super clears https://www.youtube.com/watch?v=mY3G_hjrt7A&list=PLubUquiqNQdP_H6uUmU-9f0y_LheA3Hil&index=2

https://darkpgmr.tistory.com/56

https://hellbell.tistory.com/entry/Iteratively-Reweighted-Least-Square-IRLS

http://www.cv-learn.com/20210313-ba/

센서는 모두 에러를 가지고 있기 때문에 infomration matrix 필요

error * information matrix * error

Eq{1} [e1,e2,e3][][e1,e2,e3]^T <- e1,e2,e3 are sensors

skew-matrix on information matrix meant relationship between each sensors in covariance matrix.

if we assume each sensor doesn’t impact on other, then, we can define skew matrix’s elements to “0”

diagonal elements are 1/sigma^2 which is simga is standard distribution of sensor.

from {1} we got, e(x) = (e1^2)/(sigma)^2 + (e1^2)/(sigma)^2 + (e1^2)/(sigma)^2 with that, we only care about biggest value.

to find armin(x)

1) Talyor expension of e 2) Linearization -> independent of delta x + linear dependent + quadratic dependency 3) iteration(delta x differentiation) -> H * delta x = -b 4) delta x = -H^-1 & b 5) x = x + delta x

this process is gaussian newton

**case if H is m x n matrix, we can not inverse it

using trick of linear algebra

H^t * H * dletax = H^t(-b) // pseudo inverse(when inverse matrix not possible)

delta x = H*b

**case very expensive inverse matrix method that’s why

many way to matrix decomposition is

• cholesky(matrix size small)
• conjugate gradient(matrix size big)

probabilistic notation : minimizing the error squared term is the equivalent to maximising the log-likelihood that our state vector x is on the measured point in our map.

Least Square는 즉 미지 상수 abc 를 구하는 것이다