Statistical regularization methods in problem of navigational determination of space vehicle orbits

Many problems related to determination of space vehicle systems can be reduced to solution of the linear regression problem R = AQ + xi where R 1:n is the measurement vector, Q 1:m is the vector of the unknown but fully determinable parameters subject to evaluation. It is important to be able to determine the Q parameters of space vehicle orbits under conditions when traditional methods do not ensure the required accuracy. It is possible to use regularized versions of the least squares method, replacing the minimizing problem by its different modifications. It is shown that modification of the standard least squares method procedure makes possible a considerable broadening of the region of obserability of a self-determining flight vehicle. The greatest difficulty in this algorithm is computation of the regularization coefficient k.