A hybrid localization system, comprising: a magnetic-based localization system that measures localization element positions with respect to a coordinate frame A; an impedance-based localization system that measures localization element positions with respect to a coordinate frame B; a medical device including a plurality of localization elements (17, 52, 54, 56), the plurality of localization elements comprising at least one localization element detectable by the impedance-based localization system and at least one localization element detectable by the magnetic-based localization system; at least one processor configured to express localization element positions measured by the impedance-based localization system with respect to the coordinate frame B in the coordinate frame A via application of a non-linear mapping function f, wherein f is defined such that, for a plurality of points r, each point r having a location measured with respect to coordinate frame A of Ar, and a location measured with respect to coordinate frame B of Br, f(Br)≈Ar, characterized in that the system is further comprising: a fixed reference localization element for the magnetic-based localization system, the fixed reference localization element for the magnetic-based localization system having a position, measured with respect to the coordinate frame A, of R A; a fixed reference localization element for the impedance-based localization system, the fixed reference localization element for the impedance-based localization system having a position, measured with respect to the coordinate frame B, of R B; and at least one processor configured to monitor a divergence between R A and f ( R B) and to signal an anomaly when the divergence exceeds a divergence threshold. a magnetic-based localization system that measures localization element positions with respect to a coordinate frame A; an impedance-based localization system that measures localization element positions with respect to a coordinate frame B; a medical device including a plurality of localization elements (17, 52, 54, 56), the plurality of localization elements comprising at least one localization element detectable by the impedance-based localization system and at least one localization element detectable by the magnetic-based localization system; at least one processor configured to express localization element positions measured by the impedance-based localization system with respect to the coordinate frame B in the coordinate frame A via application of a non-linear mapping function f, wherein f is defined such that, for a plurality of points r, each point r having a location measured with respect to coordinate frame A of Ar, and a location measured with respect to coordinate frame B of Br, f(Br)≈Ar, characterized in that the system is further comprising: a fixed reference localization element for the magnetic-based localization system, the fixed reference localization element for the magnetic-based localization system having a position, measured with respect to the coordinate frame A, of R A; a fixed reference localization element for the impedance-based localization system, the fixed reference localization element for the impedance-based localization system having a position, measured with respect to the coordinate frame B, of R B; and at least one processor configured to monitor a divergence between R A and f ( R B) and to signal an anomaly when the divergence exceeds a divergence threshold. a fixed reference localization element for the magnetic-based localization system, the fixed reference localization element for the magnetic-based localization system having a position, measured with respect to the coordinate frame A, of R A; a fixed reference localization element for the impedance-based localization system, the fixed reference localization element for the impedance-based localization system having a position, measured with respect to the coordinate frame B, of R B; and at least one processor configured to monitor a divergence between R A and f ( R B) and to signal an anomaly when the divergence exceeds a divergence threshold.