H. W. Sorenson, editor. Kalman Filtering: Theory and Application. IEEE Press, 1985. 24  Home/Search   Document Not in Database   Summary   Related Articles   Check

....much difficulty. However, human pose information also contains nonlinear orientation data, requiring a modification to the KF. The extended Kalman filter (EKF) provides this modification by linearizing all nonlinear models (i.e. process and measurement models) so the traditional KF can be applied[5]. Unfortunately, the EKF has two important potential drawbacks. First, the derivation of the Jacobian matrices, the linear approximators to the nonlinear functions, can be complex causing implementation difficulties. Second, these linearizations can lead to filter instability if the timestep ....

Sorenson, H. W. Kalman Filtering: Theory and Application, IEEE Press, 1985.

....compared against a detection threshold. The sonobuoy position and timing uncertainties are taken into account when computing an elliptical confidence region depicting the probable location of the sub. Effective target tracking required the development of a Kalmanfilter basedprediction method [1][5][8] for the near future position of the target. The filter contains a model of the dynamics of a generic submarine. To bring about efficient automatic buoy deployment an optimization algorithm was designed and implemented [8] To make the model relevant to the solution of the practical problem, ....

Harold W. Sorenson. 1985. Kalman Filtering: Theory and Application, IEEE Press.

....to a wall the control system uses the distance to the opposite wall. The x position is not relevant in this application we need only to know when the pool cleaner reaches the wall and it is possible to detect this with two micro switches mounted on the two bumpers of the robot. A Kalman filter [4] will use these measurements and the robots dynamic model to provide estimates of the complete state vector (x y #) t . Because the robots dynamic motion equations are non linear, we need a linearization around the previous state estimate to use a Kalman Filter (KF) 4] It is possible to make ....

....the robot. A Kalman filter [4] will use these measurements and the robots dynamic model to provide estimates of the complete state vector (x y #) t . Because the robots dynamic motion equations are non linear, we need a linearization around the previous state estimate to use a Kalman Filter (KF) [4]. It is possible to make this approximation because we only consider small angle variations, and we can consider the linear Taylor approximation of the system function. The filter used in conjunction with external and internal position estimates will minimize the internal navigation output errors ....

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Sorenson, Harold W.: Kalman filtering: theory and application.

....The processing of these measurements relies on a stochastic measurement function z k = h k (x k , linking the (noisy) measurements to the real state value. Eq. 1) is minimized by the expected value of the conditional probability distribution p(x k i ) of the state, given the measurements, [1]: x k i = E[x k i ] 2) In the remainder of the paper, the optimal state estimate indicates the state estimate given by Eq. 2) Of course, calculating an optimal state estimate is not very useful if the system has no idea how much it can rely on it. Therefore, also the uncertainty of the ....

....measurement function, i.e. if the equations x k = f k 1 (x k 1 , and z k = h k (x k , reduce to x k = F k 1 x k 1 . and z k = H k x k . then the optimal state estimate and its covariance October 22, 2001 DRAFT 4 matrix are described by the recursive Kalman Filter algorithm 1 [2] [1]. The optimal solution to a recursive estimation problem with a nonlinear process function and or a nonlinear measurement function requires that the complete description of the probability distribution p(x k i ) is computed at each time step. For some systems this probability distribution can be ....

Harold W. Sorenson, Kalman filtering: theory and application, IEEE Press, New York, NY, 1985.

....to finance, to communications, to control, and other fields. A central premise in the Kalman filter theory is that the underlying state space model is accurate. When this assumption is violated, the performance of the filter can deteriorate appreciably (see, e.g. the edited volumes [3] [4], as well as [5] which contain several discussions and articles on practical issues in Kalman filtering design. See also the simulation examples further ahead in Sec. VII) This filter sensitivity to modeling errors has led to several works in the literature on the development of robust ....

H. W. Sorenson, editor. Kalman Filtering : Theory and Application, IEEE Press, NY, 1985.

....in eqs. 23) 25) H k h x xk ; Substituting in eq. 20) A f x xk 1 . Convergence. The linearized state and measurement models are only approximations of the true models, which invalidates all properties of optimality and convergence of the KF (Denham and Pines 1966) (Sorenson 1985). The correct convergence of an EKF depends on several factors, such as the initial estimate, the nonlinearity of the equations, the order in which the measurements are processed, and the measurements themselves. Hence, no formal proof of convergence exists; only consistency checks during Monte ....

....(i.e. A 6= I and Q 6= O) multidimensional measurement vectors z, with di erent measurement space at each time step, i.e. H k 6= H l 6= I for k 6= l. For proofs of these properties the reader is referred to (De Geeter 1998) 3 Compliance is the inverse of sti ness. 12 8 Further reading (Sorenson 1985) contains an excellent collection of papers on the history of Kalman ltering. This book includes the paper of Kalman (Kalman 1960) where he proves the optimality of a recursive lter that was later named after him. Although Kalman s solution to the recursive estimation problem is the best known, ....

Sorenson, H. W. (1985). Kalman Filtering: Theory and Application. IEEE Press.

....are provided. They demonstrate the superiority in terms of performance and efficiency of the proposed recursive filter. 1Introduction The development of the Kalman filter [4] is widely regarded as one of the breakthroughs that marked the beginning of the era of modern control system theory [8]. It has found widespread applications in many areas. The Kalman filter provides an optimal recursive solution to the problem of filtering the state of a linear dynamic system, which has the following two major advantages over the Wiener filter: it is in a very simple recursive form in time domain ....

H. W. Sorenson, ed., Kalman Filtering: Theory and Application.

....ffig)k i ]x i : 6 The dotted line in Fig. 2.3 shows the state evolution of the closed loop perturbed system for some fffif; ffigg; it clearly grows unbounded and the overall cost for N = 80 is 9025:9. The closed loop pole now tends to 1:02. Similar issues arise in Kalman filtering design (e.g. [2, 31, 32, 33, 34]) 3. SOME ALTERNATIVE DESIGN METHODS. The alternative design methods that we listed before in Sec. 1 address in their own ways the sensitivity of least squares solutions to uncertain data. In this section we comment briefly on the regularized least squares method, the total least squares method, ....

....Such situations arise, in more structured forms, in Kalman filtering theory where the noise covariance matrices play the role of weighting matrices. But since these covariance matrices are not always known a priori, they need to be estimated before applying the Kalman filter equations (e.g. [34, 35]) In this way, we may end up employing perturbed weight matrices. The above cost then seeks an x that performs best in the face of the worst possible choice for the weight matrix. We can as well consider BDU formulations with an average (or stochastic) performance index, e.g. min x avg ....

H. W. Sorenson, ed., Kalman filtering: Theory and Application, IEEE Press, 1985.

....state conditions. Veverka (1992) extended the same approach to problems with non linear constraints. For dynamic 3 process data, a wide range of approaches have been employed for data reconciliation. Kalman Filters are popular for the reconciliation of linear dynamic processes (Gelb, 1974, Sorenson, 1985). When a nonlinear process model is available, data may be rectified by an extended Kalman filter or constrained Non Linear Programming (Islam et al. 1994, Liebman and Edgar 1992, Tjao and Biegler 1991, Kim et al. 1990) or a Sequential Modular Approach, Chiari et al. 1997) When fundamental ....

Sorenson, H. W., ed., "Kalman Filtering: Theory and Applications", IEEE Press, New York, (1985).

....and weights. Unfortunately, while handling non Gaussian noise, they do not propagate as GMMs in the prediction process of non linear tracking which is a major current challenge. Approximate approaches have been developed to overcome the difficulty, but they are not invariably satisfactory [3]. Recently, Gordon, Salmond and Smith [4] used a bootstrap sampling approach to solve the problem. Their track model is non parametric in that it consists merely of random samples from the track distribution. All calculations are in terms of these samples and a mean is used as the best track ....

H. W. Sorenson (editor), "Kalman Filtering: Theory and Applications", IEEE Press, New York, 1985.

....observations drive the ODE model away from the imprecise, QDE type end of the spectrum of precision and abstraction and towards the exact, fully specified ODE end. The problem of determining values for the coefficients, known as parameter estimation, is the topic of a rich body of literature[48] and the focus of many sophisticated global optimization techniques. We solve it using the ODRPACK package[10] based on orthogonal distance regression and developed at NIST. Given a data set and an ODE with unknown coefficients, ODRPACK computes values for the coefficients and returns a ....

H. W. Sorenson. Kalman Filtering: Theory and Application. IEEE Press, 1985.

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H. W. Sorenson, editor. Kalman Filtering: Theory and Application. IEEE Press, 1985. 24

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H. W. Sorenson, editor. Kalman Filtering: Theory and Application. IEEE Press, 1985.

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H.W. Sorenson, editor. Kalman Filtering: Theory and Application. IEEE Press, 1985.

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H. W. Sorenson (Ed.), Kalman Filtering: Theory and Application, IEEE Press, 1985.

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H.W. Sorenson (ed.) Kalman Filtering: Theory and Application. IEEE Press, 1985.

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H.W. Sorenson, editor. Kalman Filtering: Theory and Application. IEEE Press, 1985.

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H. W. Sorenson, editor. Kalman Filtering: Theory and Application. IEEE Press, 1985.

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H. W. Sorenson, editor. Kalman filtering: theory and application. IEEE Press, 1985.

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Harold W. Sorenson. 1985. Kalman Filtering: Theory and Application, IEEE Press.

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pp. Sorenson, H. W. (ed.), 1985: Kalman Filtering: Theory and Application. IEEE Press,

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H. W. Sorenson, editor. Kalman filtering: theory and application. IEEE, 1985.

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Sorenson, H.W., editor. Kalman filtering: Theory and application, IEEE Press, (1985).

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