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how to generate barcode using c#.net Copyright 2008 by The McGrawHill Companies Click here for terms of use in Software
Copyright 2008 by The McGrawHill Companies Click here for terms of use QRCode Creation In None Using Barcode printer for Software Control to generate, create QR image in Software applications. QRCode Reader In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. CHAPTER 5 OPTIMAL STATE ESTIMATION
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Universal Product Code Version A Printer In None Using Barcode generator for Software Control to generate, create Universal Product Code version A image in Software applications. Making Data Matrix 2d Barcode In None Using Barcode generator for Software Control to generate, create ECC200 image in Software applications. This section summarizes the linear stochastic state estimation results from the previous chapters For a linear continuoustime system such as that shown in Figure 51, to enable state estimation in discretetime, we nd the discretetime equivalent statespace model of the actual process: xk yk = = xk 1 + Guk 1 + k 1 Hxk + k (51) (52) Create Uniform Symbology Specification Code 93 In None Using Barcode maker for Software Control to generate, create USD3 image in Software applications. Scanning EAN / UCC  14 In C#.NET Using Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in .NET applications. where xk Rn , yk Rp , k Rp , and k Rn are the stochastic signals representing the state, output, measurement noise and driving noise, respectively; u Rm is a known input signal Assuming that the state is observable from the output signal, our objective is to provide an optimal estimate of the state vector The resulting algorithm is referred to as the Kalman lter The basic state estimation block diagram is shown in Figure 52 For simplicity of notation, the system is assumed to be timeinvariant and the subscript k s on the system parameter matrices have been dropped (eg, k = ) The assumption of a timeinvariant system is not a restriction on the approach The derivation does go through for and the Kalman lter is often applied to timevarying systems EAN / UCC  14 Maker In Visual C#.NET Using Barcode encoder for VS .NET Control to generate, create UCC128 image in Visual Studio .NET applications. Barcode Encoder In ObjectiveC Using Barcode encoder for iPad Control to generate, create barcode image in iPad applications. Discretetime Equivalent model x wk + y x S k+1 1 k H S k S z + dy L + k nk F Computer
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Figure 52: Discretetime state estimator
51 STATE ESTIMATION: REVIEW
In this model, k and k are signals determined by the environment The designer does not know the actual values of these signals, but formulates the problem so that the following assumptions hold: E k = 0 E k = 0 var ( k , l ) = Rk kl var ( k , l ) = Qdk kl and the crosscorrelation between k and l is zero The symbol kl represents the Kronecker delta In addition, for all k 0, xk is uncorrelated with l for all l and xk is uncorrelated with l for l k The matrices Rk and Qdk are assumed to be positive de nite and the state is assumed to be controllable from k 0 For k > 0, assuming that x+ and positive de nite P+ are known, the 0 state estimate is computed using the algorithm described below The superscripts and + denote the estimates prior and posterior to incorporating k 1 k 1 the measurement, respectively At time k, given x+ , P+ and uk 1 , the prior estimate of the state and output are computed as k x yk = x+ + Guk 1 k 1 = H xk (53) (54) When the kth measurement yk becomes available, the measurement residual is computed as (55) yk = yk yk Given the state estimation gain vector Lk , the posterior state estimate is computed as k k (56) x+ = x + Lk yk Given the above state space models for the state and state estimate, with k k x = xk x and x+ = xk x+ , the previous chapters have derived the k k following equations for the prior state estimation error, the measurement residual, and the posterior state estimation error: x k+1 yk x+ k
= = = x+ + k k H x k + k (I Lk Hk ) x Lk k k
(57) (58) (59) With reference to eqn (4125), based on eqns (57 59), the covariance of the state estimation error prior to the measurement update is given by equation: (510) P = k P+ k + Qdk k+1 k As in eqn (4126), the covariance matrix for the predicted output error is P k = Hk P Hk + Rk y k (511) CHAPTER 5 OPTIMAL STATE ESTIMATION
As in eqn (4127), the covariance matrix for the state estimation error posterior to the measurement correction is P+ = (I Lk Hk ) P (I Lk Hk ) + Lk Rk Lk k k (512) Given that the state is controllable from k , it can be shown that P and k P+ are positive de nite matrices k Note that eqns (57 59) are not used in the state estimator implementation These equations are used for analysis to attain eqns (510 512) which serve as the basis for the derivation of the optimal state estimation gain in Section 52 The optimal state estimator will be implemented using eqns (53 56), eqns (510 512), and a formula for the optimal state estimation gain

