how to generate barcode in c# asp.net gn = Ha x + Rn a b in Software

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gn = Ha x + Rn a b
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362 where Ha is derived as follows: gn = gn Rn gb b = = = g (I P)Rn ( a b x n g + (P I)Rn gb b n n [g ] + Rb ( xa
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CHAPTER 10 AHRS
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(1040) ya ) xa a + a)
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(1041)
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therefore, the measurement matrix is Ha = [ gn ] 0 Rn b (1042)
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This model indicates that this measurement does not provide useful information concerning the yaw error D ; but may allow estimation of the tilt errors N and E 10513 Magnetometer Analysis
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For the residual magnetometer measurement de ned as mn = mn mn where mn = Rn ym For the magnetometer measurement, eqn (1036) b specializes to 0 0 0 0 me Rn m (1043) mn = 0 b 0 me 0 Therefore, the magnetometer residual is modeled as mn = Hm x Rn m b where the measurement matrix is Hm = [mn ] 0 0 (1044)
This model indicates that magnetometer measurement might allow calibration of E and D However, the accuracy of estimation of E relies on the accuracy of the vertical component of mn which is location dependent When position information is not available, the magnetometer measurement matrix will be reduced to Hm = [0, 0, me ]
(1045)
which will allow calibration of the yaw
105 ERROR MODELS
Attitude Error Dynamics
Section 1051 derived the error state measurement models To complete the analysis we require a model for the dynamics of the attitude error vector The general equation is derived in Section 10521 and will be used in 11 The general equation is simpli ed for the AHRS application in Section 10522 The analysis that follows uses the navigation frame yaw and tilt error vector It could also be derived using a quaternion error vector as de ned in Exercise D4 10521 General Analysis
From Section 26, the di erential equation for the direction cosine matrix is Rn b = Rn b b nb (1046)
Based on the kinematics of eqn (1046), the estimate Rn could be comb puted as (1047) Rn = Rn ( b b ) b b ib in b ib ib where ib = [ b ] with b = u xg calculated based on the gyro outputs, b in in in in in = [ b ], b = Rb n , and n is calculated based on quantities in n the navigation system as described in eqn (257) To determine a dynamic model for (or P), set the derivative of eqn (1032) equal to the left side of eqn (1046): PRn + (I + P)Rn b b Using the de nitions b ib b in eqn (1048) simpli es as follows, PRn + (I + P)Rn b b (I + P)Rn ( b b + b b ) ib in b ib in n + (I + P)Rn ( b b ) = (I + P)Rb ib in b = Rn ( b b )Rb P (1049) ib in b n = = b b ib ib b = in b , in = (I + P)Rn ( b b ) ib in b (1048)
The term PRn ( b b )Rb has been dropped as it is second order in ib in n b the error quantities In eqn (1049), P = [ ]; therefore, the equation
CHAPTER 10 AHRS
contains only three independent terms Using eqns (223) and (B15), eqn (1049) can be written in the vector form, = Rn ( b b ) b ib in (1050)
where b is the error in the gyro measurement of the body-frame inertialib relative angular rate From eqn (257), the vector n is de ned as in n in ( + ie ) cos( ) = + ie ) sin( ) ( (1051)
ve v where = cos( )(RN +h) and = RMn Therefore, the vector b depends in +h on the error in position and velocity, which are not available to AHRS applications Further specialization of eqn (1050) is considered in Section 1142 in relation to INS applications The following section considers the special case relevant to AHRS applications
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