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The procedure for estimating polarization invariants of the backscattering matrix in horizontal-vertical basis is considered for radar observation of arbitrary nonreciprocal objects. Two polarization invariants are added to the well-known six Huynen-Euler invariants. These new invariants (nonreciprocity angle and difference in absolute phases of the symmetric and antisymmetric parts of the scattering matrix) describe the nonreciprocal properties of the object itself. With the simultaneous measurement of all eight quadratures of the scattering matrix elements, the closed-form expressions for calculating the eight polarization invariants are given. The derived expressions are the starting point for complete estimation of the polarization properties of arbitrary radar objects with a nonsymmetric scattering matrix. The given approach can be used to study various polarization effects in remote radar sensing of artificial and natural objects, and also to simulate polarization measurement processes and estimation errors caused by the measurements of scattering matrix elements at different instants.