飞控之扩展卡尔曼滤波(附matlab和C代码)
2024-05-14 16:13:27
目录
原理讲解：
数据融合效果：
matlab代码：
飞控代码：
联系作者
原理讲解：
从四元数基础到扩展卡尔曼滤波
数据融合效果：
matlab代码：
角速度和加速度均为实测数据，其中角速度单位为“rad/s”，加速度为传感器原始数据在融合迭代过程中会进行归一化处理。
clear all;
close all
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3755.45 3762.39 3760.84 3767.19 3766.3 3771.47 3768.28 3768.3 3769.8 3763.52 3763.59 3767.28 3774.06 3768.97 3760.16 3762.67 3773.06 3775.03 3776.3 3781.64 3780.91 3774.17 3771.91 3768.09 3773.93 3776.3 3773.9 3768.41 3768.9 3768.92 3769.04 3762.06 3759.58 3754.58 3760.69 3762.01 3766.85 3761.7 3758.05 3766.56 3765.89 3759.85 3762.71 3764.67 3764.76 3764.15 3759.02 3766.6 3773.25 3766.18 3762.33 3764.84 3763.24 3768.99 3767.84 3763.99 3766.14 3771.77 3766.14 3776.14 3778.32 3768.79 3764.99 3769.17 3768.46 3767.86 3763.55 3771.11 3775.05 3771.89 3771.97 3770.76 3770.92 3768.58 3768.77 3774.38 3778.41 3778.72 3770.79 3776.52 3779.89 3775.59 3768.83 3771.8 3776.73 3779.3 3779.96 3789.62 3793.67 3788.85 3787.25 3781.14 3778.51 3772.16 3765.95 3770.87 3771.73 3768.17 3761.92 3767.05 3760.11 3764.4 3769.3 3780.03 3778.05 3776.22 3774.84 3772.33 3776 3774.22 3772.02 3772.93 3768.52 3775.19 3766.45 3768.56 3776.55 3778.42 3774.4 3780.72 3778.18 3783.33 3778.49 3772.55 3776.58 3768.76 3764.36 3765.06 3762.9 3759.31 3762.48 3766.82 3768.47 3769.06 3768.65 3767.21 3768.86 3763.61 3763.44 3768.91 3768.85 3765.29 3764.04 3765.42 3771.41 3772.96 3754.97 3760.29 3758.99 3769.04 3767.84 3767.33 3769.24 3774.77 3772.22 3771.51 3777.29 3767.65 3766.03 3772.27 3779.58 3771.48 3774.5 3779.14 3772.18 3777.74 3776.98 3772.68 3765.46 3765.08 3767.25 3770.43 3769.5 3771.55 3771.06 3767.14 3769.74 3768.66 3764.49 3757.98 3761.54 3772.5 3775.47 3772.39 3762.5 3764.7 3763.29 3765.27 3765.15 3770.43 3772.76 3774.61 3773.66 3771.49 3761.09 3743.78 3749.69 3766.6 3782.32 3781.59 3779.99 3774.92 3762.46 3757.51 3753.08 3758.34 3768.35 3772.53 3773.06 3772.57 3762.49 3760.43 3767.54 3770.75 3765.99 3765.67 3769.36 3765.47 3758.5 3754.28 3760.22 3771.63 3772.2 3769.68 3775.34 3773.09 3771.52 3771.68 3771.09 3774.04 3765.49 3758.36 3763.53 3760.7 3767.62 3772.38 3769.55 3767.91 3769.78 3773.79 3776.16 3767.51 3768.43 3779.18 3779.33 3773.7 3777.78 3779.35 3780.55 3776.57 3773.25 3771.64 3776.65 3771.88 3773.87 3779.26 3770.72 3769.34 3769.89 3761.84 3764.95 3763.41 3763.22 3769.73 3780.1 3782.68 3778.51 3771.36 3771.42 3767.16 3762.21 3766.24 3765.01 3772.13 3782.17 3779.58 3772.81 3769.84 3772.14 3765.52 3765.75 3774.77 3774.34 3770.93 3766.99 3769.04 3769.02 3767.78 3769.78 3773 3769.61 3768.39 3766.28 3772.01 3770.12 3770.68 3765.96 3768.64 3771.59 3770.7 3770.47 3773.05 3768.21 3769.7 3769.97 3770.27 3771.39 3775.93 3774.09 3764.47 3770.63 3763.13 3768.7 3774.44 3773.62 3779.42 3778.15 3772.39 3777.54 3770.67 3760.81 3760.18 3764.76 3773.78 3769.19 3759.12 3760.21 3758.21 3759.47 3763.05 3775.43 3778.56 3781.33 3773.13 3778.24 3773.16 3769.52 3777.61 3771.92 3777.5 3765.14 3761.53 3757.49 3768.74 3766.56 3758.49 3767.92 3772.84 3767.65 3758.31 3765.1 3766.74 3769.53 3771.88 3770.24 3767.6 3779.44 3776.94 3778.56 3780.68 3778.53 3773.13 3778.18 3774.2 3766.92 3768.23 3764.19 3760.9 3756.81 3759.43 3761.15 3764.49 3769.73 3771.52 3769.94 3774.68 3770.45 3770.17 3771.19 3773.31 3771.25 3777.39 3777.85 3776.79 3784.53 3788.3 3777.71 3776.96 3775.22 3767.89 3774.69 3784.41 3785.86 3790.85 3781.09 3768.67 3769.85 3767.13 3770.57 3770.08 3779.66 3776.44 3770.71 3762.63 3759.06 3763.03 3778.29 3773.22 3759.5 3767.55 3765.87 3763.93 3766.24 3771.88 3772.4 3778.05 3779.95 3769.6 3767.73 3770.99 3769.96 3775.24 3776.46 3766.5 3766.1 3769.09 3769.47 3765.43 3765.43 3768.84 3772.74 3770.23 3743.87 3731.32 3559.37 3528.29 3552.15 3706.8 3866.02 3937.29 3820.35 3649.96 3617.82 3780.78 3932.34 3957.53 3881.21 3792.06 3777.32 3820.35 3870.31 3870.24 3826.98 3774.2 3744.67 3740.79 3737.28 3724.9 3720.5 3727.13 3746.99 3751.51 3747.02 3751.82 3753.68 3761.02 3775.23 3779.65 3773.43 3775.65 3776.85 3767.58 3783.59 3794.17 3807.56 3783.5 3779.49 3766.86 3768.59 3763.66 3760.85 3781.59 3789.96 3790.86 3788.29 3773.87 3765.85 3774.92 3805.1 3823.71 3809.47 3784.21 3780.08 3780.24 3780.12 3780.67 3789.82 3796.98 3783.35 3776.78 3773.66 3769.35 3783.14 3805.63 3823.97 3823.82 3836.22 3849.93 3841.83 3833.68 3819.3 3811.37 3792.42 3777.62 3767.67 3746.13 3746.41 3737.57 3756.54 3757.39 3774.36 3781.43 3796.99 3818.63 3826.05 3825.71 3841.67 3848.47 3861.96 3868.13 3868.16 3872.13 3892.78 3896 3890.05 3890.54 3897.33 3894.56 3901.33 3907.71 3903.06 3897.27 3894.82 3872.37 3858.45 3844.07 3846.66 3836.11 3862.52 3849.79 3832.8 3812.16 3801.45 3753.78 3736.73 3753.79 3723.59 3733.66 3705.07 3669.16 3644.44 3633.25 3636.73 3637.1 3640.37 3617.54 3642.7 3629.2 3636.51 3638.61 3629.78 3631.57 3641.3 3677.72 3649.32 3649.49 3666.51 3670.65 3681.86 3701.15 3684.56 3704.56 3692.7 3669.17 3649.12 3669.01 3639.75 3626.25 3633.14 3610.63 3581.04 3584.75 3542.97 3500.14 3453.09 3441.78 3437.81 3437.41 3405.94 3360.96 3281.7 3270.91 3252.21 3248.72 3194.49 3168.46 3128.92 3107.69 3107.59 3070.98 3043.26 3073.68 3051.17 3026.96 3047.45 3021.22 3046.81 3057.53 3068.47 3054.7 3039.98 3033.29 3057.51 3039.12 3008.65 3015.28 3020.37 2974.56 2998.08 2968.1 2930.39 2875.62 2842.88 2804.41 2800.57 2763.73 2752.42 2723.84 2723.93 2687.65 2645.61 2638.86 2619.47 2587 2583.12 2557.62 2520.33 2523.59 2499.17 2472.89 2452.1 2460.64 2449.24 2457.78 2459.63 2467.64 2480.54 2479.32 2490.74 2511.62 2515.55 2519.68 2532.93 2539.36 2541.7 2537.11 2538.16 2539.79 2536.6 2528.23 2503.64 2494.06 2487.93 2485.88 2479.91 2461.93 2444.46 2433.94 2424.97 2401.15 2390.74 2381.1 2366.09 2342.2 2333.4 2326.51 2321.69 2329.9 2343.57 2365.35 2399.86 2426.42 2453.71 2470.29 2473.09 2478.02 2473.87 2467.11 2447.2 2422.3 2402.43 2380.95 2367.24 2359.56 2357.88 2372.28 2375.09 2382.57 2398.79 2402.35 2419.01 2433.98 2450.49 2466.99 2480.47 2487.68 2481.67 2476.95 2468.95 2463.73 2465.48 2477.75 2489.59 2513.01 2540.44 2561.22 2553.47 2546.56 2536.38 2527.13 2520.37 2522.82 2534.28 2507.51 2464.7 2450.55 2436.66 2421.75 2407.7 2414.96 2426.01 2437.21 2445.02 2452.32 2465.36 2474.77 2472.83 2460.38 2444.23 2433.26 2422.73 2413.13 2409.33 2408.27 2420.13 2430.28 2462.2 2513.12 2576.39 2629.87 2662.99 2701.36 2718.89 2734.71 2730.66 2736.39 2733.7 2727.52 2731.94 2746.99 2761.71 2770.82 2791.65 2809.81 2821.34 2838.22 2844.03 2849.89 2844.78 2836.55 2815.19 2800.54 2790.33 2790.04 2784.57 2784.95 2799.87 2798.81 2817.84 2829.17 2835.52 2849.67 2872.09 2877.15 2894.88 2903.08 2902.2 2897.24 2896.26 2886.12 2889.77 2887.23 2926.6 2946.58 2990.44 3004.94 3017.29 3039.47 3056.29 3067.5 3101.9 3129.35 3180.64 3225.18 3261.47 3294.37 3305.71 3325.39 3347.08 3379.8 3408.72 3443.25 3451.12 3473.43 3495.41 3496.87 3496.51 3491.49 3488.67 3474.28 3475.14 3465.46 3454.76 3477.77 3475.53 3488.41 3500.5 3509.97 3524.6 3523.92 3506.73 3504.39 3512.63 3534.6 3551.97 3548.59 3573.19 3583.92 3589.21 3589.67 3586.1 3574.58 3555.89 3549.98 3553.29 3542.67 3542.97 3560.34 3590.31 3608.31 3636.38 3647 3658.66 3668.29 3693.9 3718.73 3756.68 3761.05 3786.29 3799.33 3774.77 3752.54 3758.78 3745.02 3722.72 3694.76 3707.14 3709.26 3723.08 3753.02 3885.47 4111.63 4523.21 4733.72 4539.83 4413.23 4299.15 4133.12 3996.21 3888.08 3839.52 3845.96 3893.2 3878 3849.23 3813.67 3760.87 3732.2 3737.7 3772.93 3788.76 3809.98 3800.6 3780.38 3766.15 3762.16 3784.35 3804.11 3820.54 3812.38 3784.43 3750.69 3734.01 3726.38 3721.18 3733.48 3747.11 3760.38 3751.58 3729.01 3719.57 3717.73 3721.27 3732.21 3746.35 3751.18 3746.66 3741.13 3742.68 3757.19 3770.49 3766.93 3775.78 3784.18 3777.73 3768.2 3766.54 3773.8 3774.18 3775.33 3779.8 3774.92 3779.36 3785.83 3788.21 3784.78 3784.97 3789.85 3780.86 3776.68 3775.98 3769.37 3765.18 3756.07 3758.41 3750.79 3743.14 3748.2 3761.44 3764.43 3764.28 3763.27 3768.2 3763.35 3758.67 3762.45 3760.23 3761.29 3764.03 3771.44 3780.71 3774 3768.27 3763.43 3751.97 3756.17 3758.91 3765.13 3757.59 3757.08 3752.48 3747.15 3758.05 3759.01 3779.08 3786.61 3783.45 3782.87 3779.36 3776.93 3777.48 3774.11 3781.8 3782.45 3774.4 3769.95 3768.17 3771.69 3771.47 3767.07 3758.09 3758.62 3759.27 3755.2 3760.36 3771.5 3770.04 3769.17 3770.36 3769.64 3769.95 3769.62 3770.91 3780.2 3776.64 3766.73 3776.22 3766.4 3772.88 3776.19 3774.4 3774.28 3776.57 3771.49 3771.55 3772.5 3766.35 3761.03 3762.94 3765.33 3766.86 3773.22 3768.2 3767.47 3760.04 3763.66 3759.34 3762.83 3764.34 3767.73 3771.93 3766.84 3762.68 3773.66 3779.24 3778.04 3776.39 3776.4 3781.88 3780.64 3776.1 3774.88 3773.7 3770.52 3767.67 3771.84 3765.8 3758.18 3757 3753.42 3749.13 3756.33 3755.53 3752.48 3744.12 3745.71 3759.06 3768.7 3770.33 3762.97 3757.44 3757.03 3755.92 3763.19 3764.87 3766.79 3767.61 3770.98 3780.38 3782.18 3790.24 3788.76 3781.73 3773.17 3771.8 3772.25 3775.99 3777.84 3767.07 3775.01 3779.11 3774.31 3770.23 3768.67 3769.94 3763.61 3763.44 3763.09 3760.33 3753.84 3753.89 3747.48 3746.8 3754.24 3764.17 3770.23 3762.86 3760.72 3765.08 3762.03 3769.38 3761.87 3761.38 3769.79 3774.1 3771.18 3770.46 3771.73 3774.37 3781.92 3779.82 3784.34 3781.21 3771.06 3771.9 3775.49 3775.89 3779.91 3777.84 3773.83 3781.51 3776.45 3770.14 3768.15 3767.38 3770.02 3771.25 3769.47 3774.07 3776.97 3782.75 3767.78 3760.14 3755.79 3757.9 3759.11 3771.45 3774.12 3756.11 3749.84 3746.68 3750.82 3764.96 3768.07 3763.18 3764.8 3761.52 3757.68 3755.17 3757.57 3758.51 3774.32 3771.44 3769.97 3766.58 3783.58 3783.3 3773.35 3765.63 3759.31 3762.75 3762.95 3763.81 3772.64 3776.32 3786.19 3785.36 3777.75 3768.48 3762.94 3771.45 3771.06 3770.12 3773.89 3774.2 3783 3788.19 3787.3 3793.37 3797.97 3788.68 3772.57 3773.66 3775.71 3783.52 3801.92 3819.68 3826.54 3813.62 3803.33 3808.33 3795.05 3794.52 3796.83 3797.69 3796.49 3828.74 3825.23 3807.35 3804.15 3802.62 3808.76 3821.38 3815.3 3807.12 3801.92 3803.48 3795.71 3793.07 3794.43 3785.3 3788.77 3803.93 3840.32 3888.63 3927.07 3958.19 3960.26 3939.35 3926.31 3901.72 3881.65 3815.07 3767.75 3775.77 3792.48 3797.57 3841.3 3892.14 3911.51 3922.56 3901.47 3891.99 3849.33 3846.57 3794.64 3754.44 3716.82 3685.39 3670.23 3664 3703.87 3748.85 3813.05 3908.17 3984.33 4039.62 4083.93 4062.08 4026.4 3976.73 3916.74 3877.7 3852.87 3820.81 3808.04 3790.38 3773.32 3786.79 3806.59 3800.61 3758.68 3681.68 3653.7 3657.52 3657.27 3680.27 3721.36 3716.13 3733.58 3725.42 3700 3703.72 3712.71 3726.12 3733.59 3732.71 3682.9 3591.28 3535.74 3514.05 3459.86 3383.63 3306.13 3275.07 3281.26 3291.26 3289.17 3296.5 3340.37 3393.06 3393.19 3385.24 3390.72 3390.02 3442.07 3491.7 3520.39 3477.15 3453.24 3441.1 3391.01 3370.76 3338.59 3302.22 3286.9 3260.35 3279.48 3247.47 3235.65 3174.49 3128.5 3073.97 3023.82 2976.62 2912.76 2865.36 2836.6 2794.86 2762.49 2758.74 2750.59 2754.11 2744.87 2774.74 2815.46 2868.51 2875.84 2864.97 2829.42 2780.01 2709.46 2685.36 2670.01 2675.63 2669.33 2680.56 2657.28 2615.76 2555.58 2505.23 2458.13 2448.25 2436.52 2449.06 2444.44 2446.89 2430.37 2411.54 2386 2358.67 2342.54 2374.08 2404.24 2460.41 2507.29 2533.71 2540.22 2521.73 2504.92 2487.68 2459.46 2446.01 2431.33 2433.87 2455.56 2445.31 2428.11 2412.1 2395.91 2379.92 2384.99 2387.6 2400.04 2406.06 2427.43 2441.01 2444.28 2457.14 2466.84 2453.99 2437.95 2435.71 2440.13 2440.29 2429.78 2397.92 2364.94 2330.92 2307.52 2295.05 2284.38 2269.8 2257.78 2257.53 2264.44 2264.92 2275.82 2276.18 2285.89 2289.73 2301.75 2316.37 2328.46 2344.39 2346.77 2360.03 2359.41 2361.61 2373.12 2398.92 2416.53 2418.6 2410.41 2401.68 2408.53 2442.89 2474.35 2488.6 2491.98 2473.53 2444.05 2414.87 2376.85 2344.71 2309.95 2276.65 2261.3 2244.75 2221.98 2196.98 2174.18 2174.98 2176.65 2183.2 2195.35 2253.01 2312.02 2362.22 2407.48 2456.22 2467.68 2463.34 2474.8 2465.13 2455.17 2435.31 2448.88 2440.88 2444.05 2458.91 2451.1 2467.77 2484.13 2513.03 2510.52 2502.5 2520.54 2514.43 2519.11 2523.33 2531.88 2544.55 2584.82 2608.04 2609.88 2613.25 2628.78 2640.25 2679.09 2743.72 2789.78 2811.41 2860.13 2899.73 2898.14 2938.13 2936.24 2871.02
];%最终四元数的融合结果
Q_buf=zeros(4,length(ax));%中间变量
dt=0.0025;%2.5ms
F=zeros(4,4);
H=zeros(3,4);
q=[0;0;0;1];
q_p=[0;0;0;1];
Z_p=[0;0;0];
Z=[0;0;0];
P=zeros(4,4);
Qs=0.0000001;
Q=[Qs ,0 ,0 ,0 ;0 ,Qs ,0 ,0 ;0 ,0 ,Qs ,0 ;0 ,0 ,0 ,Qs ];
I=[1 ,0 ,0 ,0 ;0 ,1 ,0 ,0 ;0 ,0 ,1 ,0 ;0 ,0 ,0 ,1 ];
Rs_a=1000;
R=[Rs_a ,0 ,0 ;0 ,Rs_a ,0 ;0 ,0 ,Rs_a ];%扩展卡尔曼数据融合
for i=(1:length(ax))%四元数更新雅克比矩阵及其转置矩阵计算F(1,1)= 1 ;F(1,2)=-gx(i)*dt*0.5;F(1,3)=-gy(i)*dt*0.5;F(1,4)=-gz(i)*dt*0.5;%求FF(2,1)=gx(i)*dt*0.5;F(2,2)= 1 ;F(2,3)= gz(i)*dt*0.5;F(2,4)=-gy(i)*dt*0.5;F(3,1)=gy(i)*dt*0.5;F(3,2)=-gz(i)*dt*0.5;F(3,3)= 1 ;F(3,4)= gx(i)*dt*0.5;F(4,1)=gz(i)*dt*0.5;F(4,2)= gy(i)*dt*0.5;F(4,3)=-gx(i)*dt*0.5;F(4,4)= 1 ;F_t=F';%求F的转置F_t%带误差的四元数更新q_p=F*q;%预测q_p%带误差的四元数单位化norm=sqrt(q_p(1)*q_p(1)+q_p(2)*q_p(2)+q_p(3)*q_p(3)+q_p(4)*q_p(4));q_p=q_p/norm;%加速度向量向量预测Z_p(1)=2*(q_p(2)*q_p(4)-q_p(1)*q_p(3)); Z_p(2)=2*(q_p(1)*q_p(2)+q_p(3)*q_p(4)); Z_p(3)=q_p(1)*q_p(1)-q_p(2)*q_p(2)-q_p(3)*q_p(3)+q_p(4)*q_p(4);%预测量单位化norm=sqrt(Z_p(1)*Z_p(1)+Z_p(2)*Z_p(2)+Z_p(3)*Z_p(3));Z_p=Z_p/norm;%预测量雅克比矩阵及其转置矩阵计算H(1,1)=-2*q_p(3); H(1,2)= 2*q_p(4); H(1,3)=-2*q_p(1); H(1,4)= 2*q_p(2);%求HH(2,1)= 2*q_p(2); H(2,2)= 2*q_p(1); H(2,3)= 2*q_p(4); H(2,4)= 2*q_p(3);H(3,1)= 2*q_p(1); H(3,2)=-2*q_p(2); H(3,3)=-2*q_p(3); H(3,4)= 2*q_p(4);H_t=H';%求H的转置H_t%加速度观测量单位化norm=sqrt(ax(i)*ax(i)+ay(i)*ay(i)+az(i)*az(i));Z(1)=ax(i)/norm;Z(2)=ay(i)/norm;Z(3)=az(i)/norm;%协方差矩阵预测P_temp1=F*P;P_temp2=P_temp1*F_t;P_p=P_temp2+Q; %计算卡尔曼增益矩阵K_temp1=P_p*H_t; %求KK_temp2=H*P_p;K_temp3=K_temp2*H_t;K_temp3=K_temp3+R;K_temp3=inv(K_temp3);K=K_temp1*K_temp3;%更新协方差矩阵P_temp1=K*H; P_temp2=I-P_temp1;P=P_temp2*P_p;%四元数最优估计Z_e=Z-Z_p; %观测量作差q_e=K*Z_e; %计算误差q=q_p+q_e; %最优估计%最优四元数单位化norm=sqrt(q(1)*q(1)+q(2)*q(2)+q(3)*q(3)+q(4)*q(4));q=q/norm;%结果保存Q_buf(:,i)=q(:);pitch(i)=57.3*sin(2*(q(3)*q(4)+q(1)*q(2)));roll(i) =57.3*tan(2*(q(1)*q(3)-q(2)*q(4))/(q(1)*q(1)-q(2)*q(2)-q(3)*q(3)+q(4)*q(4)));yaw(i) =57.3*tan(2*(q(2)*q(3)+q(1)*q(4))/(q(1)*q(1)+q(2)*q(2)-q(3)*q(3)-q(4)*q(4)));
end%四元数绘制
figure();
plot(Q_buf(1,:));hold on;
plot(Q_buf(2,:));hold on;
plot(Q_buf(3,:));hold on;
plot(Q_buf(4,:));
title('四元数');%欧拉角绘制
figure();
plot(pitch);hold on;
plot(roll);hold on;
plot(yaw);hold on;
title('欧拉角');飞控代码：
这里给出了Freertos系统中姿态解算任务代码，只需提供gx_org，gy_org，gz_org，ax_org，ay_org，az_org传感器数据即可（其中角速度单位为“rad/s”，加速度为传感器原始数据在融合迭代过程中会进行归一化处理），飞控融合效果如下。
//采样周期
static float32_t dt=0.0025;//2.5ms//欧拉角
float pitch, roll, yaw;//过程协方差矩阵
#define Qs 0.0000001
static arm_matrix_instance_f32 Q_matrix;
static float32_t Q[16]={Qs ,0 ,0 ,0 ,0 ,Qs ,0 ,0 ,0 ,0 ,Qs ,0 ,0 ,0 ,0 ,Qs };//观测协方差矩阵
#define Rs_a 1000
static arm_matrix_instance_f32 R_matrix;
static float32_t R[9]= {Rs_a ,0 ,0 ,0 ,Rs_a ,0 ,0 ,0 ,Rs_a };//四阶单位矩阵
static arm_matrix_instance_f32 I_matrix;
static float32_t I[16]={1 ,0 ,0 ,0 ,0 ,1 ,0 ,0 ,0 ,0 ,1 ,0 ,0 ,0 ,0 ,1 };//四元数
static float32_t q[4]={1,0,0,0},q_p[4]={1,0,0,0},q_e[4]={0,0,0,0};
static arm_matrix_instance_f32 q_matrix ,q_p_matrix ,q_e_matrix;//状态方程雅克比矩阵及其转置
static float32_t F[16], F_t[16];
static arm_matrix_instance_f32 F_matrix,F_t_matrix;//观测值相关向量
static float32_t Z[3], Z_p[3], Z_e[3];
static arm_matrix_instance_f32 Z_matrix,Z_p_matrix,Z_e_matrix;//观测方程雅克比矩阵及其转置
static float32_t H[12], H_t[12];
static arm_matrix_instance_f32 H_matrix,H_t_matrix;//状态协方差相关矩阵
static float32_t P[16], P_p[16], P_temp1[16], P_temp2[16];
static arm_matrix_instance_f32 P_matrix,P_p_matrix,P_temp1_matrix,P_temp2_matrix;//扩展卡尔曼增益相关矩阵
static float32_t K[12] ,K_temp1[12] ,K_temp2[12] ,K_temp3[9];
static arm_matrix_instance_f32 K_matrix,K_temp1_matrix,K_temp2_matrix,K_temp3_matrix;//IMU任务
void imu_task(void * pvParameters)
{float32_t norm;float ax,ay,az,gx,gy,gz;float gx_offset=0,gy_offset=0,gz_offset=0;/*imu初始化*/{//过程协方差矩阵Q_matrix.numRows=4;Q_matrix.numCols=4;Q_matrix.pData =Q;//观测协方差矩阵 R_matrix.numRows=3;R_matrix.numCols=3;R_matrix.pData =R;//四阶单位矩阵I_matrix.numRows=4;I_matrix.numCols=4;I_matrix.pData =I;//四元数状态向量及其预测向量q_matrix.numRows=4; q_p_matrix.numRows=4; q_e_matrix.numRows=4;q_matrix.numCols=1; q_p_matrix.numCols=1; q_e_matrix.numCols=1;q_matrix.pData =q; q_p_matrix.pData =q_p; q_e_matrix.pData =q_e;//状态方程雅克比矩阵及其转置F_matrix.numRows=4; F_t_matrix.numRows=4;F_matrix.numCols=4; F_t_matrix.numCols=4;F_matrix.pData =F; F_t_matrix.pData =F_t;//重力观测向量及观测量的预测向量Z_matrix.numRows=3; Z_p_matrix.numRows=3; Z_e_matrix.numRows=3;Z_matrix.numCols=1; Z_p_matrix.numCols=1; Z_e_matrix.numCols=1;Z_matrix.pData =Z; Z_p_matrix.pData =Z_p; Z_e_matrix.pData =Z_e;//观测方程雅克比矩阵及其转置H_matrix.numRows=3; H_t_matrix.numRows=4;H_matrix.numCols=4; H_t_matrix.numCols=3;H_matrix.pData =H; H_t_matrix.pData =H_t;//系统协方差矩阵及系统协方差预测矩阵P_matrix.numRows=4; P_p_matrix.numRows=4; P_temp1_matrix.numRows=4; P_temp2_matrix.numRows=4;P_matrix.numCols=4; P_p_matrix.numCols=4; P_temp1_matrix.numCols=4; P_temp2_matrix.numCols=4;P_matrix.pData =P; P_p_matrix.pData =P_p; P_temp1_matrix.pData =P_temp1; P_temp2_matrix.pData =P_temp2;//扩展卡尔曼增益 K_matrix.numRows=4; K_temp1_matrix.numRows=4; K_temp2_matrix.numRows=3; K_temp3_matrix.numRows=3; K_matrix.numCols=3; K_temp1_matrix.numCols=3; K_temp2_matrix.numCols=4; K_temp3_matrix.numCols=3; K_matrix.pData =K; K_temp1_matrix.pData =K_temp1;K_temp2_matrix.pData =K_temp2; K_temp3_matrix.pData =K_temp3;//角速度零偏读取for(int i=0;i<4000;i++){gx_offset+=gx_org;gy_offset+=gy_org;gz_offset+=gz_org;vTaskDelay(configTICK_RATE_HZ/400);}gx_offset/=4000.0f;gy_offset/=4000.0f;gz_offset/=4000.0f;//加速度读取及单位化arm_sqrt_f32 (ax_org*ax_org+ay_org*ay_org+az_org*az_org,&norm);//加速度读取及单位化Z[0]=ax_org/norm;Z[1]=ay_org/norm;Z[2]=az_org/norm;//初始俯仰翻滚角度计算pitch=asinf(Z[1]);roll=(Z[2]>0)?atanf(-Z[0]/Z[2]):atanf(-Z[0]/Z[2])+3.14159f;yaw =0;//初始四元数计算 q[0]=cos(pitch/2)*cos(roll/2)*cos(yaw/2) - sin(pitch/2)*sin(roll/2)*sin(yaw/2);q[1]=cos(roll/2)*cos(yaw/2)*sin(pitch/2) + cos(pitch/2)*sin(roll/2)*sin(yaw/2);q[2]=cos(pitch/2)*cos(yaw/2)*sin(roll/2) - cos(roll/2)*sin(pitch/2)*sin(yaw/2);q[3]=cos(pitch/2)*cos(roll/2)*sin(yaw/2) + cos(yaw/2)*sin(pitch/2)*sin(roll/2);}/*imu更新(耗时140us)*/while(1){ //读取传感器数据gx=gx_org-gx_offset;gy=gy_org-gy_offset;gz=gz_org-gz_offset;ax=ax_org;ay=ay_org;az=az_org;//四元数更新雅克比矩阵及其转置矩阵计算F[0] = 1 ;F[1] =-gx*dt*0.5f;F[2] =-gy*dt*0.5f;F[3] =-gz*dt*0.5f;//求FF[4] =gx*dt*0.5f;F[5] = 1 ;F[6] = gz*dt*0.5f;F[7] =-gy*dt*0.5f;F[8] =gy*dt*0.5f;F[9] =-gz*dt*0.5f;F[10]= 1 ;F[11]= gx*dt*0.5f;F[12]=gz*dt*0.5f;F[13]= gy*dt*0.5f;F[14]=-gx*dt*0.5f;F[15]= 1 ;arm_mat_trans_f32(&F_matrix,&F_t_matrix);//求F的转置F_t//带误差的四元数更新arm_mat_mult_f32(&F_matrix,&q_matrix,&q_p_matrix);//预测q_p//带误差的四元数单位化arm_sqrt_f32 (q_p[0]*q_p[0]+q_p[1]*q_p[1]+q_p[2]*q_p[2]+q_p[3]*q_p[3],&norm);q_p[0]/=norm;q_p[1]/=norm;q_p[2]/=norm;q_p[3]/=norm;//加速度向量向量预测Z_p[0]=2*(q_p[1]*q_p[3] -q_p[0]*q_p[2]); //重力加速度预测Z_p[1]=2*(q_p[0]*q_p[1] +q_p[2]*q_p[3]); Z_p[2]=q_p[0]*q_p[0] - q_p[1]*q_p[1] - q_p[2]*q_p[2] + q_p[3]*q_p[3];//预测量单位化arm_sqrt_f32 (Z_p[0]*Z_p[0]+Z_p[1]*Z_p[1]+Z_p[2]*Z_p[2],&norm); //单位化Z_p[0]/=norm; Z_p[1]/=norm; Z_p[2]/=norm; //预测量雅克比矩阵及其转置矩阵计算H[0 ]=-2*q_p[2]; H[ 1]= 2*q_p[3]; H[ 2]=-2*q_p[0]; H[ 3]= 2*q_p[1];//求HH[4 ]= 2*q_p[1]; H[ 5]= 2*q_p[0]; H[ 6]= 2*q_p[3]; H[ 7]= 2*q_p[2];H[8 ]= 2*q_p[0]; H[ 9]=-2*q_p[1]; H[10]=-2*q_p[2]; H[11]= 2*q_p[3];arm_mat_trans_f32(&H_matrix,&H_t_matrix);//求H的转置H_t//加速度观测量单位化arm_sqrt_f32 (ax*ax+ay*ay+az*az,&norm);Z[0]=ax/norm;Z[1]=ay/norm;Z[2]=az/norm;//协方差矩阵预测arm_mat_mult_f32(&F_matrix,&P_matrix,&P_temp1_matrix); arm_mat_mult_f32(&P_temp1_matrix,&F_t_matrix,&P_temp2_matrix);arm_mat_add_f32(&P_temp2_matrix,&Q_matrix,&P_p_matrix);//计算卡尔曼增益矩阵arm_mat_mult_f32(&P_p_matrix,&H_t_matrix,&K_temp1_matrix); //求Karm_mat_mult_f32(&H_matrix,&P_p_matrix,&K_temp2_matrix);arm_mat_mult_f32(&K_temp2_matrix,&H_t_matrix,&K_temp3_matrix);arm_mat_add_f32(&K_temp3_matrix,&R_matrix,&K_temp3_matrix);arm_mat_inverse_f32(&K_temp3_matrix,&K_temp3_matrix);arm_mat_mult_f32(&K_temp1_matrix,&K_temp3_matrix,&K_matrix);//更新协方差矩阵arm_mat_mult_f32(&K_matrix,&H_matrix,&P_temp1_matrix); arm_mat_sub_f32(&I_matrix,&P_temp1_matrix,&P_temp2_matrix);arm_mat_mult_f32(&P_temp2_matrix,&P_p_matrix,&P_matrix);//四元数最优估计arm_mat_sub_f32(&Z_matrix,&Z_p_matrix,&Z_e_matrix); //观测量作差arm_mat_mult_f32(&K_matrix,&Z_e_matrix,&q_e_matrix);//计算误差arm_mat_add_f32(&q_p_matrix,&q_e_matrix,&q_matrix); //最优估计//单位化四元数arm_sqrt_f32 (q[0]*q[0]+q[1]*q[1]+q[2]*q[2]+q[3]*q[3],&norm);q[0]/=norm;q[1]/=norm;q[2]/=norm;q[3]/=norm;//四元数转欧拉角pitch=57.3f*asinf (2*(q[2]*q[3]+q[0]*q[1]));roll =57.3f*atan2f (2*(q[0]*q[2]-q[1]*q[3]),q[0]*q[0]-q[1]*q[1]-q[2]*q[2]+q[3]*q[3]);yaw +=57.3f*dt*(gz_org-gz_offset);//释放CPU使用权vTaskDelay(configTICK_RATE_HZ/400);}
}联系作者：
微xin:cxw3020302521 可获取飞控源码、硬件等资料。
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