altos: Correct model error covariance matrix

Finally found a couple of decent references on how to set the model
(process) error covariance matrix. The current process matrix turns
out to be correct for a continuous kalman filter (which isn't
realizable, of course). For a discrete filter, the error in modeled
acceleration (we model it as a constant) needs to be propogated to the
speed and position portions of the matrix.

The correct matrix is seen in this paper:

On Reduced-Order Kalman Filters For GPS Position Filtering
	J. Shima
	6/2/2001

This references an older paper which is supposed to describe the
derivation of the matrix:

Singer, R.A., “Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets,”
IEEE Transactions of Aerospace and Electronic Systems, AES-5, July 1970, pp. 473-483.

This change has a minor effect on the computed correction
coefficients; it should respond more reasonably to acceleration
changes now.

Signed-off-by: Keith Packard <keithp@keithp.com>

diff --git a/src/kalman/kalman.5c b/src/kalman/kalman.5c
index cfb7abea4ff1435fe8c666433f9455081f014735..46fa8e1fdefecbcd9dad65a9e1208c4bb2df306a 100755 (executable)
--- a/src/kalman/kalman.5c
+++ b/src/kalman/kalman.5c
@@ -55,6 +55,12 @@ real default_σ_m = 5;
 real default_σ_h = 20;
 real default_σ_a = 2;
 
+real[3,3] model_error(t, Φ) = multiply_mat_val ((real[3,3]) {
+               { t**5 / 20, t**4 / 8, t**3 / 6 },
+               { t**4 /  8, t**3 / 3, t**2 / 2 },
+               { t**3 /  6, t**2 / 2, t }
+       }, Φ);
+
 parameters_t param_both(real t, real σ_m, real σ_h, real σ_a) {
        if (σ_m == 0)
                σ_m = default_σ_m;
@@ -87,11 +93,7 @@ parameters_t param_both(real t, real σ_m, real σ_h, real σ_a) {
  * Model error covariance. The only inaccuracy in the
  * model is the assumption that acceleration is constant
  */
-               .q = (real[3,3]) {
-                       { 0, 0, 0 },
-                       { 0, 0, 0 },
-                       {.0, 0, σ_m**2 },
-               },
+               .q = model_error (t, σ_m**2),
 /*
  * Measurement error covariance
  * Our sensors are independent, so
@@ -140,11 +142,7 @@ parameters_t param_baro(real t, real σ_m, real σ_h) {
  * Model error covariance. The only inaccuracy in the
  * model is the assumption that acceleration is constant
  */
-               .q = (real[3,3]) {
-                       { 0, 0, 0 },
-                       { 0, 0, 0 },
-                       {.0, 0, σ_m**2 },
-               },
+               .q = model_error (t, σ_m**2),
 /*
  * Measurement error covariance
  * Our sensors are independent, so
@@ -191,11 +189,7 @@ parameters_t param_accel(real t, real σ_m, real σ_a) {
  * Model error covariance. The only inaccuracy in the
  * model is the assumption that acceleration is constant
  */
-               .q = (real[3,3]) {
-                       { 0, 0, 0 },
-                       { 0, 0, 0 },
-                       {.0, 0, σ_m**2 },
-               },
+               .q = model_error (t, σ_m**2),
 /*
  * Measurement error covariance
  * Our sensors are independent, so
@@ -236,11 +230,7 @@ parameters_t param_vel(real t) {
  * Model error covariance. The only inaccuracy in the
  * model is the assumption that acceleration is constant
  */
-               .q = (real[3,3]) {
-                       { 0, 0, 0 },
-                       { 0, 0, 0 },
-                       {.0, 0, σ_m**2 },
-               },
+               .q = model_error (t, σ_m**2),
 /*
  * Measurement error covariance
  * Our sensors are independent, so