Intuition “It is easier to approximate a probability distribution than it is to approximate an arbitrary nonlinear function” Idea We perform a nonlinear transformation $h(x)$ on the 1D gaussian distribution (left), the result is a more complicated 1D distribution (right).
2022-07-21
Linearization Error Recap: The EKF works by linearizing the nonlinear motion and measurement models to update the mean and covariance of the state. The difference between the linear approximation and the nonlinear function is called linearization error
2022-07-21
What’s in a State? We can think of the vehicle state as composed of two parts $$ \underbrace{\mathbf{x}}_{\text{True state|}}=\underbrace{\hat{\mathbf{x}}}_{\text{Nominal state ("Large")}}+\underbrace{\delta \mathbf{x}}_{\text{Error state ("small")}} $$ 💡 Idea Instead of doing Kalman Filter in the full state (which might have lots of complicated nonlinear behaviours).
2022-07-20
Motivation Linear systems do not exist in reality. We have to deal with nonlinear discrete-time systems $$ \begin{aligned} \underbrace{\mathbf{x}_{k}}_{\text{current state}}&=\mathbf{f}_{k-1}(\underbrace{\mathbf{x}_{k-1}}_{\text{previous state}}, \underbrace{\mathbf{u}_{k-1}}_{\text{inputs}}, \underbrace{\mathbf{w}_{k-1}}_{\text{process noise}}) \\\\ \underbrace{\mathbf{y}_{k}}_{\text{measurement}}&=\mathbf{h}_{k}(\mathbf{x}_{k}, \underbrace{\mathbf{v}_{k}}_{\text{measurement noise}}) \end{aligned} $$ How can we adapt Kalman Filter to nonlinear discrete-time systems?
2022-07-20
Intuition Example Estimation of the 1D position of the vehicle. Starting from an initial probabilistic estimate at time $k-1$ Note: The initial estimate, the predicted state, and the final corrected state are all random variabless that we will specify their means and covariances.
2022-07-19
The Kalman filter is an efficient recursive filter estimating the internal-state of a linear dynamic system from a series of noisy measurements. Applications of Kalman filter include Guidance Navigation Control of vehicles, aircraft, spacecraft, and ships positioned dynamically 💡 The basic idea of Kalman filter is to achieve the optimal estimate of the (hidden) internal state by weightedly combining the state prediction and the measurement.
2022-06-24
2022-06-22
Let’s take 10.0.0.0/8 as an example. The address 10.0.0.0/8 comprises of two parts IP address (10.0.0.0) the global addressing scheme used under Internet Protocol Subnet or IP block (/8) divide the IP addresses into small blocks/ranges.
2021-04-01
CSMA/CD CSMA/CD = Carrier Sense Multiple Access with Collision Detection Media access control method used in early Ethernet technology Carrier Sense Multiple Access Carrier: transmission medium that carries data, e.g.
2021-03-15
TCP = Transmisson Control Protocol How TCP starts and closes session? Three stages of TCP Session starting Data transmission Session ending This three stages make TCP a connect-oriented and reliable protocol.
2021-03-15