I actually find the EnKF more intuitive than the Kalman Filter. Its easier for me to understand what an ensemble of samples is doing than to visualize what the whole gaussian distribution is doing if you know what mean.
I have a problem that only my C matrix presents nonlinearities, can i use the extended kalman filter using jacobians only in the C matrix? What should i do ?
1- in the literature, there's always emphasis on the weights of the sigma points in UKF, could you elaborate the importance of weights for the sigma points in the prediction and update of the next state P ? 2- is their a solution for the non-positive definite P in the sigma points generation step ?
1. Weights of the sigma points depend on a few unscented transformation parameters (such as alpha, beta, kappa), which in turn control the spread of the sigma points around the mean state estimate. How the sigma points are spread is important because UKF can only track unimodal (single-peak) state distributions. If the state distribution is not unimodal, but you would like to track one of the peaks, adjusting the spread of the sigma points so that they are all near this peak can yield reasonable results. Weights can also impact the results due to numerical issues. For instance, large weights (typically corresponds to tightly packed sigma points) is more likely to cause numerical issues. 2. A non-positive definite P can only arise due to numerical issues. If P is not positive definite, one solution is to perturb it to make it positive-definite. An alternative approach is reducing the chance of numerical issues by ensuring the state estimation is well scaled (states have similar magnitudes). For more information, I'd recommend the references on the following page: en.wikipedia.org/wiki/Unscented_transform
