测绘学报
測繪學報
측회학보
ACTA GEODAETICA ET CARTOGRAPHICA SINICA
2015年
2期
168-173,182
,共7页
聂志喜%王振杰%欧吉坤%姬生月
聶誌喜%王振傑%歐吉坤%姬生月
섭지희%왕진걸%구길곤%희생월
动态相对定位%基线长约束%线性化近似%余项影响%诊断条件
動態相對定位%基線長約束%線性化近似%餘項影響%診斷條件
동태상대정위%기선장약속%선성화근사%여항영향%진단조건
dynamic relative positioning%baseline length constraint%linear approximation%remainder term’s influence%discriminant condition
GNSS 动态相对定位中常附加非线性的基线长约束进行解算,而 LAMBDA 方法只能处理无约束或者线性约束的模型,为了应用 LAMBDA 方法,应对非线性约束条件进行线性化近似。通常附加该约束后,模糊度固定成功率会提高,但对于超短基线有时反而会降低。何种条件下附加线性化近似的基线长约束条件可以提高模糊度固定成功率尚未有定论。本文基于附加基线长约束的 GNSS 相对定位数学模型,推导基线长约束条件线性化近似余项对浮点解的最大影响值公式,给出基线长约束能否线性化近似的诊断条件。当该条件满足时,线性化近似余项影响可以忽略,附加线性化近似的基线长约束可以改善浮点解解算精度,提高模糊度固定成功率;若不满足,则线性化近似余项影响可能不可以忽略,附加约束会因浮点解有偏不能固定为正确的模糊度,并通过算例验证了相关结论。
GNSS 動態相對定位中常附加非線性的基線長約束進行解算,而 LAMBDA 方法隻能處理無約束或者線性約束的模型,為瞭應用 LAMBDA 方法,應對非線性約束條件進行線性化近似。通常附加該約束後,模糊度固定成功率會提高,但對于超短基線有時反而會降低。何種條件下附加線性化近似的基線長約束條件可以提高模糊度固定成功率尚未有定論。本文基于附加基線長約束的 GNSS 相對定位數學模型,推導基線長約束條件線性化近似餘項對浮點解的最大影響值公式,給齣基線長約束能否線性化近似的診斷條件。噹該條件滿足時,線性化近似餘項影響可以忽略,附加線性化近似的基線長約束可以改善浮點解解算精度,提高模糊度固定成功率;若不滿足,則線性化近似餘項影響可能不可以忽略,附加約束會因浮點解有偏不能固定為正確的模糊度,併通過算例驗證瞭相關結論。
GNSS 동태상대정위중상부가비선성적기선장약속진행해산,이 LAMBDA 방법지능처리무약속혹자선성약속적모형,위료응용 LAMBDA 방법,응대비선성약속조건진행선성화근사。통상부가해약속후,모호도고정성공솔회제고,단대우초단기선유시반이회강저。하충조건하부가선성화근사적기선장약속조건가이제고모호도고정성공솔상미유정론。본문기우부가기선장약속적 GNSS 상대정위수학모형,추도기선장약속조건선성화근사여항대부점해적최대영향치공식,급출기선장약속능부선성화근사적진단조건。당해조건만족시,선성화근사여항영향가이홀략,부가선성화근사적기선장약속가이개선부점해해산정도,제고모호도고정성공솔;약불만족,칙선성화근사여항영향가능불가이홀략,부가약속회인부점해유편불능고정위정학적모호도,병통과산례험증료상관결론。
Additional nonlinear baseline length constraint is often used for GNSS dynamic relative positio‐ning ,but the LAMBDA method can only deal with linear constraint model .So ,it is necessary to linearize and approximate nonlinear constraint conditions .Linearized approximate constraint usually increases the success rate of fixing integer ambiguity ,but for the ultra‐short baseline ,the opposite results may be derived .When will the linearized approximate baseline length constraint can improve the success rate of fixing ambiguity ?This article attempts to answer these questions .Firstly ,the float solution’s maximum influence value formula is derived when using linearized approximate baseline length constraint ,based on GNSS relative positioning model ;Secondly ,a discriminant condition is given to determine whether baseline length constraint can be linear approximation .When the condition is met ,the influence can be ignored , linearized approximate baseline length constraint can improve the accuracy of float solution and increase the success rate of fixing ambiguity ,on the contrast , the influence may not be ignored , linear approximation will result in a biased float solution and the ambiguity cannot befixed correctly ;At last ,the foregoing conclusions are verified with some numerical example in this paper .