{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MIT2_017JF09_p33

# MIT2_017JF09_p33 - 33 POSITIONING USING RANGING 2D CASE 119...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 33 POSITIONING USING RANGING: 2D CASE 119 33 Positioning Using Ranging: 2D Case 1. Two sensors, denoted 1 and 2 and located at different locations in the x − y plane, make a range measurements to a target t . Let the range from Sensor 1 to the target be r 1 and let the range from Sensor 2 to the target be r 2 ; we call the sensor locations [ x 1 , y 1 ] and [ x 2 , y 2 ], and the target location [ x t , y t ]. sensor 1 sensor 2 target y x What are the two equations describing the target’s [ x t , y t ] position in the horizontal plane, based on the range measurements from the two devices? 2. Sketch these constraints for the fixed sensor locations x 1 = 0, y 1 = 0, x 2 = 1, and y 2 = 0, for two different target locations a) x t = 2 , y t = 0, and b) x t = 0 . 5 , y t = 0 . 5. This is a total of four circles to draw. 3. Consider your two constraints for a given target location; there are two unknowns [ x t , y t ], so we ought to be able to solve for them. First, solve for x t by subtracting the two constraint equations, such that the x 2 t and y t 2 terms go away; be sure you take advantage of the fact that x 1 = y 1 = y 2 = 0! This will let you derive a clean expression for x t . Then, put this value for x t into the constraint equation for Sensor 1, and solve for y t . There will be two solutions for y t , because this array can’t distinguish which side the target is on....
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

MIT2_017JF09_p33 - 33 POSITIONING USING RANGING 2D CASE 119...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online