102 that may be generated by the control module 104 and/or the control module 122. In Equation (1),

${\hat{v}}_{y}^{C E}$

represents a lateral velocity estimate (e.g., an output of a first model as further explained below),

${\hat{v}}_{x}^{C E}$

represents a longitudinal velocity estimate (e.g., an output of the first model),

${\hat{v}}_{y}^{B M}$

represents another lateral velocity estimate (e.g., an output of a second model as further explained below),

$\begin{matrix} q_{{\hat{v}}_{y}^{C E}}, & q_{p pmc, {\hat{v}}_{y}^{C E}}, & q_{{\hat{v}}_{y}^{CE}} & and & r_{PPMC, {\hat{v}}_{y}^{C E}}^{k} \end{matrix}$

represent gains for the first model,

$\begin{matrix} q_{{\hat{v}}_{y}^{B M}}, & q_{p pmc, {\hat{v}}_{y}^{CE}} & and & r_{PPMC {\hat{v}}_{y}^{C E}}^{k} \end{matrix}$

represent gains for the second model, v_y,RTKand v_x,RTKare ground truth signals (e.g., reference signals), and U is the number of data points that are available in a signal. For example, if a velocity signal of 1 second with sampling rate of 0.01 second is employed, U will be 100. In this example, the correlation coefficient is a Pearson product-moment correlation coefficient (PPMC), which is a measure of association of two signals (e.g., how much the signatures of the two signals are similar). Additionally, the RMSE components are provided, as represented with the square root functions. Depending on the optimization problem, the values of each term may be adjusted.

$\begin{matrix} J = q_{{\hat{v}}_{y}^{CE}} \sqrt{\frac{\sum_{i = 1}^{U} {({\hat{v}}_{y}^{CE, i} - v_{y, RTK}^{i})}^{2}}{U}} + q_{ppmc, {\hat{v}}_{y}^{C E}} ❘ r_{PPMC, {\hat{v}}_{y}^{C E}}^{k} - 1 ❘ + q_{{\hat{v}}_{x}^{CE}} \sqrt{\frac{\sum_{i = 1}^{U} {({\hat{v}}_{x}^{CE, i} - v_{x, RTK}^{i})}^{2}}{U}} + q_{{\hat{v}}_{y}^{B M}} \sqrt{\frac{\sum_{i = 1}^{U} {({\hat{v}}_{y}^{BM, i} - v_{y, RTK}^{i})}^{2}}{U}} + q_{ppmc, {\hat{v}}_{y}^{C E}} ❘ r_{PPMC {\hat{v}}_{y}^{C E}}^{k} - 1 ❘ & Equation (1) \end{matrix}$

Then, after gain values for each identified driving condition are optimized, the control module 104 may implement a scheduling technique to select appropriate gain values for use in vehicle control. For example, after optimized gain values for identified driving conditions are known, the control module 104 determines a current driving condition associated with the vehicle 102 (e.g., while the vehicle 102 is moving). In various embodiments, the current driving condition may be determined based on one or more vehicle characteristics received or otherwise detected by one or more of the sensors 106, 108, 110. For example, the control module 104 may determine that the current driving condition is a low surface friction coefficient driving condition, or another suitable driving condition based on a lateral acceleration (a_y) value provided by one of the sensors 106, 108, 110, slip ratio values for each wheel 114, 116, 118, 120, etc.

Once a current driving condition is determined, the control module 104 then selects a gain set of the optimized collection of gain sets. For example, the control module 104 may store each identified driving condition and its associated optimized gains. Then, after a driving condition is determined, the control module 104 can select a particular set of optimized gains (e.g., gain values) for the determined driving condition. In this way, the set of gains selected are specific to the current driving condition.

Then, the vehicle system 100 may control one or more vehicle operations of the vehicle 102 based on the optimized gain values of the selected gain set. For example, the selected set of optimized gains may then be used with a particular control system for determining a characteristic of the vehicle 102. For instance, the set of optimized gains may be used as filter gains (e.g., Kalman filter gains) in the control system for velocity estimation of the vehicle 102 or another control parameter of the vehicle 102. In such examples, the control module 104 may generate a control signal for the vehicle control module 112 based on the control parameter of the vehicle 102 (e.g., the velocity estimation of the vehicle 102, etc.). The vehicle control module 112 may then control an operation of the vehicle 102, such as a motion and/or a trajectory of the vehicle 102 based on the control signal.

In various embodiments, the complexity of determining optimal values for different gain sets may increase exponentially by adding more dimensions to the N-dimensional space, as explained above. In other words, when more dimensions are added, more gain values are optimized during the optimization process. As such, in some examples, a system can be broken down into smaller independent subsystems, where gain values of each subsystem can be optimized separately. As one example, the independent subsystems may be represented by two or more models, such a kinematic model and a dynamic model. By relying on smaller subsystems for optimizing gain values instead of one system, the optimization process may experience reduced computational cost and faster convergence to global optimum values when using, for example, the optimization process.

For example, FIG. 2 depicts one example of a control module 204 that may be employed as or a part of the control module 104 and/or the control module 122 of FIG. 1. As shown, the control module 204 includes two models 226, 228 (e.g., two subsystems). Although FIG. 2 illustrates two models, it should be appreciated that in some examples additional models or subsystem may be employed if desired.

The models 226, 228 may be any suitable model types. For example, the model 226 may be a Kalman filter with a dynamic model, and the model 228 may be a kinematic model. In other examples, any other suitable models may be employed.

In the example of FIG. 2, the control module 204 separately optimizes a first subset of gain sets for the model 226 and another second subset of the gain sets for the model 228. For example, the first subset of the gain sets may be optimized as explained above. During this time, the control module 204 may freeze (e.g., maintain, not change, etc.) gain values (if known) for the second subset. Likewise, when the second subset is optimized, the control module 204 may freeze gain values (if known) for the first subset. With this approach Equation (1) above may be broken into two cost function equations (J₁, J₂) represented by Equations (2) and (3) below.

$\begin{matrix} J_{1} = q_{{\hat{v}}_{y}^{CE}} \sqrt{\frac{\sum_{i = 1}^{U} {({\hat{v}}_{y}^{CE, i} - v_{y, RTK}^{i})}^{2}}{U}} + q_{ppmc, {\hat{v}}_{y}^{C E}} ❘ r_{PPMC, {\hat{v}}_{y}^{C E}}^{k} - 1 ❘ + q_{{\hat{v}}_{x}^{CE}} \sqrt{\frac{\sum_{i = 1}^{U} {({\hat{v}}_{x}^{CE, i} - v_{x, RTK}^{i})}^{2}}{U}} & Equation (2) \end{matrix}$

$\begin{matrix} J_{2} = q_{{\hat{v}}_{y}^{B M}} \sqrt{\frac{\sum_{i = 1}^{U} {({\hat{v}}_{y}^{BM, i} - v_{y, RTK}^{i})}^{2}}{U}} + q_{ppmc, {\hat{v}}_{y}^{C E}} ❘ r_{PPMC {\hat{v}}_{y}^{C E}}^{k} - 1 ❘ & Equation (3) \end{matrix}$

In the example of FIG. 2, the control module 204 may rely on an output of one of the models 226, 228 (e.g., subsystems) for determining vehicle control states. For example, and as explained above, a current driving condition may be determined and optimized gain values for that driving condition are selected. In this example, the gain values are broken into two subsets, which were optimized separately for the two different models 226, 228.

Then, and as shown in FIG. 2, the model 226 receives inputs 230, such as one or more vehicle characteristics received or otherwise detected by one or more of the sensors 106, 108, 110 of FIG. 1. The control module 204 can then determine a vehicle control state (e.g., a lateral velocity estimate and a longitudinal velocity estimate) using the model 226 based on the subset of the selected gain values for the model 226 and the received inputs. In this example, the model 226 provides an output 232 representing the vehicle control state to the model 228. The control module 204 then determines a vehicle control state (e.g., a lateral velocity estimate) using the model 228 based on the vehicle control state from the model 226 and the subset of the selected gain values for the model 228. The model 228 may then provide an output 234 representing the vehicle control state (e.g., a lateral velocity estimate). The control module 204 may generate a control signal based on the vehicle control states and/or parameters for control of one or more vehicle operations as explained above.

In various embodiments, fusion logic may be implemented to smoothly transition between different driving conditions and provide superior performance in real-time. For example, the fusion logic may be used to smoothen the transition between control states for different driving conditions and avoid sharp changes in gains which may affect the estimation performance. In some examples, the fusion logic may be implemented with a low pass filter.

FIG. 3 illustrates one example control module 304 implementing such gain scheduling logic and that may be employed as or a part of the control module 104 of FIG. 1. As shown in FIG. 3, the control module 304 includes a driving state module 306 for determining a current driving condition and corresponding control state, a fusion module 308 for smoothly transitioning between selected gains when the driving condition changes, and models 326, 328. In the example of FIG. 3, the models 326, 328 may be similar to the models 226, 228 of FIG. 2. For example, the model 326 may be a kinematic model, and the model 328 may be a dynamic model.

In the example of FIG. 3, the driving state module 306 receives various inputs 330, such as one or more vehicle characteristics received or otherwise detected by one or more of the sensors 106, 108, 110 of FIG. 1. In various embodiments, the inputs 330 may include, for example, a lateral acceleration (a_y) value, slip ratio values for each vehicle wheel, etc.

Then, based on the received inputs 330, the driving state module 306 determines a current driving condition and corresponding control state. For example, the driving state module 306 is shown as including three driving control states 332, 334, 336 corresponding to three driving conditions. In various embodiments, the driving conditions may include a normal operating condition, a low surface friction condition, a high lateral acceleration condition, or other suitable driving conditions. While the example of FIG. 3 illustrates three driving control states 332, 334, 336 corresponding to three driving conditions, it should be appreciated that more or less driving control states and corresponding driving conditions may be employed if desired.

In such examples, the driving state module 306 may initially begin in one of the driving states 332, 334, 336, such as a driving state corresponding to a normal operating condition. In such examples, the control module 304 may select an appropriate set of optimized gain values for that driving condition for use by the models 326, 328, as explained above. For example, the control module 304 may provide one subset of the selected optimized gain values for the model 326 and another subset of the selected optimized gain values for the model 328, as indicated by arrows between the fusion module 308 and the models 326, 338. In various embodiments, the selected gain values for the driving condition may pass through the fusion module 308 without disturbance.

If, however, the driving condition changes, the control module 304 transitions to another one of the driving states 332, 334, 336. For example, the driving state module 304 may then transition to a different one of the driving control states 332, 334, 336 when a new driving condition is determined based on the received inputs 330. For instance, if the received inputs 330 satisfy a particular set of conditions (e.g., thresholds), the driving state module 304 may determine a new current driving condition and transition from one state (e.g., the driving control state 332) to another state (e.g., the driving control state 334 or the driving control state 336). Once a new current driving condition is determined, the control module 304 selects a new set of optimized gain values for that driving condition. In such examples, the driving state module 304 may pass the new driving control state and/or the newly selected optimized gain values to the fusion module 308.

Then, the fusion module 308 may blend the first set of optimized gain values for the previous driving condition into the new set of optimized gain values for the new driving condition to provide a smooth transition. In various embodiments, the fusion module 308 may include one or more components, such as a low pass filter, etc. for incrementally changing the gains from one set of values to another set of values.

Once the optimized gain values are blended into the new set of optimized gain values by the fusion module 308, subsets of the new optimized gain values are provided to the models 326, 338. This is represented by the arrows between the fusion module 308 and the models 326, 338. For instance, one subset of the selected optimized gain values is provided for the model 326 and another subset of the selected optimized gain values is provided for the model 328.

The models 326, 328 then determine vehicle control states in a similar manner as the models 226, 228 of FIG. 2. For instance, the model 326 determines a vehicle control state (e.g., a lateral velocity estimate and a longitudinal velocity estimate) based on its subset of optimized gain values and outputs the vehicle control state to the model 328. Then, the model 328 determines a vehicle control state (e.g., a lateral velocity estimate) based on the vehicle control state from the model 326 and its subset of optimized gain values. The model 328 then provides an output representing the vehicle control state (e.g., a lateral velocity estimate), which can be used to generate a control signal for controlling one or more vehicle operations as explained above.

FIG. 4 illustrates an example control process 400 employable by the vehicle system 100 of FIG. 1 for identifying or determining driving conditions, and FIGS. 5-6 illustrate example control processes 500, 600 employable by the vehicle system 100 of FIG. 1 for selecting a gain set from a group of optimized gain sets for controlling a vehicle. Although the example control processes 400, 500, 600 are described in relation to the vehicle system 100, the control module 104, the vehicle 102 of FIG. 1, any one of the control processes 400, 500, 600 may be employable by another suitable vehicle system, control module, and/or vehicle.

As shown in FIG. 4, the control process 400 begins at 402 by setting a number of driving conditions to one. The control process 400 then proceeds to 404. At 404, control determines optimal gains for the driving condition (e.g., a normal operating condition). In various embodiments, the control module 104 and/or the control module 122 of FIG. 1 may be employed to determine optimal gain values for this driving condition as explained above. The control process 400 then proceeds to 406.

At 406, control quantifies an estimation performance determined based on the determined optimal gain values for the driving condition. In various embodiments, the estimation performance may be quantified according to conventional techniques. The control process 400 then proceeds to 408, where control determines whether an accuracy threshold for the estimation performance is met. For example, the control module 104 may compare the quantified estimation performance obtained in 406 to one or more thresholds. If the accuracy threshold is not met (e.g., the quantified estimation performance is less than a threshold), control proceeds to 410.

At 410, control adds another driving condition to the set. For example, if the initial driving condition was a normal operating condition, a low surface friction condition and/or a high surface friction condition may be added to differentiate from the normal operating condition. Then, the control process 400 returns to 404 where control determines optimal gains for each driving condition (e.g., a normal operating condition and a low surface friction condition). The control process 400 then proceeds again to 406 where control quantifies estimation performances determined based on the determined optimal gain values for the driving conditions. Then, the control process 400 proceeds to 408 again, where control determines whether accuracy thresholds for the estimation performances are met as explained above. This cycle of adding new driving conditions repeats until the accuracy thresholds are met. Once the accuracy thresholds are met (e.g., the quantified estimation performances are smaller than a threshold), control proceeds to 412 where the driving condition(s) may be stored for subsequent use. The control process 400 then ends as shown in FIG. 4.

In FIG. 5, the control process 500 begins at 502 by receiving optimized gain sets for different driving conditions. In various embodiments, the driving conditions may be determined with the control process 400 of FIG. 4, may be predefined, etc. Additionally, and as explained above, the control module 122 of FIG. 1 may optimize a set of gain values for each driving condition and then transmit the optimized gain values for the different driving conditions to the control module 104 of the vehicle 102. In such examples, the gain values may be optimized based on collected data sets from multiple different vehicles including or not including the vehicle 102. With this configuration, the gain values may be optimized offline and remote from the vehicle 102. In other examples, the control module 104 may receive the optimized gain sets (or gain values) from an internal source (e.g., another control module in the vehicle 102 similar to the control module 104). In such cases, the gain values may be optimized based on collected data sets from the vehicle 102 and in real-time. In either example, the gain values may be optimized by implementing an optimization algorithm, splitting a control system into independent subsystems, etc. as explained above. The control process 500 then proceeds to 504.

At 504, the control module 104 receives vehicle characteristics. For example, and as explained above, the sensors 106, 108, 110 of FIG. 1 and/or other suitable sensors associated with the vehicle 102 may detect vehicle characteristics, such as acceleration (e.g., lateral acceleration, longitudinal acceleration, etc.), an angular velocity of each wheel 114, 116, 118, 120, etc. The control module 104 may then use parts of the received vehicle characteristics and/or other known characteristics to determine other vehicle characteristics, such as wheel slip ratios for each wheel 114, 116, 118, 120. The control process 500 then proceeds to 506.

At 506, the control module 104 determines a current driving condition associated with the vehicle 102 based on the received and/or determined vehicle characteristics. For example, based on a lateral acceleration of the vehicle 102, wheel slip ratios of the wheels 114, 116, 118, 120, and/or other possible vehicle characteristics, the control module 104 can determine a current driving condition, such as, for example, a normal operating condition, a low surface friction condition, a high lateral acceleration condition, or another suitable driving condition. In various embodiments, the current driving condition is one of the driving conditions determined with the control process 400 of FIG. 4, one of the predefined driving conditions, etc. The control process 500 then proceeds to 508.

At 508, the control module 104 selects a gain set of the group of optimized gain sets based on the driving condition associated with the vehicle 102. For example, if the current driving condition is a first driving condition (e.g., a low surface friction condition), the control module 104 may select a first set of optimized gain values (e.g., filter gains). If, however, the current driving condition is a second driving condition (e.g., a high lateral acceleration condition), the control module 104 may select a second set of optimized gain values different than the first set of optimized gain values. The control process 500 then proceeds to 510.

At 510, the control module 104 determines one or more vehicle control states (e.g., a lateral velocity estimate) of the vehicle 102. For example, the optimized gain values and vehicle characteristics (e.g., the received and/or determined vehicle characteristics) may be used by one or more filters in the control module 104 and/or another control system to determine a vehicle control state (e.g., a lateral velocity estimate) of the vehicle 102.

In various embodiments, the control system may be split into two or more independent subsystems, as explained above. In such examples, the control module 104 may select a particular set of optimized gain values at 508, with a subset of the optimized gain values being employed by each subsystem (e.g., each filter). For example, if two subsystems are employed (e.g., during optimization and vehicle control), a first subsystem or model can determine one or more vehicle control states (e.g., a lateral velocity estimate and a longitudinal velocity estimate) based on the subset of selected gain values for the first model and vehicle characteristics, at 510. Then, a second subsystem or model can determine a vehicle control state (e.g., a lateral velocity estimate) based on the subset of selected gain values for the second model and an output of the first model (e.g., the one or more vehicle control states), at 510.

The control process 500 then proceeds to 512, where the control module 104 generates a control signal based on the vehicle control state (e.g., a lateral velocity estimate). Then, the control module 104 may transmit the control signal to the vehicle control module 112. The control process 500 then proceeds to 514, where the vehicle control module 112 controls at least one operation of the vehicle 102 based on the control signal. The control process 500 then proceeds to 516.

At 516, the control module 104 determines whether a current driving condition has changed. This determination may be made based on the received and/or determined vehicle characteristics. For example, the control module 104 may periodically, randomly, substantially continuously, etc. determine a current driving condition associated with the vehicle 102, as explained above. If a current or new driving condition is determined to be different than the previous driving condition (e.g., a change in the driving condition is detected), the control process 500 proceeds to 518. If, however, no change is detected, the control process 500 proceeds to 522.

At 518, the control module 104 selects a new set of optimized gain values based on the new driving condition associated with the vehicle 102. In various embodiments, and as explained above, the optimized gain values may include subsets for independent subsystems. The control process 500 proceeds to 520.

At 520, the control module 104 blends the optimized gain values for the previous driving condition into the new optimized gain values for the new driving condition to provide a smooth transition. In various embodiments, the control module 104 may include one or more components, such as a low pass filter, etc. for incrementally changing the gains from one set of values to another set of values. The control process 500 then returns to 510.

At 522, the control module 104 determines whether the vehicle is operational. For example, the control module 104 may receive a signal when the vehicle 102 is in a power on mode, moving, etc. If the control module 104 determines that the vehicle is operational (e.g., is not in a power on mode), the control process 500 returns to 516. Otherwise, if the control module 104 determines that the vehicle is not operational, the control process 500 may end as shown in FIG. 5.

In FIG. 6, the control process 600 is similar to the control process 500 of FIG. 5 but includes additional steps. For example, and as shown in FIG. 6, the process 600 begins at 602, where the gain sets for different driving conditions are optimized. More specifically, at 602, the control module 104 optimizes, for each driving condition, a first subset of gain values for a first model (e.g. a first subsystem) in the control module 104. The control process 600 then proceeds to 604 and 606. At 604, the control module 104 freezes the first subset of optimized gain values, and at 606, the control module 104 optimizes, for each driving condition, a second subset of gain values for a second model (e.g. a second subsystem) in the control module 104. In such examples, the driving conditions may be determined with the control process 400 of FIG. 4, may be predefined, etc., and the gain values may be optimized (separately) by implementing an optimization algorithm, etc. as explained above.

The control process 600 of FIG. 6 then proceeds to 504, 506, 508 as explained above relative to FIG. 5. Next, the control process 600 proceeds to 608, 610.

At 608, the control module 104 determines one or more first vehicle control states based on the first subset of optimized gain values. For example, and as explained above, the first model (e.g., the model 226 of FIG. 2, the model 326 of FIG. 3, etc.) of the control module 104 may determine one or more vehicle control states (e.g., a lateral velocity estimate and a longitudinal velocity estimate) based on the first subset of optimized gain values and vehicle characteristics.