EBook - Mathematical Methods for Robotics and Vision Part 11 potx

... solve a particular type of estimation problem, namely, the estimation problem for the observationequation(7.12)with a linear function and n Gaussian zero-mean noise with the indentity matrix for ... 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 accurate results...

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” ... 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

... 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

... 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 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 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

... 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. 3.2. THE SINGULAR VALUE DECOMPOSITION 27 where and . Equivalently, Proof. This proof is adapted...

Ngày tải lên: 14/08/2014, 11:20

... 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: ... “Kalman filter-based algorithms for estimating depth from image sequences,” InternationalJournal of Computer Vision, 3(3):20 9-2 36, September 1989; and T.J. Broida, S. Chandrashekhar, and R...

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