State Space Local Level Step

Problem

Perform one step of a local level state space model. Given the current level and variance p, an observation, process noise q, and observation noise r: predict p_pred = p + q, compute K = p_pred / (p_pred + r), and return [level + K * (obs - level), (1 - K) * p_pred].

Return a gain of 0.0 when the denominator is zero.

Hint

Process noise raises the prior variance before the measurement update.

Test cases

case 1

in: [10,1,12,0.5,2]

expected: [10.857142857142858,0.8571428571428571]

case 2

in: [0,1,1,0,1]

expected: [0.5,0.5]

case 3

in: [5,0,5,1,3]

expected: [5,0.75]

case 4

in: [0,2,10,0,1]

expected: [6.666666666666666,0.6666666666666667]

Starter codePython

def state_space_local_level_step(level, p, obs, q, r):
    # Your code here
    pass

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