c Notice that now ( ) the entries are zero for , for both and ,so ... own right. 1. 1 Who Should Take This Class The main goal of this class is to present a collection of mathematical tools for both understandingand solving problems...

Ngày tải lên: 14/03/2014, 14:20

... the equality ofleft- and right-hand side. When this process is finished, is in echelon form. In particular, if the matrix is square and if all columns have a pivot, then is upper-triangular. “Stop” ... of : Skip no-pivot columns If is zero for every , then increment by 1. If exceeds stop. Row exchange Now and is nonzero for some . Let be one such value of .If , exchange rows and o...

Ngày tải lên: 14/08/2014, 11:20