Maximizing Log Likelihood in Nonlinear State Sequence Estimation, Slides of Robotics

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Nonlinear Optimization for Estimation

n General: find most likely state sequence given observations z:

n For Gaussian v, w:

Problem Setting

max

x,v,w

log P (v, w)

s.t. ∀t xt+1 = f (xt, ut) + wt

zt = g(xt) + vt

min

x,v,w

t

￿wt￿

2

2 +^

t

￿vt￿

2 2

s.t. ∀t xt+1 = f (xt, ut) + wt

zt = g(xt) + vt

n Given:

n For k=0, 1, 2, …, T

n Solve

n Observe z

t+ “Model Predictive Estimation” min x,v,w k ￿ t= ￿wt￿ 2 2 + k ￿ t= ￿vt￿ 2 2 s.t. ∀t : 0 ≤ t ≤ k xt+1 = f (xt, ut) + wt zt = g(xt) + vt