Hi, I am implementing an unscented Kalman filter in python for estimating the states of car motion and geometry of the road. My concepts are a bit unclear regarding the Kalman Filter update and predict step. I have two questions, first question is that I am confused between the actual state estimation, measured estimation, and the ground truth. Second, I am confused that how the state will be updated with respect to the equations of car motion and road geometry with the evolution of time
Have a look at https://au.mathworks.com/help/control/ug/kalman-filter-design.html;jsessionid=5e7e55143a36e2eb092acf4d9460
https://www.semanticscholar.org/paper/Introduction-to-random-signals-and-applied-kalman-Brown-Hwang/b3b0dcfa63e3bc5a932069c272b518acdf06fb57?p2df
Your questions is a set of basic concepts of standard Kalman filter. I would recommend Handbook of Applicable Mathematics, Statistics // ed. W..Ledermann, E. Lloyd, Wiley,1984.
visit these links below
Kalman filter apply using python
https://arxiv.org/ftp/arxiv/papers/1204/1204.0375.pdf
https://www.coursera.org/lecture/state-estimation-localization-self-driving-cars/lesson-1-the-linear-kalman-filter-7DFmY
Muhammad Ali Sergey Borodachev Adnan Majeed
Thank you for the responses. As far as I understand after studying the provided links, actual state estimation is the estimation of states after the update step (xhat); measured estimation is the measurements obtained in Kalman filter from the sensors and then used in the update step, and the ground truth is the actual measurements from the sensors. Kindly correct me if I misunderstood anything. Thanks
1) there are two updates at an instant: the time update means to use a model to predict the states from the previous observation epoch to the current one while the measurement update is then conducted using the current measurements at the current observation epoch based on the time-updated states. The measurements are usually not directly corresponding to the states, but could be modeled as the functions of the states.
2) the actual measurements cannot be said the ground truth. In case you have the ground truth, you may use the ground truth to verify your estimated states. I do not know what ground truth you have. You may explain it a little bit.
Jianguo Wang
Thank you very much for your response and detailed description. Could you please also explain a bit more regarding how the measurements can be modeled as the functions of the states?
The dataset which I have only contains the measurements for estimating the state without the ground truth, so, in the case as per my understanding, the measurements (without the addition of noise) can be the ground truth?
I would appreciate it if you could explain it. Thanks
In my work, mostly related to the positioning, for example, when you use a GPS receiver to measure the spatial distance from a GPS satellite to my receiver, this distance is modelled as the unknown coordinates (X/Y/Z as three of the states) of the receiver's location simply by using the equation of d = sqrt[(Xs-Xr)^2 +(Ys-Yr)^2+(Zs-Zr)^2] without considering additional terms for simplification! We assume that the satellite position Xs/Ys/Zs are known, by the way.
No, the measurements are not the ground truth. any other measurements at a higher accuracy level, i.e. the errors in them are small enough to be ignored in comparison with your current measurements, may be used as their truth.
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