KALMAN FILTER (Part 2)

Hello everyone. Hope you all will be fine. Now let’s move to the 2nd block mentioned in the flow chart named as “Calculate the Current Estimate”. The flow chart mentioned in the previous is as follow

Actually, there are 3 things are important to be calculated.

  • Kalman Gain (Method to calculate the Kalman Gain)
  • Current Estimate
  • The Error in new Estimate

Therefore, there are 3 important equations to calculate the above-mentioned items.

For Kalman Gain, the equation is as follow

  • KG = Kalman Gain
  • EEST = Error in Estimate
  • EMEA = Error in Measurement

For calculating the current estimate

where

  • ESTt= Current Estimate
  • EST(t-1)= Previous Estimate
  • KG = Kalman Gain
  • MEA = Measured Value

For calculating the error in new estimate the equation is as follow

Which will eventually become after solving

Now let’s take a numerical example to implement the above mentioned 3 sets of equations

Example 1:

Let’s say we have to apply Kalman filter on a temperature measuring device and suppose the actual temperature is 52°C and we have an initial estimate of 48°C and initial error in estimate comes out to be 2°C. The initial measurement given by the temperature measuring device is 55°C and the error of the device is 4°C

  • Initial Estimate = E_est(t-1)=  48°C
  • Initial Error in Estimate = E_est= 2°C
  • Initial Measurement = MEA = 55°C
  • Error in Measurement = E_MEA = 04

Solution:

  • First of all, we will calculate the Kalman gain

  • The next thing is to calculate the Current Estimate based on the following equation

  • The last thing is to calculate the error in the new estimate based on the following equation

These are the calculations based on the kalman filter. Hope you have started understanding the Kalman filter. As mentioned in the previous blog it is a recursive iterative process, therefore, we will become close to the real value in the short number of cycles. In the above-mentioned example, we will perform the calculations again & again and we will get close to the real value in a short time.

 

For Kalman filter Introduction (Part 1) click on the following link

KALMAN FILTER INTRODUCTION

 

 

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