CET 318 The Eighth Lecture 8, Mathematical Model 1. Point Positioning Book:p.183-202 Dr Guoding Zhou 1.1 Point Positioning with Code ranges Epoch at t Additional Satellites(Simultaneously): L Code Range Observation Equatio )2 R/()=pf(t)+c△6() R2()=√x(p2+(Y2(NY2+20)12)+cB p (t) p!(1) R()=x0四+(Y:0+2(区+c8 △6{(U) R(=x-四3+(Y:1x3+:02+0 Measured distance: p{(t)=√(x()-x,)2+(Y(t)-Y)2+(z{()-z)2 Additional Epoch: Combined bias lock biases must be △6;(t)=6(1)+6,(t) tation message in the form of thre Combined Known Unknown coefficients ao, a, a y with a reference △6(t)=a0+a1(1-1)+a2(1-1) Observation Equation R/()-c△8(t)=p(t)-c△6,(t nknown1 Dr. Guoqing Zhou 8. Mathematical Model CET 318 Book: p. 183-202 1. Point Positioning 1.1 Point Positioning with Code Ranges 1. Code Range Observation Equation Measured Distance: ( ) ρ (t) c δ (t) j = + ∆ i j i j i R t R (t) j i δ (t) j ∆ i ρ (t) j i c R (t) j i i j Epoch at t ρ (t) j i δ (t) j ∆ i ρ (t) (X (t) - X ) (Y (t) - Y ) (Z (t) - Z ) 2 i j i 2 i j i 2 i j = i + + j i ( ) (X (t) - X ) (Y (t) - Y ) (Z (t) - Z ) c δ (t) 1 i 2 i 2 1 i 2 1 i 1 1 Ri t = i + i + i + ∆ ( ) (X (t) - X ) (Y (t) - Y ) (Z (t) - Z ) c δ (t) 2 i 2 i 2 2 i 2 2 i 2 2 Ri t = i + i + i + ∆ ( ) (X (t) - X ) (Y (t) - Y ) (Z (t) - Z ) c δ (t) 3 i 2 i 2 3 i 2 3 i 3 3 Ri t = i + i + i + ∆ ( ) (X (t) - X ) (Y (t) - Y ) (Z (t) - Z ) c δ (t) 4 i 2 i 2 4 i 2 4 i 4 4 Ri t = i + i + i + ∆ Additional Satellites (Simultaneously): An additional epoch, new satellite clock biases must be modeled due to clock drift. Fortunately, the satellite clock information is transmitted via the broadcast navigation message in the form of three polynomial coefficients a0, a1, a2 with a reference time tc. Additional Epoch: 2 0 1 2 j δ (t) ( ) ( ) c c ∆ = a + a t − t + a t − t δ (t) δ (t) δ (t) i j j ∆ i = + Combined Bias: Combined Known Unknown ( ) c δ (t) ρ (t) c δ (t) i j − ∆ = − ∆ j i j i R t Observation Equation: Known Unknown