how to generate barcode in c# asp.net Error State Dynamic Model in Software

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Error State Dynamic Model
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The error state vector is x = [ n, e, , RL , RR ] , where each error term is de ned as x = x x In this section, we will also use the following variables to decrease the complexity of the resulting equations: uL = RL L , uR = RR R , and u = ( L + uR )/2 u
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GPS AIDED ENCODER-BASED DR
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Each of these quantities is computable as an average over any time increment based on the encoder readings Forming the di erence of the Taylor series expansion of eqn (99) and eqn (915) results in the error state equations n = 1 uL RL + uR RR u sin( ) + n cos( ) 2 RL RR 1 uL RL + uR RR + u cos( ) + e sin( ) 2 RL RR uR 1 uL RL RR + L RL RR (919) (920) (921)
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The error models for RR and RL are given by eqns (912 913) The error state equations can be put into be in the standard form of eqn (457) with L R 0 0 sin( ) u cos( ) u cos( ) u 2RL 2RR L R 0 0 u cos( ) u sin( ) u sin( ) 2RL 2RR 1 uL 1 uR (922) F(t) = 0 0 L 0 L RL RR 0 R 0 0 0 0 0 0 0 R and = I5 where = [ n , e , , L , R ] 2 2 2 Let 1 , 2 , and 3 denote the PSD s of n , e , and , respectively These process driving noise terms are included in the model due to the fact that the assumptions will not be perfectly satis ed For example, the wheels may slip or the surface may not be perfectly planar The wheel slip is a function of wheel speed or acceleration Similarly, the e ect of a non-planar surface on the computed position is a function of the speed Therefore, the 2 2 2 quantities 1 , 2 , and 3 and hence the Q matrix are sometimes de ned to be increasing functions of the speed u and/or the acceleration (ie as indicated by the change u)
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GPS Aiding
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Using the navigation state vector de ned in eqn (914), this section presents the GPS measurement prediction and the GPS measurement residual equations that would be used by the Kalman lter Using the estimate of the vehicle position p and the ECEF position of the i-th satellite pi , which is computed from the ephemeris data as discussed in Appendix C, the computed range to the i-th satellite vehicle (SV) is x R( , pi ) = pe pi
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(923)
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95 GPS AIDING In this computation, pe = pe + Re pt 0 t
(924)
where pe is the estimated ECEF position of the system, pe is the ECEF 0 n position of the origin of the t-frame, and pt = [ , e, hr ] is the estimated tangent plane position of the system The matrix Re is the constant rotat tion matrix from the t-frame to the ECEF frame The following discussion will assume that there is information available about the common mode errors related to the i-th satellite It will be de noted as i for pseudorange (see eqn (87)) and as i for carrier phase (see eqn (827)) This information could be obtained, for example, from di erential corrections If there is no information available about the common mode errors, then i = 0, i = 0, and methods such as the Schmidt Kalman lter or state augmentation could be used to accommodate the GPS time correlated errors The pseudorange is a function of both the range R(x, p) and the receiver clock bias c tr (see Section 843) The designer can choose between (at least) two approaches to handling the receiver clock error These choices are discussed in the following two subsections
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