GNSS中多频观测值的组合形式

心已赠人 2023-02-14 10:42 11阅读 0赞

> **以GPS为例，L1、L2、L5三个频点，为1575.42，1227.60，1176.45MHZ；对应波长为：**
> 
> **1 光速=299792458 米/秒(米每秒)**
> 
> 基频：10.23MHZ； L1为154倍基频， L2为120倍基频， L3为115倍基频，
> 
> **λ1=c/L1= 0.190293672798365≈19厘米；**
> 
> **λ2=c/L2= 0.244210213424568≈24.4厘米；**
> 
> **λ5=c/L5= 0.254828048790854≈25.5厘米；**
> 
> **f1:f2:f3=（1/λ1）:（1/λ2）：（1/λ5）=154：120：115；**
> 
> ![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3d1d3VrdTEyMw_size_16_color_FFFFFF_t_70][]
> 
> ![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3d1d3VrdTEyMw_size_16_color_FFFFFF_t_70 1][]
> 
> ![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3d1d3VrdTEyMw_size_16_color_FFFFFF_t_70 2][]

## 一、无电离层组合模式/Iono-free/IF： ##

> 不同频点电离层延迟关系： L1和L2频点
> 
> I2=(f1^2/f2^2)\*I1;
> 
> I2=(λ2^2/(λ1^2)\*I1;

以GPS L1和L2频点为例，介绍无电离层组合：

### 1. IF伪距表达式 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3d1d3VrdTEyMw_size_16_color_FFFFFF_t_70 3][]

推导过程如下：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3d1d3VrdTEyMw_size_16_color_FFFFFF_t_70 4][]

### 2. IF载波相位表达式：3种 ###

考虑载波相位观测值中，r/卫星-接收机距离为真实距离，既单独将模糊度/N 拿出来构成载波相位观测值；

有两种形式：

*  形式1：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3d1d3VrdTEyMw_size_16_color_FFFFFF_t_70 5][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3d1d3VrdTEyMw_size_16_color_FFFFFF_t_70 6][]

既无电离层载波为：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3d1d3VrdTEyMw_size_16_color_FFFFFF_t_70 7][]

*  形式2：

形式1和形式2的区别为：形式1单位为“m”,形式2单位为“Cycle”

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3d1d3VrdTEyMw_size_16_color_FFFFFF_t_70 8][]

推导过程：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3d1d3VrdTEyMw_size_16_color_FFFFFF_t_70 9][]

*  形式3：

L1、L2载波相位观测值 φ1和φ2，假定是接收机输出的载波值（既模糊度都隐藏在里面），实际数据处理中，拿到的也是这种数据，因此这种形式在实际中用的比较多！

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3d1d3VrdTEyMw_size_16_color_FFFFFF_t_70 10][]

该表达式在各类文献资料中最为常见, 通过对比系数可知, 该式在形式与上文中 IF 载波相位表达式 1 相似, 区别在于, 此处等式右侧的L1、L2载波相位观测量应以米为单位, 若获得的原始载波相位观测量单位为周, 则应将该值乘以各自波长之后再代入, 但这时由于载波相位观测量中的模糊度值并未求出, 因此最终计算得到的 IF 载波相位观测量也受模糊度影响。

汇总如下：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3d1d3VrdTEyMw_size_16_color_FFFFFF_t_70 11][]

## 二、 ##

单频点载波相位测量误差为α；经过双差后，双差测量误差为2α

参考：

《GPS原理与接收机设计》

[GPS Iono-free观测量的4种表达式 ][GPS Iono-free_4_]

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[GPS Iono-free_4_]: https://mp.weixin.qq.com/s/lUIwhjLckn27ogjQqayhvg