Kalman tracking

The example analyzed here is one of the simplest problems because it is two-dimensional with respect to the vectors state. The example illustrates the Kalman tracking for a system model, which is controllable and observable. To this aim, we use the following system model and prior statistics ... 

A control system that contains a LQ Regulator/Tracking controller together with a Kalman filter state estimator as shown in Figure 9.8 is called a Linear Quadratic Gaussian (LQG) control system. 

The target state vector tk measured by the multilateration procedure can be considered directly as a target plot input of the association process. In this case, the input of the Kalman filter describes the same parameters that the internal state vector does. It is characteristic for the plot-to-track association procedure that the measurement equation contains directly the target state vector tk which is influenced by noise ftsk only ... 

The respective Kalman filter equations for the position correction and prediction steps can now be formulated based on equations (18) and (19), (20) or (21) accordingly for the different mentioned association schemes. Since the measurement equation is nonlinear in case of range-velocity-to-track or frequency-to-track association, the Extended Kalman filter is used for this particular application [16]. 

Figure 3.88 Numerical example of the Kalman filter tracking.

Using an earlier version of the dynamic model given in Section IV,6, Kiparissides et al (1980b) illustrated the use of such an extended Kalman Filter to infer JV(f), VJit), AJit), and X(f) from measurements taken only on conversion [X(f)J using UV turbidity spectra. Jo and Bankoff (197Q used these filters to track some of the moments of the MWD of PVAc in a solution polymerization process using measurements made on refractive index and viscosity. 

The proposed strategies for stabilization of gas-lifted oil wells are offline methods which are unable to track online dynamic changes of the system. However, system parameters such as flow rate of injected gas and also noise characteristic are not constant with respect to time. An adaptive Linear Quadratic Gaussian (LQG) approach is presented in this paper in which the state estimation is performed using an Adaptive Unscented Kalman Filter (AUKF) to deal with unknown time-varying noise statistics. State-feedback gain is adaptively calculated based on Linear Quadratic Regulator (LQR). Finally, the proposed control scheme is evaluated on a simulation case study. 

These measurement points may be clustered for road surface detection and obstacle detection. Tracking these measurements over time, as implemented, for example by Kalman filtering, not only yields high reliability and accuracy, but also enables acquisition of information that is not directly observable in an image, such as speed or acceleration. 

The track finding stage is based on a standard Kalman filter pattern recognition approach [8] which starts with the seed parameters. The trajectory is extrapolated to the next tracker layer and compatible hits are assigned to the track on the basis of the... 

Muon reconstruction, after local-pattern recognition is performed in two stages stand-alone reconstruction based on information from the muon system only and global reconstmction including the hit information of the silicon tracker. Standalone reconstruction starts from track segments in the muon chambers and muon trajectories are built from the inside to the outside using the Kalman filter technique. After the trajectory is built, a second Kalman filter, working from outside in, is applied to determine the track parameters. In the end, the track is extrapolated to the nominal interaction point and a vertex-constrained fit of the track parameters is performed. 

Data processor That portion of a radar system designed to operate on the narrow-band signal out of the signal processor, e.g., thresholding, Kalman filtering, tracking, etc. Dwell-to-dwell processing is... 

Similar to other vision-based tracking systems [34], our system rehes on the visual tracking of a pattern composed of a set of features arranged in a known geometry. An example of a pattern would be a checkerboard with a known number of rows and columns, where the intersection of black and white squares serves as a feature. The particularity of our approach is that we do not require the detection of the whole pattern. Instead, we use a Kalman-filter based approach [38] to simultaneously perform... 

Among different monitoring techniques like Kalman filters and various Data Reconciliation schemes, Kalman filter presents good variance reduction, estimation of process variables and better tracking in dynamic changes of the process (Benqliiou et al 2002). This performance, however, varies with the position and quality (variance) of the sensors. This paper focuses on the determination of the optimal sensor placement for the use of Kalman filtering. 

There has been a significant amount of work reported on controlling composition during copolymerization reactions. The Kalman filter method is based on a linear approximation of the nonlinear process [55] but has problems with stability and convergence [56-58]. For that reason, numerous nonlinear methods have been developed. Kravaris et al. [59] used temperature tracking as another nonlinear method to control copolymer composition. Model predictive control (MPC) [60-63], as well as nonlinear MPC (NLMPC) [64-67] algorithms have been suggested for control of nonlinear systems. 

Ristic B, Arulampalam S, Gordon N (2004) Beyond the Kalman filter particle filters for tracking applications. Artech House, Boston... 

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