Please answer all questions on the image I would deeply appreciate it

1 Extended Kalmen Filter Linearizetien The metien medel fer a differential drive eensidered in the example dissemed in seetien 6.13 in the lecture netes is simplied, i.e., it assumes that the rehet either translates hut dees net retate {em g and t] = [3] er it retates hut dees net translate {em = and 1H] g U]. The fellewing reedel instead eensidered the ease whem the rehet ean mmre aleng a eireular are {we assume at = l fer simpliey]: me + 1] = 1r{f]+ -:f-f-3in9{ + 'jlsmwm + my] ms + 1] = me + fgmsem 3'3 ees{3{t] + run] {1] se+ 1] = em we] 1. Write the linearized rnetien rnedel fer this state transmn equatien. 2. The given rnedel is net dened whim TH] = , i.e., when the rehet translates enly. Write the rnedel that sheuld he used when the rehet translates enly, and write its linearizatiea 3. Is the ahmre rnedel aeeurate fer the ease where the rehet retates hut dees net translate? Explain and 1m answer. If it is net, write an updated rnedel and its linearizatien