A new estimation method based on sparse optimization was proposed. This method alleviated the ill-posedness by decreasing the dimension of parameter space. The sparse representation of the trajectory was achieved by using the B-spline function. An optimization model for trajectory estimation was constructed according to the relationship between the measurement data and the trajectory, and was solved by using the Gauss-Newton method. In this model, the number of the parameters to be estimated was determined by the number of the spline knots. A sparse optimization model for optimal knot selection was established by using the discontinuity of high order derivative of spline at the knots. This model was solved by using a convex optimization approach, and the number of knots was minimized. Simulation results showed that the sparse optimization method can dramatically improve the estimation accuracy of trajectory during the incomplete measured interval.