(35S) Most probable position of a vessel

04252017, 04:46 AM
(This post was last modified: 06152017 01:16 PM by Gene.)
Post: #1




(35S) Most probable position of a vessel
After obtaining several lines of position (LOP) from celestial observation, navigator is faced with one more challenge  combine all those lines into a single point, so called most probable position of his vessel, or MPP.
This program works with LOPs represented as azimuth and offset vectors relative to same origin (such as assumed position, or D.R. position). Each LOP with given AZ and D contributes the equation dx*sin(AZ)+dy*cos(AZ)=D to the system. If there are 3 or more LOPs the overdefined system can be solved for dx and dy using least squares method. The formulas work out to be A=sum(sin(AZi)^2) B=sum(sin(AZi)*cos(AZi)) C=sum(cos(AZi)^2) D=sum(sin(AZi)*Di) E=sum(cos(AZi)*Di) DET=A*CB*B dx=(D*CE*B)/DET dy=(E*CD*B)/DET Here AZi,Di are azimuth vectors and offsets of LOPs, and resulting dx and dy is an offset vector relative to same origin as LOPs. In another words, dx and dy is a correction to previous assumed position obtained by taking into account the observations. Operating instructions: Switch to degrees mode. XEQ L002  initializes routine, then enter AZ_i <ENTER> D_i <R/S> (Az_i is azimuth of ith intercept in degrees, D_i is offset in nautical miles, positive for "towards", negative for "away") After all pairs are entered, XEQ L003 calculates dx and dy in nm. This offset should be applied to previous assumed position to obtain a "fix". Code:
Example: Select degrees mode. XEQ L002 (output:0, ready for data entry) 95 <Enter> 15.1 <r/s> (output: 1=LOPs entered so far) 191 <Enter> 16.3 <r/s> (output: 2=LOPs entered so far) 242 <Enter> 0.5 <r/s> (output: 3=LOPs entered so far) 340 <Enter> 30.0 <r/s> (output: 4=LOPs entered so far) XEQ L003 Result: rX=24.84 (latitude offset, the fix is 24.8 nm to the south of assumed position) rY=14.08 (longitude offset, the fix is 14.1 nm to the east of assumed position) 

04252017, 11:41 AM
Post: #2




RE: (35s) Most probable position of a vessel
(04252017 04:46 AM)nsg Wrote: After obtaining several lines of position (LOP) from celestial observation, navigator is faced with one more challenge  combine all those lines into a single point, so called most probable position of his vessel, or MPP. 

04262017, 01:21 AM
(This post was last modified: 04262017 01:42 AM by nsg.)
Post: #3




RE: (35s) Most probable position of a vessel  
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