International cooperation and technology transfer

Fras, Mojca Kosmatin

Bibliographic data

Monograph

Persistent identifier:: 856490555

Author:: Fras, Mojca Kosmatin

Title:: International cooperation and technology transfer

Sub title:: Ljubljana, Slovenia, February 2 - 5, 2000 : proceedings of the workshop

Scope:: VI, 163 Seiten

Year of publication:: 2000

Place of publication:: London

Publisher of the original:: RICS Books

Identifier (digital):: 856490555

Illustration:: Illustrationen, Diagramme

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Monograph

Collection:: Earth sciences

Chapter

Title:: A LOW COST MOBILE MAPPING SYSTEM. A. Vettore, A. Guarnieri

Document type:: Monograph

Structure type:: Chapter

'r V ’ V = a o, r (t) = {x(t),y(t),z(t)} (4) This model can be applied in different operating modes, employing as state vectors whether pseudoran ge or carrier phase osservables, as collected by only one receiver or in differential mode. Note that (4) represents a costant acceleration model, in which vectors v and a incorporates the linear and angular components. In order to take into account the error introduced by our unique positioning device (GPS) we use following formula: s(t)=f{s(t)-t}+w(t) (5) where s(t) is the state vector; f(t) describes mathematically the nonlinear relationship between parameters in s(t) and the process; w(t) models sensor (rover receiver) syste matic errors, which are considered as white Gaussian noise with covariance Q. In order to determine the components of s(t), kinematic measurements are employed according to the formula below: z* =H-s(i) + n* (6) where z k measurements vector collected at discrete time t k ; H matrix of measuring states; n k measurement Gaussian error with covariance R. cp(t) angle of tangent to trajectory at time t; co(t) angular velocity of the van; v(t) linear velocity; a(t) linear acceleration; wl(t), w2(t) Gaussian 2D positional error components. Since we are interested in planimetrie survey, we consider only the (X,Y) GPS coordinates as computed by differential correction in post-processing, therefore the matrix form of equation (6) becomes: k* =X k +n hk [^2,* — yk y n 2,k (8) where Z] k ) z 2 , k components ov measurements vector at step k; n i,k> n 2 , k Gaussian components of measurement stochastic errors vector. In this way the matrix of osservable states assumes following form: 0 0 1 0 0 0 0 0 0 0 0\ being the state vector s(i)={x(i) y{t) (pit) 00(f) v(t) a{t) ait)} (9) 00) 4. STATE VECTOR ESTIMATE. Since the Extended Kalman Filter (EKF) represents the optimal estimate procedure in case of uncorrelated measurements and Gaussian noise with null average, the employed algorithm can be summarized by follo wing formulas: In more detail our nonlinear kinematic model is composed by following 7 differential equations: x(t) = vit)-COSi(p) yit) = v(0 • sen(<p) (pit) = coit) < (bit) = ait) (7) v(t) = ait) ait) = 0 + w, it) ait) = 0 + w 2 it) where x(t), y(t) 2D vehicle coordinates on mapping frame E m ; • Prediction step, s(k + \\k) = ft(s(k\ky) (ll) P(* + ll/t) = <P(k\k) ■ P(k\k) ■ ®(k\k) +Q(k) (12) • Update step, 'A(k + 1) = H • P(k + 1 lit) • H'+R (13) Uk +1) = P(k +11 *) • H'-A(* + 1)“' (14) s(fc + llfc + l) = s(fc + llfc) + L(fc + l)-.... ■[z(k + \)-U-s(k + l\k)] U5)

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