(μ1,Σ1)=(zk→,Rk) .

I think I need read it again,

Explanation of Kalman Gain is superb.

Thanks a lot

Thanks in advance. ]]>

x[k+1] = Ax[k] + Bu[k]. I assumed that A is Ak, and B is Bk.

Then, when re-arranging the above, we get:

x[k] = Ax[k-1] + Bu[k-1]. I assumed here that A is A_k-1 and B is B_k-1. This suggests order is important. But, on the other hand, as long as everything is defined …. then that’s ok. Thanks again! Nice site, and nice work. ]]>

Similarly \(B_k\) is the matrix that adjusts the final system state at time \(k\) based on the control inputs that happened over the time interval between \(k-1\) and \(k\). We could label it however we please; the important point is that our new state vector contains the correctly-predicted state for time \(k\).

We also don’t make any requirements about the “order” of the approximation; we could assume constant forces or linear forces, or something more advanced. The only requirement is that the adjustment be represented as a matrix function of the control vector.

]]>If we’re trying to get xk, then shouldn’t xk be computed with F_k-1, B_k-1 and u_k-1? It is because, when we’re beginning at an initial time of k-1, and if we have x_k-1, then we should be using information available to use for projecting ahead…. which means F_k-1, B_k-1 and u_k-1, right? Not F_k, B_k and u_k. ]]>