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Vision Systems - Applications Part 10

Tham khảo tài liệu 'vision systems - applications part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Bearing-only Simultaneous Localization and Mapping for Vision-Based Mobile Robots 351 r is independent on a . Formulas are derived for computing the PDF Probability Density Function when an initial observation is made. The updating of the PDF when further observations arrive is explained in Section 5.2.A. 5.1 Method description Let p r a be the PDF of the landmark position in polar coordinates when only one observation has been made. We characterize p r a when r and a are independent. Let p denote the measured landmark bearing. Assume that the error range for the bearing is . The landmark position is contained in the vision cone which is formed by two rays rooted at the observation point with respect to two bearings P- and p see Figure 11 . Figure 11. The vision cone is rooted at the observation point. The surface of the hashed area is approximately rdrda for small da and dr The surface of the hashed area in Figure 11 for small dr and da can be computed as n r dr 2 -nr2 da 1 2 rdr dr 2 da rdrda 2n 2 Because the probability of the landmark being in the vision cone is 1 we have rdrda 1 7 In Equation 7 R.iiiL and Rmin are the bounds of the vision range interval. We define F R as the probability of the landmark being in the area r a r e Rmin R ae P- P F R can be represented as F R iCCfr rdrda 8 352 Vision Systems Applications We define T R A as the probability of the landmark being in the dotted area in Figure 11. Since V R A F R A - F R we have T R A jp p r a rdrda 9 If the range r and the angle a are independent then T R A is constant with respect to R . That is d R A 0 . From Equation 9 we derive dF R A _ dF R dR dR Because of the independence of a and r p r a can be factored as p r a f r g a 10 11 Without loss of generality we impose that Jg a da 1. After factoring Equation 8 becomes F R r f r r dr . Because of the property of the integration we have Rmin f R R dR J 12 From Equations 10 and 12 we deduce that f R A R A f R R . Therefore f R A - f R A R f R A 0 . By