Taylor series expansion In most common Taylor series approach y=f(x1,x2,x3,x4) yo+ ay=f(x)+(xAx x=( x2,x3, 4) The estimation is made using the difference between the observations and the expected values based on apriori values for the parameters The estimation returns adjustments to apriori parameter values 03/1203 12540Lec10 Linearization Since the linearization is only an approximation, the estimation should be iterated until the adjustments to the parameter values are zero For GPs estimation Convergence rate is 100 1000: 1 typically(ie, a 1 meter error in apriori coordinates could results in 1-10 mm of non linearity error)03/12/03 12.540 Lec 10 7 Taylor series expansion • In most common Taylor series approach: • The estimation is made using the difference between • The estimation returns adjustments to apriori y = f (x1, x2, x3, x4 ) y0 y = f (x) x 0 + ∂f (x) ∂x Dx x = (x1, x2, x3, x4 ) the observations and the expected values based on apriori values for the parameters. parameter values + D 03/12/03 12.540 Lec 10 8 Linearization • Since the linearization is only an approximation, the estimation should be iterated until the adjustments to the parameter values are zero. • For GPS estimation: Convergence rate is 100- 1000:1 typically (ie., a 1 meter error in apriori coordinates could results in 1-10 mm of non￾linearity error). 4