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How noise covariance matrix and process covariance matrix helps in improving the state estimate, can some one explain intuitively without mathematics ?

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  • $\begingroup$ they really don’t improve a state estimate without noise, you use a state observer. The reason why you use a filter is when measurements are noisy. A KF needs measurement noise because it is based on that assumption. Noise is also used to model uncertainty in the model but this doesn’t improve the accuracy of the state estimates $\endgroup$ – Stanley Pawlukiewicz Nov 23 '18 at 5:20
  • $\begingroup$ Hi ? you have your answer, would you mind leaving some feedback? Upvote if useful, accept if answered, or ask further questions if still confused. $\endgroup$ – Fat32 Dec 3 '18 at 15:44
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Considering a linear dynamic system framework, if there were no noises in the process equation and measurement equation, then one could use deterministic means to compute the state exactly, without any need for an estimator.

However, the unavoidable presence of noise in the state transition and the measurements make it impossible to compute the state exactly but only approximately. As the measurements are not true but in error.

Kalman filter (similar to other statistical estimators) improve the state computation by referring to the statistical character of the noise present in the measurements and state transtitions. Kalman filter also benefits from the dynamic equation of the system in predicting the state update.

So those noise covariance matrices are used to specify the Kalman gain K, which tries to correct the error in the deterministic computation of the state update.

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