Kalman Likelihood 1D

Problem

Compute the Gaussian log likelihood of a one-dimensional Kalman filter innovation: -0.5 * (ln(2*pi) + ln(p + r) + innovation^2 / (p + r)), where innovation = obs - prior.

Return 0.0 if p + r is not positive.

Hint

The innovation variance is prior variance plus observation noise variance.

Test cases

case 1

in: [0,1,0,1]

expected: -1.2655121234846454

case 2

in: [0,1,2,1]

expected: -2.2655121234846454

case 3

in: [5,2,5,3]

expected: -1.723657489421723

case 4

in: [0,0,3,1]

expected: -5.418938533204672

Starter codePython

import math
def kalman_likelihood_1d(prior, p, obs, r):
    # Your code here
    pass

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