EBook - Mathematical Methods for Robotics and Vision Part 5 ppt

... 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 ... most problems in robotics, vision, and arguably every other science or endeavor take on the form of optimization problems. One is that the desired goal may not be achievable, a...

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 ... be nonzero for some . We have a a a 0 so that a a (2.6) as desired. The converse is proven similarly: if a a “iff” means “if and only if.” CS 2 05 Mathematical Methods for Robo...

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” ... 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 of...

Ngày tải lên: 10/08/2014, 02:20

... 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 choice of , and minimum-norm ... 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 righ...

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 ... 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 that the...

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) ... x u 98 CHAPTER 7. STOCHASTIC STATE ESTIMATION 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 norm of the state covariance matrix vs time Figure 7 .5: After an initial in...

Ngày tải lên: 10/08/2014, 02:20

... transformation. The columns of are called eigenvectors, and the diagonal entries of are called eigenvalues. −2 −1 0 1 2 −2 −1 .5 −1 −0 .5 0 0 .5 1 1 .5 2 Figure 5. 1: Effect of the transformation (5. 5) ... point-to-pointtransformation is not. Matrices represent point-to-pointtransformations. The eigenvalue problem amounts to finding axes q q that are mapped into themselves by the origi...

Ngày tải lên: 14/08/2014, 11:20

... 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

... 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: 14/08/2014, 11:20