{"id":69204,"date":"2020-12-14T10:30:20","date_gmt":"2020-12-14T15:30:20","guid":{"rendered":"https:\/\/ibkrcampus.com\/?p=69204"},"modified":"2022-11-21T09:46:45","modified_gmt":"2022-11-21T14:46:45","slug":"how-to-create-kalman-filter-in-python-part-ii","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/how-to-create-kalman-filter-in-python-part-ii\/","title":{"rendered":"How to Create Kalman Filter in Python – Part II"},"content":{"rendered":"\n

See Part I<\/a> of this series to get started with the Statistical terms and concepts used in Kalman Filter.<\/em><\/p>\n\n\n\n

Equations in Kalman Filter<\/h2>\n\n\n\n

Kalman Filter is a type of prediction algorithm. Thus, the Kalman filter\u2019s success depends on our estimated values and its variance from the actual values. In Kalman Filter, we assume that depending on the previous state, we can predict the next state.<\/p>\n\n\n\n

At the outset, we would like to clarify that this article on the Kalman filter tutorial is not about the derivation of the equations but trying to explain how the equations help us in estimating or predicting a value. Now, as we said earlier, we are trying to predict the value of something which cannot be directly measured. Thus, there will obviously be some error in the predicted value and the actual value.<\/p>\n\n\n\n

If the system itself contains some errors, then it is called measurement noise. For example, if the weighing scales itself shows different readings for the same football player, it will be measurement noise.<\/p>\n\n\n\n

If the process when the measurement takes place has certain factors which are not taken into account, then it is called as process noise. For example, if we are predicting the Apollo Rocket\u2019s position, and we could not account for the wind during the initial blast off phase, then we will encounter some error between the actual location and the predicted location.<\/p>\n\n\n\n

Kalman Filter is used to reduce these errors and successfully predict the next state.<\/p>\n\n\n\n

Now, supposing we pick out one player and weigh that individual 10 times, we might get different values due to some measurement errors.<\/p>\n\n\n\n

Mr. Rudolf Kalman developed the status update equation taking into account three values, ie<\/p>\n\n\n\n