|
| 1 | +(FPCore (dt r) |
| 2 | + :name "Kalman filter per K" |
| 3 | + :pre (and (> dt 0) (> r 0)) |
| 4 | + ; initializing matrices |
| 5 | + (let ([p00 25.0] |
| 6 | + [p01 0.0] |
| 7 | + [p02 0.0] |
| 8 | + [p10 0.0] |
| 9 | + [p11 10.0] |
| 10 | + [p12 0.0] |
| 11 | + [p20 0.0] |
| 12 | + [p21 0.0] |
| 13 | + [p22 1.0] |
| 14 | + |
| 15 | + [f00 1.0] |
| 16 | + [f01 dt] |
| 17 | + [f02 (* 0.5 (* dt dt))] |
| 18 | + [f10 0.0] |
| 19 | + [f11 1.0] |
| 20 | + [f12 dt] |
| 21 | + [f20 0.0] |
| 22 | + [f21 0.0] |
| 23 | + [f22 1.0] |
| 24 | + |
| 25 | + [q00 (* 0.25 (* dt (* dt (* dt dt))))] |
| 26 | + [q01 (* 0.5 (* dt (* dt dt)))] |
| 27 | + [q02 (* 0.5 (* dt dt))] |
| 28 | + [q10 (* 0.5 (* dt (* dt dt)))] |
| 29 | + [q11 (* dt dt)] |
| 30 | + [q12 dt] |
| 31 | + [q20 (* 0.5 (* dt dt))] |
| 32 | + [q21 dt] |
| 33 | + [q22 1]) |
| 34 | + ; axbT_33(P, F, P) |
| 35 | + (let ([p00* (+ (+ (* p00 f00) (* p01 f01)) (* p02 f02))] |
| 36 | + [p01* (+ (+ (* p00 f10) (* p01 f11)) (* p02 f12))] |
| 37 | + [p02* (+ (+ (* p00 f20) (* p01 f21)) (* p02 f22))] |
| 38 | + [p10* (+ (+ (* p10 f00) (* p11 f01)) (* p12 f02))] |
| 39 | + [p11* (+ (+ (* p10 f10) (* p11 f11)) (* p12 f12))] |
| 40 | + [p12* (+ (+ (* p10 f20) (* p11 f21)) (* p12 f22))] |
| 41 | + [p20* (+ (+ (* p20 f00) (* p21 f01)) (* p22 f02))] |
| 42 | + [p21* (+ (+ (* p20 f10) (* p21 f11)) (* p22 f12))] |
| 43 | + [p22* (+ (+ (* p20 f20) (* p21 f21)) (* p22 f22))]) |
| 44 | + ; axb_33(F, P, P) |
| 45 | + (let ([p00** (+ (+ (* f00 p00*) (* f01 p10*)) (* f02 p20*))] |
| 46 | + [p01** (+ (+ (* f00 p01*) (* f01 p11*)) (* f02 p21*))] |
| 47 | + [p02** (+ (+ (* f00 p02*) (* f01 p12*)) (* f02 p22*))] |
| 48 | + [p10** (+ (+ (* f10 p00*) (* f11 p10*)) (* f12 p20*))] |
| 49 | + [p11** (+ (+ (* f10 p01*) (* f11 p11*)) (* f12 p21*))] |
| 50 | + [p12** (+ (+ (* f10 p02*) (* f11 p12*)) (* f12 p22*))] |
| 51 | + [p20** (+ (+ (* f20 p00*) (* f21 p10*)) (* f22 p20*))] |
| 52 | + [p21** (+ (+ (* f20 p01*) (* f21 p11*)) (* f22 p21*))] |
| 53 | + [p22** (+ (+ (* f20 p02*) (* f21 p12*)) (* f22 p22*))]) |
| 54 | + ; a_add_b_33(P, Q, P) |
| 55 | + (let ([p00*** (+ p00** q00)] |
| 56 | + [p01*** (+ p01** q01)] |
| 57 | + [p02*** (+ p02** q02)] |
| 58 | + [p10*** (+ p10** q10)] |
| 59 | + [p11*** (+ p11** q11)] |
| 60 | + [p12*** (+ p12** q12)] |
| 61 | + [p20*** (+ p20** q20)] |
| 62 | + [p21*** (+ p21** q21)] |
| 63 | + [p22*** (+ p22** q22)]) |
| 64 | + ; update_K |
| 65 | + (let ([K0 (/ p00*** (+ p00*** r))] |
| 66 | + [K1 (/ p10*** (+ p00*** r))] |
| 67 | + [K2 (/ p20*** (+ p00*** r))]) |
| 68 | + K0)))))) |
| 69 | + |
| 70 | +(FPCore (x0 x1 x2 dt r sensor) |
| 71 | + :name "Kalman filter per x" |
| 72 | + :pre (and (> dt 0) (> r 0) (> sensor 0)) |
| 73 | + ; initializing matrices |
| 74 | + (let ([p00 25.0] |
| 75 | + [p01 0.0] |
| 76 | + [p02 0.0] |
| 77 | + [p10 0.0] |
| 78 | + [p11 10.0] |
| 79 | + [p12 0.0] |
| 80 | + [p20 0.0] |
| 81 | + [p21 0.0] |
| 82 | + [p22 1.0] |
| 83 | + |
| 84 | + [f00 1.0] |
| 85 | + [f01 dt] |
| 86 | + [f02 (* 0.5 (* dt dt))] |
| 87 | + [f10 0.0] |
| 88 | + [f11 1.0] |
| 89 | + [f12 dt] |
| 90 | + [f20 0.0] |
| 91 | + [f21 0.0] |
| 92 | + [f22 1.0] |
| 93 | + |
| 94 | + [q00 (* 0.25 (* dt (* dt (* dt dt))))] |
| 95 | + [q01 (* 0.5 (* dt (* dt dt)))] |
| 96 | + [q02 (* 0.5 (* dt dt))] |
| 97 | + [q10 (* 0.5 (* dt (* dt dt)))] |
| 98 | + [q11 (* dt dt)] |
| 99 | + [q12 dt] |
| 100 | + [q20 (* 0.5 (* dt dt))] |
| 101 | + [q21 dt] |
| 102 | + [q22 1]) |
| 103 | + ; axbT_33(P, F, P) |
| 104 | + (let ([p00* (+ (+ (* p00 f00) (* p01 f01)) (* p02 f02))] |
| 105 | + [p01* (+ (+ (* p00 f10) (* p01 f11)) (* p02 f12))] |
| 106 | + [p02* (+ (+ (* p00 f20) (* p01 f21)) (* p02 f22))] |
| 107 | + [p10* (+ (+ (* p10 f00) (* p11 f01)) (* p12 f02))] |
| 108 | + [p11* (+ (+ (* p10 f10) (* p11 f11)) (* p12 f12))] |
| 109 | + [p12* (+ (+ (* p10 f20) (* p11 f21)) (* p12 f22))] |
| 110 | + [p20* (+ (+ (* p20 f00) (* p21 f01)) (* p22 f02))] |
| 111 | + [p21* (+ (+ (* p20 f10) (* p21 f11)) (* p22 f12))] |
| 112 | + [p22* (+ (+ (* p20 f20) (* p21 f21)) (* p22 f22))]) |
| 113 | + ; axb_33(F, P, P) |
| 114 | + (let ([p00** (+ (+ (* f00 p00*) (* f01 p10*)) (* f02 p20*))] |
| 115 | + [p01** (+ (+ (* f00 p01*) (* f01 p11*)) (* f02 p21*))] |
| 116 | + [p02** (+ (+ (* f00 p02*) (* f01 p12*)) (* f02 p22*))] |
| 117 | + [p10** (+ (+ (* f10 p00*) (* f11 p10*)) (* f12 p20*))] |
| 118 | + [p11** (+ (+ (* f10 p01*) (* f11 p11*)) (* f12 p21*))] |
| 119 | + [p12** (+ (+ (* f10 p02*) (* f11 p12*)) (* f12 p22*))] |
| 120 | + [p20** (+ (+ (* f20 p00*) (* f21 p10*)) (* f22 p20*))] |
| 121 | + [p21** (+ (+ (* f20 p01*) (* f21 p11*)) (* f22 p21*))] |
| 122 | + [p22** (+ (+ (* f20 p02*) (* f21 p12*)) (* f22 p22*))]) |
| 123 | + ; a_add_b_33(P, Q, P) |
| 124 | + (let ([p00*** (+ p00** q00)] |
| 125 | + [p01*** (+ p01** q01)] |
| 126 | + [p02*** (+ p02** q02)] |
| 127 | + [p10*** (+ p10** q10)] |
| 128 | + [p11*** (+ p11** q11)] |
| 129 | + [p12*** (+ p12** q12)] |
| 130 | + [p20*** (+ p20** q20)] |
| 131 | + [p21*** (+ p21** q21)] |
| 132 | + [p22*** (+ p22** q22)]) |
| 133 | + ; update_K |
| 134 | + (let ([K0 (/ p00*** (+ p00*** r))] |
| 135 | + [K1 (/ p10*** (+ p00*** r))] |
| 136 | + [K2 (/ p20*** (+ p00*** r))]) |
| 137 | + ; predict_x |
| 138 | + (let ([x0* (+ x0 (+ x1 (* 0.5 (* dt (* dt x2)))))] |
| 139 | + [x1* (+ x1 x2)] |
| 140 | + [x2* x2]) |
| 141 | + (let ([y (- sensor x0*)]) |
| 142 | + ; update_x |
| 143 | + (let ([x0** (+ x0* (* K0 y))] |
| 144 | + [x1** (+ x1* (* K1 y))] |
| 145 | + [x2** (+ x2* (* K2 y))]) |
| 146 | + x0**))))))))) |
| 147 | + |
| 148 | +(FPCore (dt r) |
| 149 | + :name "Kalman filter per P" |
| 150 | + :pre (and (> dt 0) (> r 0)) |
| 151 | + ; initializing matrices |
| 152 | + (let ([p00 25.0] |
| 153 | + [p01 0.0] |
| 154 | + [p02 0.0] |
| 155 | + [p10 0.0] |
| 156 | + [p11 10.0] |
| 157 | + [p12 0.0] |
| 158 | + [p20 0.0] |
| 159 | + [p21 0.0] |
| 160 | + [p22 1.0] |
| 161 | + |
| 162 | + [f00 1.0] |
| 163 | + [f01 dt] |
| 164 | + [f02 (* 0.5 (* dt dt))] |
| 165 | + [f10 0.0] |
| 166 | + [f11 1.0] |
| 167 | + [f12 dt] |
| 168 | + [f20 0.0] |
| 169 | + [f21 0.0] |
| 170 | + [f22 1.0] |
| 171 | + |
| 172 | + [q00 (* 0.25 (* dt (* dt (* dt dt))))] |
| 173 | + [q01 (* 0.5 (* dt (* dt dt)))] |
| 174 | + [q02 (* 0.5 (* dt dt))] |
| 175 | + [q10 (* 0.5 (* dt (* dt dt)))] |
| 176 | + [q11 (* dt dt)] |
| 177 | + [q12 dt] |
| 178 | + [q20 (* 0.5 (* dt dt))] |
| 179 | + [q21 dt] |
| 180 | + [q22 1]) |
| 181 | + ; axbT_33(P, F, P) |
| 182 | + (let ([p00* (+ (+ (* p00 f00) (* p01 f01)) (* p02 f02))] |
| 183 | + [p01* (+ (+ (* p00 f10) (* p01 f11)) (* p02 f12))] |
| 184 | + [p02* (+ (+ (* p00 f20) (* p01 f21)) (* p02 f22))] |
| 185 | + [p10* (+ (+ (* p10 f00) (* p11 f01)) (* p12 f02))] |
| 186 | + [p11* (+ (+ (* p10 f10) (* p11 f11)) (* p12 f12))] |
| 187 | + [p12* (+ (+ (* p10 f20) (* p11 f21)) (* p12 f22))] |
| 188 | + [p20* (+ (+ (* p20 f00) (* p21 f01)) (* p22 f02))] |
| 189 | + [p21* (+ (+ (* p20 f10) (* p21 f11)) (* p22 f12))] |
| 190 | + [p22* (+ (+ (* p20 f20) (* p21 f21)) (* p22 f22))]) |
| 191 | + ; axb_33(F, P, P) |
| 192 | + (let ([p00** (+ (+ (* f00 p00*) (* f01 p10*)) (* f02 p20*))] |
| 193 | + [p01** (+ (+ (* f00 p01*) (* f01 p11*)) (* f02 p21*))] |
| 194 | + [p02** (+ (+ (* f00 p02*) (* f01 p12*)) (* f02 p22*))] |
| 195 | + [p10** (+ (+ (* f10 p00*) (* f11 p10*)) (* f12 p20*))] |
| 196 | + [p11** (+ (+ (* f10 p01*) (* f11 p11*)) (* f12 p21*))] |
| 197 | + [p12** (+ (+ (* f10 p02*) (* f11 p12*)) (* f12 p22*))] |
| 198 | + [p20** (+ (+ (* f20 p00*) (* f21 p10*)) (* f22 p20*))] |
| 199 | + [p21** (+ (+ (* f20 p01*) (* f21 p11*)) (* f22 p21*))] |
| 200 | + [p22** (+ (+ (* f20 p02*) (* f21 p12*)) (* f22 p22*))]) |
| 201 | + ; a_add_b_33(P, Q, P) |
| 202 | + (let ([p00*** (+ p00** q00)] |
| 203 | + [p01*** (+ p01** q01)] |
| 204 | + [p02*** (+ p02** q02)] |
| 205 | + [p10*** (+ p10** q10)] |
| 206 | + [p11*** (+ p11** q11)] |
| 207 | + [p12*** (+ p12** q12)] |
| 208 | + [p20*** (+ p20** q20)] |
| 209 | + [p21*** (+ p21** q21)] |
| 210 | + [p22*** (+ p22** q22)]) |
| 211 | + ; update_K |
| 212 | + (let ([K0 (/ p00*** (+ p00*** r))] |
| 213 | + [K1 (/ p10*** (+ p00*** r))] |
| 214 | + [K2 (/ p20*** (+ p00*** r))]) |
| 215 | + ; update_P |
| 216 | + (let ([eyekh00 (- 1 K0)] |
| 217 | + [eyekh01 0.0] |
| 218 | + [eyekh02 0.0] |
| 219 | + [eyekh10 (- K1)] |
| 220 | + [eyekh11 1.0] |
| 221 | + [eyekh12 0.0] |
| 222 | + [eyekh20 (- K2)] |
| 223 | + [eyekh21 0.0] |
| 224 | + [eyekh22 1.0]) |
| 225 | + ; axb_33(&eyekh, P, P) |
| 226 | + (let ([p00**** (+ (+ (* eyekh00 p00***) (* eyekh01 p10***)) (* eyekh02 p20***))] |
| 227 | + [p01**** (+ (+ (* eyekh00 p01***) (* eyekh01 p11***)) (* eyekh02 p21***))] |
| 228 | + [p02**** (+ (+ (* eyekh00 p02***) (* eyekh01 p12***)) (* eyekh02 p22***))] |
| 229 | + [p10**** (+ (+ (* eyekh10 p00***) (* eyekh11 p10***)) (* eyekh12 p20***))] |
| 230 | + [p11**** (+ (+ (* eyekh10 p01***) (* eyekh11 p11***)) (* eyekh12 p21***))] |
| 231 | + [p12**** (+ (+ (* eyekh10 p02***) (* eyekh11 p12***)) (* eyekh12 p22***))] |
| 232 | + [p20**** (+ (+ (* eyekh20 p00***) (* eyekh21 p10***)) (* eyekh22 p20***))] |
| 233 | + [p21**** (+ (+ (* eyekh20 p01***) (* eyekh21 p11***)) (* eyekh22 p21***))] |
| 234 | + [p22**** (+ (+ (* eyekh20 p02***) (* eyekh21 p12***)) (* eyekh22 p22***))]) |
| 235 | + p00****)))))))) |
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