output voltage of mr sensor will be zero valued thus as the roll rate u03c9 s of the vehicle is essentially constant the analog output voltage of mr sensor 116 generally describes a sinusoid over time as shown in fig3 wherein the zero crossing points 312 of the sinusoid 310 correspond to instances in time when sensitive axis 212 of mr sensor 116 is perpendicular to magnetic field 214 the vertical axis in fig3 is the output voltage v out of mr sensor 116 and the horizontal axis represents time t referring now to fig4 a graphical representation of the orientation of a local magnetic field relative to the vehicle body coordinate frame for determining a roll error measurement residual in accordance with the present invention will be discussed specifically fig4 shows the orientation of the local magnetic field 214 with respect to the vehicle body frame when sensitive axis 212 of mr sensor 116 is perpendicular to magnetic field 214 at a zero crossing point 312 of the output of mr sensor 116 axes xb 210 yb 410 and zb 412 represent the roll pitch and yaw axes respectively of the vehicle body at the time of a zero crossing 312 in the sinusoidal analog output of mr sensor 116 sensitive axis 212 is perpendicular to magnetic field 214 however if there is error in the navigation solution 39 s estimate of vehicle attitude an estimate m 416 of the unit vector m 414 along sensitive axis 212 will.