卡尔曼滤波器：卡尔曼滤波器：基于速度测量预测位置

# Kalman-Filter This sample application uses a Kalman filter to predict a position based on speed measurement. ## Kalman filter algorithm The [Kalman filter](https://en.wikipedia.org/wiki/Kalman_filter) equations are simplified for the application. + ### Vectors and matrices: F : the state-transition model H : the measurement model Q : the covariance of the process noise R : the covariance of the measurement noise x0: the initial state P0: the initial error covariance + ### Equations: <img src="/images/kalman_filter_equations.JPG" width="60%" height="60%"> + ### Kalman filter calculation: <img src="/images/kalman_filter_calculation.JPG" width="75%" height="75%"> ## Example A train travels at a constant speed of 80 km/h. The speed is measured every 100 ms. The speed is filtered and the current position is predicted using a Kalman filter. + ### Vectors and matrices: <img src="/images/process_model.JPG" width="13%" height="13%"> + ### A priori prediction of the position: <img src="/images/process_calculation.JPG" width="45%" height="45%"> + ### Speed measurement with noise: <img src="/images/measurement_calculation.JPG" width="65%" height="65%"> + ### Plotted speed and predicted position: <img src="/images/train_speed_and_position.PNG" width="100%" height="100%"> + ### Plotted kalman gain and error covarinace: <img src="/images/kalman_gain_and error_covariance.PNG" width="100%" height="100%"> ## Important files - **train_position_prediction.py** : Calculates the train position and plots the results - **speed_measurement.py** : Simulates the speed measurement - **kalman_filter.py** : Predicts the position. ## Installation and usage Clone the repository ```sh $ cd <your workspace folder> $ git clone https://github.com/embmike/Kalman-Filter.git ``` You can use the code for example on your computer with [Anaconda](https://www.anaconda.com/) or via cloud computing with [Google Colaboratory](https://colab.research.google.com/) ## Licence This project is licensed under the terms of the [](https://opensource.org/licenses/MIT)