Abstract: Objective Computers may encounter the problem of numerical instability and output a wrong bit errorrate(BER)when decoding navigation satellite convolutional codes with the maximum a posterioriprobability(MAP)algorithm.Subsequently,this will affect the validity and the accuracy of the posi-tioning results.To address this problem,first a detailed analysis was executed.Based on this analy-sis,an improved MAP algorithm normalized with the maximum state metric is proposed,thus thequestion of numerical instability can be solved while still maintaining the original algorithm’s optimalperformance.Simulations further validate the effectiveness of this algorithm’s improvement.