ECE432: Homework 2 Kalman Filtering

1 Equations To restate the contents of the notes in a way that more closely reflects my own implementation: Consider the case of modeling a single dimensional first order PDE: x(t+∆t) = x(t) + ẋ∆t ẋ(t+∆t) = ẋ(t) We assume that there will be some noise in the actual process, as well as some noise in our ability to measure the state process. More exactly, we introduce wi and vi for each time step, which represent the process noise and measurement noise respectively, and which are both assumed to be drawn from a normal distribution. Let Q be the covariance matrix for w, and R the covariance matrix for v. Let zi be the measured value of xi. Now we have an updated set of equations: xi+1 = xi + ẋi∆t+ [wi]1 ẋi+1 = ẋ(t) + [wi]2 zi = xi + vi We express these relations in matrix form like so: