The Kalman Filter: Theory Of The Estression Theory

1.6 Kalman Filter
The triplets of change capture and correct forms the conceptual basis for the Kalman filter and it can be stated as follows:
Change + Capture =.>Correct
The ‘+’ sign above has a deep significance in the way the present and the new information are combined to have progress in the correct direction based on an appropriate criterion.
The origin of such a global Kalman filter in Estimation Theory can be traced since ancient times. Its progress is similar to any physical theory moving randomly across intuition, experiments and mathematical framework.

Kalman Filter Concept
The Kalman filter equations are recursive and it is helpful to estimate the time varying state variables and parameter from unifying earlier results that he
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The filter can be understood from different perspectives. The modeling of the state of a system is subjective and the system measurements are objective. Generally the knowledge being uncertain and the measurements are corrupted by noise, the Kalman filter combines the two to expand the knowledge front. Another way to look at the Kalman filter is that it combines or assimilates the information from two sources namely uncertain system and measurement models in a statistically consistent way. One other way of understanding the Kalman filter is that it matches the model and the measurement and in the process improves both by suppressing the noise in the measurement improves the accuracy of the state and the parameters in it. There could be many criteria of combining the model and the measurements. Each one could give different results but the criterion to accept any result is that the estimates should be meaningful, reasonable, acceptable and useable. Thus one should note that one cannot be at the truth but around the truth. The only way to reach the truth or other words get to know the absolute source from which the data has come about is to have infinite data together with an algorithm being capable of reaching the truth. The basic structure of Kalman filter is shown in figure …show more content…
The goal of filter tuning chases every variant of the Kalman filter which can at best be minimized but not completely ignored if one desires to get near optimal solutions. Further it becomes difficult for one to infer if the performance of the variants of Kalman filter are due to their formulation or filter tuning! It should be remarked that in the best spirit of the estimation theory in particular the recursive Kalman filter approach even if X0, P0, Q, R and Q namely the initial states, their covariance, parameters in the state and measurement equations, the measurement and state process noise covariance are not available or inaccurately known the filter should still have the ability to estimate all the above from the ‘observables’ that are measured and commencing not too far from the proper estimates for the algorithm to converge. One would like to have the initial choice of all the unknowns should not be very critical. The filter should be self-consistent in estimating all the

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