Importance of Kalman Gain parameter in Kalman filters

Kalman filter gain parameter plays a very important role in kalman filter estimation, In the last blog I’ve given an introduction on what are Kalman filters and why to use them.

Kalman filter gain decides how much of the new measurement has to be considered for the estimation. Here is the formula for Kalman gain.

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KalmanGain = Error In Estimation / (Error in estimation + Error in measurement) .
If the error in measurement in small then the value of Kalman Gain would be close to 1. If the error in estimation is large then value heads towards 0.
Here is the update equation for the state using the Kalman gain.

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As you can see in the above equation, If the Kalman gain (KG) is close to 0, this implies that the error in the measured value from the sensor is really high and thus they are unstable. In this scenario we don’t want the contribution of the measured value to be notable on the prediction, this is controlled by the additive factor for the previous estimation, this quantity is meager when the KG value is close to 0, and thus it just slightly adds up to the previous estimation, so the Kalman gain(KG) helps invest better confidence on the estimation rather than on the measurement.

On the other hand, If the Kalman Gain is close to 1, that is in case where the error in estimation is really high compared to the error in the measurement from the sensors, The additive value for the previous estimate in the update equation above will be significant, thus the updated value will considerably different from the estimation since the contribution from the measurement will be higher.
Thus Kalman filter gain helps to weigh the contribution of the difference between the previous estimate and the current measurement to update the previous estimate to arrive at the new estimate.