Kalman Smoother Variance

Problem

Perform the variance recursion of the Rauch-Tung-Striebel smoother. Given the filtered variance p_filtered, the predicted variance p_predicted, and the smoothed variance at the next time step p_smoothed_next, return p_filtered + J^2 * (p_smoothed_next - p_predicted) where J = p_filtered / p_predicted.

If p_predicted is zero, return p_filtered unchanged.

Hint

The weight J shrinks the future variance correction onto the filtered state.

Test cases

case 1

in: [1,2,1.5]

expected: 0.875

case 2

in: [0.5,1,0.4]

expected: 0.35

case 3

in: [2,2,2]

expected: 2

case 4

in: [1,0,3]

expected: 1

case 5

in: [0.5,2,0.5]

expected: 0.40625

Starter codePython

def kalman_smoother_variance(p_filtered, p_predicted, p_smoothed_next):
    # Your code here
    pass

5 test cases · run your code against them in the editor