11 votes
Accepted

What sensors can be fused using the Kalman Filter framework

Remark: I will answer this using the Linear framework of the Kalman Filter but the idea is the same. The Kalman Filter basically propagate and fuses Gaussian Distributions in order to calculate the ...
  • 42.5k
5 votes
Accepted

Linear Time-Invariant system without State-space form

This seems like a homework problem, but I'll bite. The thing with a state-space representation is that it needs to have finite dimension: $$ x_{k+1} = \mathbf{A} x_k + \mathbf{B} u_k\\ y_k = \mathbf{C}...
  • 23.1k
5 votes
Accepted

Intuition for $\mathbf{P} = \mathbf{0}$ in steady-state when $\mathbf{Q} = \mathbf{0}$ (Kalman filter)

We each have different life experiences to fuel our intuition, but try this one out: Let $\mathbf A = 1$ and $\mathbf Q = 0$, and $\mathbf C = 1$ -- i.e., the actual state variable just doesn't change,...
  • 9,171
4 votes

What sensors can be fused using the Kalman Filter framework

Are there types of measurements that are not compatible for sensor fusion? Can any measurement be fused to better inform the underlying model? Any sensor that gives you more information about the ...
  • 9,171
3 votes
Accepted

How to linearize this state space model and write it in discrete form?

You have $$ f\left(\mathbf x, u\right) = \begin{bmatrix}\frac{-1}{T}\tau+\frac{K}{T} u \\ \frac{\tau}{mr} \\ 0 \end{bmatrix} \tag a $$ From which you (eventually) derive $$ \mathbf {A}_d=\begin{...
  • 9,171
2 votes
Accepted

How does sampling jitter affect state estimation?

I'm just making this up on the fly. There's got to be at least one paper out there on this, or sections in Kalman filtering books. Supposing that Δtk is distributed normally, does this just come out ...
  • 9,171
2 votes
Accepted

How to check that the state observer works appropriately?

Try looking at the error term $$e(k) = \mathbf{y}(k) - \mathbf{C}_d\cdot\hat{\mathbf{x}}(k)$$ and testing it for whiteness. If the state estimate is good, then all the predictable component will be ...
  • 23.1k
2 votes

Kalman Filter EM Estimation of Covariances

I think there is a bug in your code. In KalmanFilter(), observation_matrices=H is probably not what we want. By the reference in ...
  • 21
1 vote

For continuous systems that in Quasi-static / Static Equilibrium are Memoryless?

You're confusing the meanings of "static" and "has memory". Static, in the sense of "static equilibrium" just means the system is sitting still and will remain sitting ...
  • 9,171
1 vote

Why is it necessary to have two state variables

It's useful to think in the definition of a Markov state: all information about the state at $t+1$ can be derived from state at time $t$ and control at time $t$, ONLY. No information older than $t$ ...

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