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Abstract

With correctly resolved integer ambiguities, a GNSS user can fully exploit the high precision of the carrier-phase observations, whereas incorrectly fixed ambiguities are likely to result in large estimation errors. An alternative to fixing the ambiguities is to use the best integer-equivariant (BIE) estimator, which always provides MSE-optimal results, regardless of the strength of the underlying observation model. A scalar sequential approximation of the BIE estimator (SBIE), using a concept similar to integer bootstrapping (IB), was shown to provide close-to-optimal results, while being computational less demanding as no integer search is needed. Recently, the principle of IB was generalized to a vectorial form, in which the sequential ambiguity fixing is applied to ambiguity blocks instead of single ambiguities. Analogously, we generalize the scalar sequential SBIE to a vectorial sequential form in this contribution. Two specific examples based on different integer-equivariant estimators are formulated, and their properties and performance are analyzed through numerical simulation examples. They are evaluated with respect to SBIE and compared to the corresponding counterparts from the vectorial IB estimators with fixed ambiguities.