Position estimation without the range error covariance matrix Let u denote the node with unknown position, and let the position of reference node j be (xj, yj). Denote by rj,u the range measurement. It has been shown that the position estimate of the unknown can be updated according to (9.3)–(9.7).

(a) Using the information provided in Example 9.3, compute the next position estimate, given the current position estimate is (0.56,0.49).

(b) Now assume the error covariancematrix R of the range estimates is known, with R ¼

1 0 0 0 0 0:1 0 0 0 0 2 0 0 0 0 3 2

64 3

75

:

Use (9.8) to compute two consecutive position estimates, given an initial estimate of its position is (0,0).