how to generate barcode in c# asp.net Aiding Measurement Models in Software

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Aiding Measurement Models
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Each of the following subsections presents the model used to predict the value of an aiding measurement and derives the measurement model used in the Kalman lter error estimation approach
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Attitude and Yaw Prediction
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The attitude sensor is only used for initializing the roll and pitch estimates: (0) (0) = yE (0) (1250)
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The yaw angle is initialized based on the output of the magnetometer as (0) = y (0) (1251)
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CHAPTER 12
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LBL AND DOPPLER AIDED INS
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Given (0) = [ (0), (0), (0)] , the initial rotation matrix Rp can be comt puted according to the de nition preceding eqn (243) Let var( (0)) = 2 2 2 PE = diag([ E , E , ]) where E was de ned in Section 1222 Then, var( (0)) = P = T PE T where T is de ned in eqn (280) After initialization is complete, the magnetometer is used as an aiding signal until deactivated by the mission planner As an aiding signal, the magnetometer output is predicted to be y = (1252) Because = 1 and is the third element of , the magnetometer T error model is (1253) y = s 1 + T where s = [0, 0, 1] Therefore, h = 0 0 s 1 T 0 0 0 (1254)
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where 0 = [0, 0, 0] The measurement variance is
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(1255)
Doppler Prediction
Based on the model of Section 1223, the i-th Doppler measurement is predicted to be e tp bp (1256) y Di = v p + p l p i D Assuming that lp and bp are exactly known, the residual Doppler meai D surement for the i-th beam is yDi = (bp ) ( v + [lp ] bg + [lp ] g ) + Di i D D Therefore, hDi = 0 (bp ) i 0 0 (bp ) [lp ] i D 0 (1258) (1257)
and the measurement variance is R Di = =
2 2 (bp ) [lp ] g I[lp ] (bp ) + Di i i D D 2 2 2 2 |lD bi |2 g + Di
(1259)
The variance RDi is positive The noise on the measurement yDi is correlated to the process noise because the quantity g appears in both ex2 pressions Due to the fact that lD 2 bi 2 |lD bi |2 g is signi cantly 2 smaller than Di , this correlation is ignored in the Kalman lter implementation Methods for dealing with correlation between the process and measurement noise are discussed in for example, [96]
125 AIDING MEASUREMENT MODELS
Depth Prediction
Given the model of the pressure measurement from eqn (1217), the pressure measurement is predicted according to yp = s p p p + Rt lp + bp (1260)
Therefore, the pressure measurement residual is yp = s p s [lt ] + p p where lt = Rt lp This yields the measurement model p p p hp = s 0 s [lt ] p Rp =
2 p
(1261)
(1262)
and the measurement variance is (1263)
LBL Prediction
Given the model from eqn (1218) and the measured value of ti , the LBL measurement is predicted to be 1 1 pi S(t0 ) + S(ti ) pi + Ti (1264) yLi = c(t0 ) c(t1 ) where the estimated AUV transceiver location S(t) and estimated vehicle location p(t) in tangent frame are related by St (t) = pt (t) + Rt (t)lp p L Let di (t) = di (t) = 1 pi S(t) c(t) 1 pi S(t) c(t) (1265) (1266)
where c(t) = c0 + c(t) and c(t) = c0 + (t) The rst order Taylor s series c expansion for di is di (t) = di (t) + Di (t) x(t) where Di (t) = yLi
di x x= (t) x
With this notation, the i-th LBL residual is
= yLi yLi = = di (t0 ) + di (ti ) + Ti + Li di (t0 ) + di (ti ) + Ti di (t0 ) di (t0 ) + di (ti ) di (ti ) + Li
= Di (t0 ) x(t0 ) + Di (ti ) x(ti ) + Li = Di (t0 ) (t0 , ti ) + Di (ti ) x(ti ) + Li (1267)
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