EBook - Mathematical Methods for Robotics and Vision Part 8 pdf

... can be reduced to a first-order system of the form (6.1) by introducing the -dimensional vector x . . . . . . With this definition, we have for 69 68 CHAPTER 5. EIGENVALUES AND EIGENVECTORS ... 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 -th col...

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: 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

... 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

... guns 7.3. 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: ... other hand, depend on the constants as follows: Im 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...

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) ... matrices, and the Kalman filter makes optimal use of this informationfor a proper weightingof each of the scalar equations in (7.23). Better information ought to yield more accurat...

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

... 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

... 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” ... from row 3 for both and c to yield , c c There is one zero row in the left-hand side, and the rank of and that of is , the number of nonzero rows. The residual system is (compatible)...

Ngày tải lên: 14/08/2014, 11:20