Hi, Thank you very much for your valuable help and support. I have got the point. i was busy with your nice articular (reference point determination with a new mathematical model...).

Actually, I did a program using Matlab code contain two parts: The first Part is automatic detection of the target from surrounding objects in the laser point cloud. The second part is computing the geometric centre of the detected target. for example for the pyramid faces i used Plane intersection algorithm after each face separately detected. The problem is I don't know how to calculate statistically the precision of the apex as your JAG3D did very well with cone and sphere...

How to calculate σxyz of the pyramid apex. What I did so far is σxyz (apex)= σx(face1)+σx(face2)+σx(face3)+σx(face3). This is diffidently incorrect. therefore I would like to help me, how to propagate these error to determine the σapex. I also tried to solve it using inverse plan equation such as [ σa1σx+σb1σy+σc1σz=1; σa2σx+σb2σy+σc2σz=1; σa3σx+σb3σy+σc3σz=1; σa4σx+σb4σy+σc4σz=1]. The 4 set of parameters ( σa1,σb1,σc1 to σa4,σb4,σc4) are known from fitting each face separately using JAG3D and then, what is left is the σx,σy,σz. This method is also I'm not happy with it.

A copy of separate data of each face of the pyramid are as follows

face1
-8.7740 10.2929 -0.2645
-8.7546 10.2701 -0.3177
-8.8042 10.2864 -0.2647
-8.7602 10.2767 -0.2908
-8.7154 10.3041 -0.2639
-8.7347 10.2841 -0.2905
-8.7470 10.2985 -0.2641
-8.8216 10.3067 -0.2113
-8.8498 10.2977 -0.2114
-8.7888 10.3102 -0.2109
-8.8108 10.2940 -0.2379
-8.7844 10.3051 -0.2378
-8.7524 10.3050 -0.2374
-8.7637 10.3184 -0.2109
-8.8621 10.3120 -0.1847
-8.8280 10.3142 -0.1843
-8.7998 10.3231 -0.1842
-8.7734 10.3298 -0.1841
-8.7055 10.3322 -0.2103
-8.7251 10.3155 -0.2372
-8.6989 10.3245 -0.2371
-8.7321 10.3238 -0.2106
-8.6751 10.3405 -0.2103
-8.7436 10.3375 -0.1838
-8.7142 10.3427 -0.1837
-8.6877 10.3555 -0.1837
-8.6584 10.3609 -0.1835
Face2
-8.9011 10.3140 -0.4292
-8.8979 10.3103 -0.4021
-8.8503 10.2982 -0.4009
-8.8934 10.3051 -0.3204
-8.8922 10.3037 -0.3744
-8.8957 10.3077 -0.3475
-8.8903 10.3014 -0.2660
-8.8403 10.2866 -0.3192
-8.8439 10.2908 -0.3733
-8.8447 10.2917 -0.3463
-8.7987 10.2798 -0.3454
-8.7972 10.2781 -0.3185
-8.8420 10.2886 -0.2651
-8.8414 10.2879 -0.2920
-8.7972 10.2781 -0.2914
-8.8914 10.3028 -0.2118
-8.8913 10.3026 -0.2390
-8.8911 10.3024 -0.1848
-8.8431 10.2899 -0.2381
Face 3
-8.7668 10.3218 -0.4267
-8.8744 10.3263 -0.4560
-8.7807 10.3382 -0.4543
-8.8118 10.3373 -0.4551
-8.8147 10.2984 -0.4003
-8.8596 10.3091 -0.4282
-8.8263 10.3121 -0.4275
-8.7545 10.3073 -0.3992
-8.7821 10.3024 -0.3996
-8.7932 10.3154 -0.4269
-8.7576 10.2737 -0.3445
-8.8032 10.2850 -0.3726
-8.7698 10.2880 -0.3719
-8.6894 10.3576 -0.4529
-8.7478 10.3424 -0.4536
-8.7209 10.3506 -0.4534
-8.7354 10.3278 -0.4262
-8.7101 10.3377 -0.4259
-8.7437 10.2946 -0.3717
Face 4
-8.6503 10.3510 -0.3985
-8.6315 10.3681 -0.3985
-8.6334 10.3705 -0.4520
-8.6954 10.3203 -0.3985
-8.6694 10.3337 -0.3982
-8.6744 10.3396 -0.4252
-8.6550 10.3567 -0.4252
-8.6332 10.3702 -0.4251
-8.7059 10.2929 -0.3174
-8.7298 10.2782 -0.3441
-8.7117 10.2996 -0.3713
-8.7069 10.2940 -0.3442
-8.6881 10.3115 -0.3442
-8.7283 10.2765 -0.3173
-8.6858 10.3089 -0.3174
-8.6907 10.3147 -0.3712
-8.6435 10.3430 -0.3173
-8.6684 10.3324 -0.3711
-8.6662 10.3298 -0.3440
-8.6463 10.3463 -0.3711
-8.6288 10.3650 -0.3712
-8.6454 10.3453 -0.3443
-8.6273 10.3631 -0.3443
-8.7063 10.2933 -0.2904
-8.6863 10.3095 -0.2636
-8.6875 10.3109 -0.2905
-8.6632 10.3263 -0.2636
-8.6636 10.3268 -0.2903
-8.6423 10.3415 -0.2903
-8.6206 10.3550 -0.2634
-8.6220 10.3567 -0.3174
-8.6235 10.3586 -0.2903
-8.6664 10.3301 -0.2369
-8.6401 10.3389 -0.2366
-8.6232 10.3582 -0.2099
-8.6199 10.3542 -0.2366