# Development Status and Service Performance Preliminary Analysis for BDSBAS
## 3 Message User Algorithms and Service Performance Evaluation Methods
### Service Integrity Evaluation Method  
With the continuous improvement of the service accuracy of GNSS core constellations such as the GPS and BDS, SBAS systems pay more attention to the service integrity augmentation. In the actual navigation processing, users usually do not know their true position error (PE), they can only compute the protection levels (PL), taking all relevant error sources into account associated with the observation geometry and integrity data provided by the SBAS system. The definition of the system integrity performance requirement includes an alert limit (AL) against which the requirement can be assessed. If the PL is too large to be contained within the AL, the SBAS service will be indicated as not available. We used the monitoring receivers with precisely known coordinates evenly distributed in the service area to analyze the BDSBAS service integrity. Once a PE of any monitoring receiver exceeds the AL without receiving an alert in time, while the calculated PL is smaller than the AL, a piece of hazardously misleading information (HMI) exists. The SBAS service integrity orders that the HMI probability (\(P_{HMI}\)) should be less than a certain probability. ICAO provides specific requirements of \(P_{HMI}\) for different operations. The evaluation method of SBAS service integrity is shown as follows:  
1. During the testing period, the starting and ending epochs are indicated as \(t_{start}\) and \(t_{endt}\), respectively, and the observation sampling interval is expressed as T.
2. The position coordinates of the monitoring receivers are calculated with BDSBAS broadcast information. The deviation of the estimate coordinates from the true coordinates of the receivers are computed and divided into horizontal position errors (HPE) and vertical position errors (VPE). The time series of HPE and VPE are taken as the statistical samples.
3. The associated integrity messages of BDSBAS are used to compute the horizontal protection levels (HPL) and vertical protection levels (VPL) for the monitoring receivers.
4. At epoch \(i\), comparing the HPE value and HPL value against the horizontal alert limit (HAL) value. If the three values satisfy the relationship as HPL < HAL < HPE, it indicates a horizontal HMI event, \(Bool(x)\) is set equal to 1, otherwise, \(Bool(x)\) is set equal to 0. Meanwhile, comparing the VPE value, VPL value against the vertical alert limit (VAL) value, if the three values satisfy VPL < VAL < VPE, it indicates a vertical HMI event, and \(Bool(y)\) is set equal to 1, otherwise, \(Bool(y)\) is set equal to 0.
5. Using all the experimental samples, the probability of HMI of service integrity is determined as: \[P_{HMI}=1-\frac{\sum\limits_{t=t_{start},inc=Top}^{t_{end}-Top}\left\{\prod \limits_{i=t,inc=T}^{t+Top}Integrity\_Flag(i)\right\}}{\frac{t_{end}-t_{start}} {Top}}\] \[Integrity\_Flag(i)=\begin{cases}0,&\left(Bool(x)_{i}+Bool(y)_{i}\right)>0\\ 1,&\mathit{other}\end{cases}\] (5) where \(Integrity\_Flag(i)\) is the service integrity indicator, where \"0\" indicates integrity risk occurred and \"1\" indicates there is no integrity risk; \(P_{HMI}\) is the probability of HMI; \(Top\) is the service sample interval and usually is set to 150 s for APV I approach; T is observation data sampling interval.