EBook - Mathematical Methods for Robotics and Vision Part 4 docx

... the discrepancies between left- and right-hand sides of the equations. 3 .4. LEAST-SQUARES SOLUTION OF A HOMOGENEOUS LINEAR SYSTEMS 33 which is the projection of the right-hand side vector b onto the ... following components: for for When written as a function of the vector c, this is y c Notice that there is no other choice for y, which is therefore unique: minimum residual forces the...

Ngày tải lên: 10/08/2014, 02:20

... variables 4. 1 .4 Stokes’ and divergence theorems and potential fields of three variables 4. 1.5 Diffusion and flow problems 4. 2 Partial differential equations and sparse linear systems 4. 2.1 Finite ... collection of mathematical tools for both understandingand solving problems in robotics and computer vision. Several classes at Stanford cover the topics presented in thi...

Ngày tải lên: 10/08/2014, 02:20

... 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 immediately that x x and hence, ... 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 s...

Ngày tải lên: 10/08/2014, 02:20

... lemma. Lemma 5 .4. 7 If for an matrix we have , then for every , the norm of the -th row of equals the norm of its -th column. Proof. From we deduce x x x x x x (5.13) If x e , the -th column of ... canonical form. Finally, in sections 6 .4 and 6.5, we set up and solve a particular differential system as an illustrative example. 6.1 Scalar Differential Equations of Order Higher than...

Ngày tải lên: 10/08/2014, 02:20

... 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 undefined for . This function returns the arctangent ... 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...

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) ... available information by grouping equations 7.20 and 7.21 into one, and packaging the error covariances into a single, block-diagonal matrix. Thus, we have y x n 7 .4. BLUE ES...

Ngày tải lên: 10/08/2014, 02:20

... collection of mathematical tools for both understandingand solving problems in robotics and computer vision. Several classes at Stanford cover the topics presented in this class, and do so in ... want to understandrobotics or vision, youshould take classes in these subjects, since this course is not on robotics or vision. On the other hand, if you do plan to study robotics,...

Ngày tải lên: 14/03/2014, 14:20