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摘要:
多星座组合导航提供更多的可用卫星，但也增大接收机计算复杂度，选取部分可见星代替全部可见星进行接收机位置解算成为选星算法研究的热点。粒子群优化（PSO）选星算法将PSO算法引入到选星过程中，该方法能够减少选星时间，实现北斗/GPS组合星座快速选星。研究了该算法的关键参数包括惯性权重因子、加速系数、种群大小等对PSO选星算法性能的影响，并针对搜索过程容易陷入局部最优问题，提出自适应模拟退火粒子群优化（ASAPSO）选星算法，该算法通过引入随适应值大小自适应调整进化参数及结合模拟退火算法调整粒子速度，以增强算法跳出局部极值的能力。采用实际数据对算法进行验证，结果表明：ASAPSO选星算法在保证选星时间的同时，能够提高算法搜索结果的准确性，其性能优于PSO选星算法。
Abstract:Multi-constellation integrated navigation can provide users with more visible satellites; however, the computational complexity of the navigation receiver will also be increased. Therefore, part visible satellites are selected instead of all visible satellites for receiver position solution, which becomes a hot spot in satellite selection algorithm research. The particle swarm optimization (PSO) is introduced into the satellite selection process by the PSO fast satellite selection algorithm. Through this method, not only the time for selecting satellite is reduced, but also the fast selection of the Beidou/GPS integrated constellation is implemented. The influence of the algorithm's key parameters such as inertia weighting factor, acceleration coefficient and population size on the performance of PSO satellite selection algorithm is studied. In addition, since PSO satellite selection algorithm is easy to fall into the local optimum for the search process, the adaptive simulated annealing particle swarm optimization (ASAPSO) algorithm is proposed to optimize the process of satellite selection algorithm. Moreover, the adaptive adjustment of evolutionary parameters with adaptive value, the adjustment of particle velocity in combination with simulated annealing algorithm are introduced in order to enhance the ability of the algorithm to jump out of local extremum. The algorithm is verified by using real navigation data, and the results demonstrate that the ASAPSO algorithm not only can ensure the satellite selection time, but also can improve the accuracy of the search results. Moreover, the performance of the ASAPSO satellite selection algorithm is better than that of the PSO satellite selection algorithm.
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图 1 PSO和ASAPSO选星算法GDOP变化
Figure 1. GDOP changes in PSO and ASAPSO satellite selection algorithm
图 2 PSO、改进PSO及ASAPSO选星算法的GDOP计算误差
Figure 2. GDOP calculation error of PSO, improved PSO and ASAPSO satellite selection algorithm
表 1 惯性权重对PSO选星算法性能的影响
Table 1. Effect of inertia weight on PSO satellite selection algorithm performance
惯性权重
ω平均
GDOP最大
GDOP最小
GDOP平均选星耗时/s 0.4 2.320 4 2.364 5 2.251 0 1.517 0.6 2.314 5 2.419 6 2.251 0 1.566 0.8 2.318 5 2.358 5 2.251 0 1.546 0.9 2.288 0 2.419 6 2.251 0 1.548 1.0 2.345 7 2.370 7 2.251 0 1.527 1.1 2.299 8 2.481 1 2.251 0 1.626 1.2 2.327 3 2.540 2 2.251 0 1.538 1.3 2.343 4 2.370 7 2.251 0 1.561 1.4 2.352 9 2.460 5 2.251 0 1.544 1.6 2.342 5 2.426 9 2.251 0 1.539 
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表 2 加速系数对算法性能的影响
Table 2. Effect of acceleration factor on algorithm performance
加速系数 c1/c2 平均
GDOP最大
GDOP最小
GDOP平均选星耗时/s c1=1，c2=4 0.25 2.339 4 2.380 1 2.251 0 1.559 c1=1，c2=2 0.5 2.348 3 2.540 2 2.251 0 1.573 c1=1，c2=1 1 2.355 1 2.419 6 2.251 0 1.616 c1=1.5，c2=1.5 1 2.381 9 2.540 2 2.251 0 1.566 c1=2，c2=2 1 2.295 1 2.347 4 2.251 0 1.569 c1=0.5，c2=0.5 1 2.403 5 2.540 2 2.251 0 1.557 c1=0.25，c2=0.25 1 2.357 7 2.509 9 2.251 0 1.578 c1=4，c2=2 2 2.298 5 2.370 7 2.251 0 1.573 c1=2，c2=1 2 2.308 3 2.419 6 2.251 0 1.638 c1=1，c2=0.5 2 2.366 2 2.419 6 2.251 0 1.565 c1=3，c2=1 3 2.329 4 2.460 5 2.251 0 1.579 c1=4，c2=1 4 2.317 9 2.370 7 2.251 0 1.581
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表 3 种群规模对算法性能的影响
Table 3. Effect of population sizes on algorithm performance
种群规模M 平均
GDOP最大
GDOP最小
GDOP平均选星耗时/s 30 2.405 439 541 2.509 928 411 2.251 0 0.546 194 8 50 2.332 476 761 2.419 611 127 2.2510 0.828 243 7 70 2.289 530 344 2.364 511 595 2.251 0 1.127 988 2 90 2.308 514 516 2.358 491 188 2.251 0 1.441 279 7 100 2.292 758 802 2.419 611 127 2.251 0 1.586 975 4 110 2.317 243 548 2.419 611 127 2.251 0 1.793 920 8 120 2.326 449 813 2.540 188 469 2.251 0 1.924 731 8 150 2.312 394 223 2.370 668 208 2.251 0 2.491 832 2 180 2.283 993 701 2.334 593 796 2.251 0 2.775 929 5 200 2.306 857 579 2.370 668 208 2.251 0 3.123 896 5
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